EP1488482A2 - Amplifiers and light sources employing s-band erbium-doped fiber and l-band thulium-doped fiber with distributed suppression of amplified spontaneous emission (ase) - Google Patents

Abstract

The present invention provides an Erbium-Doped Fiber Amplifier (EDFA) and a source that employs the EDFA for generating light in an S-band of wavelengths. A fiber amplifier (10) in a depressed cladding or W-profile fiber has a core (12) doped with the active material (18) and defined by a core cross-section and a refractive index no. A depressed cladding (14) of index n1 surrounds the core (12) and a secondary cladding (16) of index n2 surrounding the depressed cladding (14). The fiber amplifier is pumped a level of high relative inversion D, such that the active material exhibits positive gains in a short wavelength band and high gains in a long wavelength band. In one embodiment, the core cross-section, the depressed cladding cross-section and the refractive indices no, n1, and n2 are selected to provide distributed ASE suppression at wavelengths longer than cutoff wavelength λc over the length of fiber amplifier (10). In another embodiment, such selection provides a roll-off loss curve about a cutoff wavelength λc. The roll-off loss curve yields losses at least comparable to the high gains in the long wavelength band and losses substantially smaller than the positive gains in the short wavelength band. To obtain the desired roll-off loss curve the refractive index no in the core is selected such that an effective index neff experienced by the confined mode maximizes a roll-off slope of the roll-off loss curve before the cutoff wavelength.

Description

Amplifiers and Light Sources Employing S-Band Erbium-Doped

Fiber and L-band Thulium-Doped Fiber with Distributed

Suppression of Amplified Spontaneous Emission (ASE)

RELATED APPLICATIONS

This application is related to U.S. Application numbers 09/825,148, filed 2 April 2001, 10/095,303, filed 8 March 2002, 10/163,557, filed 5 June 2002, 10/194,680, filed 12 July 2002, and 10/348,802, filed 21 January 2003.

FIELD OF THE INVENTION

The present invention relates generally to fiber amplifiers with a W-profile, and in particular to S-band Er-doped fiber amplifiers with depressed cladding and distributed suppression of amplified spontaneous emissions (ASE) in the C- and L- bands, to a Tm-doped fiber amplifier for amplification in the L-band, to a method for fabricating such fibers, to a method for designing such fiber amplifiers, and to light sources employing such fiber amplifiers for producing broadband and narrowband light in the S-band.

BACKGROUND OF THE INVENTION

Optical waveguides are designed to guide light of various modes and polarization states contained within a range of wavelengths in a controlled fashion. Single-mode optical fiber is the most common waveguide for long-distance delivery of light. Other waveguides, such as diffused waveguides, ion- exchanged waveguides, strip-loaded waveguides, planar waveguides, and polymer waveguides are commonly used for guiding light over short distances and especially for combining or separating light of different wavelengths, optical frequency mixing in nonlinear optical materials, modulating light and integrating many functions and operations into a small space.

In essence, a waveguide is a high refractive index material, usually referred to as the core in an optical fiber, immersed in a lower index material or structure, usually referred to as the cladding, such that light injected into the high index material within an acceptance cone is generally confined to propagate through it. The confinement is achieved because at the interface between the high and low index materials the light undergoes total internal reflection (TIR) back into the high index material.

The performance of fiber amplifiers depends on a number of parameters including pumping efficiency, level of population inversion of the ions in the active core, amplified spontaneous emission (ASE) competing with the useful amplified signal, cross-sections and refractive indices of the active core and of the cladding surrounding the active core. In many fiber amplifiers ASE is a major obstacle to effective amplification of the desired signal and thus ASE has to be suppressed.

The problem of amplifying optical signals for long distance transmission was successfully addressed by the development of

Erbium doped fiber amplifiers (EDFAs) . An EDFA consists of a length of silica fiber with the core doped with ionized atoms

(Er³⁺) of the rare earth element Erbium. The fiber is pumped with a laser at a wavelength of 980 nm or 1480 nm. The doped, pumped fiber is optically coupled with the transmission fiber so that the input signal is combined with the pump signal in the doped fiber. An isolator is generally needed at the input and/or output to prevent reflections that would convert the amplifier into a laser. Early EDFAs could provide 30 to 40 dB of gain in C-band extending between 1530 to 1565 nm with noise figures of less than 5 dB. Recently, EDFAs have been developed that can provide 25 dB of gain in the L-band (1565 to 1625 nm) as well as in the C-band.

There is great interest in the telecommunications industry to make use of the optical spectrum range with wavelengths shorter than those currently achievable with conventional C- band and L-band EDFAs. This wavelength range, commonly called the "S-band" or ^λλshort-band" is poorly defined because there is no consensus on the preferred amplifier technology. In general, however, the S-band is considered to cover wavelengths between about 1425 nm and about 1525 nm.

The gain in the S-band typically observed in EDFAs is limited by several factors, including incomplete inversion of the active Erbium ions and by amplified spontaneous emissions (ASE) or lasing from the high gain peak near 1530 nm. Unfortunately, at present no efficient mechanism exist for suppressing ASE at 1530 nm and longer wavelengths in an EDFA.

Most waveguides are designed to prevent injected light from coupling out via mechanisms such as evanescent wave out- coupling (tunneling) , scattering, bending losses and leaky- mode losses. A general study of these mechanisms can be found in the literature such as L.G. Cohen et al . , "Radiating Leaky- Mode Losses in Single-Mode Lightguides with Depressed-Index Claddings", IEEE Journal of Quantum Electronics, Vol. QE-18, No. 10, October 1982, pp. 1467-72. In this reference the authors describe the propagation of light in more complex lightguides with claddings having a variation in the refractive index also referred to as depressed-clad fibers. L.G. Cohen et al . teach that varying the cladding profile can improve various quality parameters of the guided modes while simultaneously maintaining low losses. Moreover, they observe that depressed-index claddings produce high losses to the fundamental mode at long wavelengths. Further, they determine that W-profile fibers with high index core, low index inner cladding and intermediate index outer cladding have a certain cutoff wavelength above which fundamental mode losses from the core escalate. These losses do not produce very high attenuation rates and, in fact, the authors study the guiding behavior of the fiber near this cutoff wavelength to suggest ways of reducing losses.

U.S. Pat. Nos. 5,892,615 and 6,118,575 teach the use of W- profile fibers similar to those described by L.G. Cohen, or QC fibers to suppress unwanted frequencies and thus achieve higher output power in a cladding pumped laser. Such fibers naturally leak light at long wavelengths, as discussed above, and are more sensitive to bending than other fibers. In fact, when bent the curvature spoils the W or QC fiber's ability to guide light by total internal reflection. The longer the wavelength, the deeper its evanescent field penetrates out of the core of the fiber, and the more likely the light at that wavelength will be lost from the core of the bent fiber. Hence, bending the fiber cuts off the unpreferred lower frequencies (longer wavelengths) , such as the Raman scattered wavelengths, at rates of hundreds of dB per meter.

Unfortunately, the bending of profiled fibers is not a very controllable and reproducible manner of achieving well-defined cutoff losses. To achieve a particular curvature the fiber has to be bent, e.g., by winding it around a spool at just the right radius . Di ferent fibers manufactured at different times exhibit variation in their refractive index profiles as well as core and cladding thicknesses. Therefore, the right radius of curvature for the fibers will differ from fiber to fiber. Hence, this approach to obtaining high attenuation rates is not practical in manufacturing.

Moreover, the relatively high absorption losses and low gains over the S-band render the selection of fiber and fiber profile in producing an EDFA that amplifies signals in the S- band very difficult. In fact, the problems are so severe that the prior art teaches interposition of external filters between EDFA sections to produce an S-band EDFA.

For example, Ishikawa et al . disclose a method of fabricating an S-band EDFA by cascading five stages of silica-based EDFA and four ASE suppressing filters in Ishikawa et al . , "Novel 1500 nm-Band EDFA with discrete Raman Amplifier", ECOC-2001, Post Deadline Paper. In Ishikawa et al . ' s experimental setup, the length of each EDA is 4.5 meters. The absorption of each suppressing filter at 1.53 μm is about 30 dB and the insertion losses of each suppressing filter at 1.48 μm and 0.98 μm are about 2 dB and 1 dB respectively. The pumping configuration is bi-directional, using a 0.98 μm wavelength to keep a high population inversion of more than D≥0.7 (D refers to relative inversion) . The forward and backward pumping powers are the same and the total pumping power is 480 mW. Ishikawa et al . show a maximum gain of 25 dB at 1518.7 nm with 9 dB gain tilt.

In a similar vein, U.S. Pat. No. 5,260,823 to Payne et al . teaches an EDFA with shaped spectral gain using gain-shaping filters. The inventors take advantage of the fact that the EDFA is distributed to interpose a number of the gain-shaping filters along the length of the EDFA, rather than just placing one filter at the end of the fiber. Yet another example of an approach using a number of filters at discrete locations in a wide band optical amplifier is taught by Srivastava et al . in U.S. Pat. No. 6,049,417. In this approach, the amplifier employs a split-band architecture where the optical signal is split into several independent sub-bands, which then pass in parallel through separate branches of the optical amplifier. The amplification performance of each branch is optimized for the sub-band which traverses it.

Unfortunately, these prior methods are complicated and not cost-effective, as they require a number of filters. Specifically, in the case of Ishikawa et al . , five EDFAs, four ASE suppressing filters, and high pump power are required. Also, each of the ASE suppressing filters used by either method introduces an additional insertion loss of 1-2 dB. The total additional insertion loss is thus about 4-8 dB.

Another approach to providing amplification in the S-band has focused on fiber amplifiers using Thulium as the lasing medium doped into a Fluoride fiber core (TDFAs) . See, for example, "Gain-Shifted Dual-Wavelength-Pumped Thulium-Doped-Fiber Amplifier for WDM Signals in the 1.48-1.51-μm Wavelength Region" by Tadashi Kasamatsu, et. al., in IEEE Photonics Technology Letters, Vol. 13, No. 1, January 2001, pg. 31-33 and references therein. While good optical performance has been obtained using TDFAs, this performance has only been possible using complex, non-standard and/or expensive pumping schemes. Also, TDFAs suffer from the problems inherent to their Fluoride fiber host material, namely high fiber cost, poor reliability and difficulty splicing to standard silica fibers used elsewhere in the amplifier system. Still other approaches to producing amplification systems based on rare-earth doped fiber amplifiers and cascaded amplifiers or pre-amplifiers followed by amplifiers are described in U.S. Patents 5,867,305; 5,933,271 and 6,081,369 to Waarts et al . and in U.S. Patent 5,696,782 to Harter et al . The teachings in these patents focus on deriving high peak power pulses at high energy levels. The amplifiers described in these patents are not suitable for producing broadband and narrowband sources for the S-band.

In view of the aforementioned difficulties in obtaining high attenuation rates in W-profile fibers as well as the selection of fiber and fiber profile in producing an EDFA that amplifies signals in the S-band, more recent prior art teaches distributed suppression of ASE at wavelengths longer than a cutoff wavelength in fiber amplifiers such as EDFAs. This is achieved by engineering fiber parameters including the index profile and cross sections of the core and cladding layer including the use of a W-profile refractive index. The approach is discussed in more detail in the above-referenced U.S. Patent Application 10/095,303.

Although effective in suppressing ASE at wavelengths longer than the cutoff wavelength, the EDFA' s cross-section enables the coupling of radiation at wavelengths below the cutoff wavelength between the core and the cladding. This effect, also known as cladding mode resonance, produces artifacts or cladding mode coupling losses in the short wavelength range of interest where the signal is to be amplified. For a general discussion of cladding mode coupling losses the reader is referred to Akira Tomita et al . , "Mode Coupling Loss in Single-Mode Fibers with Depressed Inner Cladding", Journal of Lightwave Technology, Vol. LT-1, No. 3, September 1983, pp. 449-452.

Cladding mode loss is a problem encountered in fiber Bragg gratings. One solution is to extend a photosensitive region in the core beyond the core to suppress cladding mode losses as taught in U.S. Pat. No. 6,351,588 to Bhatia et al . entitled "Fiber Bragg Grating with Cladding Mode Suppression". U.S. Pat. No. 6,009,222 to Dong et al . also teaches to take advantage of a W-profile refractive index to confine the core mode and cladding modes thus reducing their overlap and coupling. Related alternatives to confining the core mode to suppress cladding mode losses are found in U.S. Pat. No. 5,852,690 to Haggans et al . and U.S. Pat. No. 6,005,999 to Singh et al .

Unfortunately, the approaches which are useful in suppressing cladding mode losses and avoiding cladding mode resonance in fiber Bragg gratings can not be applied to fiber amplifiers. That is because of fundamental differences in fabrication, construction and operating parameters between fiber Bragg gratings and fiber amplifiers with distributed suppression of ASE.

Clearly, there is a need for a fiber amplifier with distributed suppression of ASE at wavelengths longer than a cutoff wavelength that is able to suppress cladding mode resonance or the coupling of radiation between the core and cladding at wavelengths shorter than the cutoff wavelength. It would be particularly useful to provide an EDFA having these capabilities where the wavelengths below the cutoff wavelength are contained in the S-band. Moreover, it would be an advance in the art to provide a fiber amplifier exhibiting net gains over the S-band with low pump power and without requiring external filters. In particular, it would be an advance to provide an EDFA with distributed ASE suppression in the C-band and L-band or substantially at 1530 nm and longer wavelengths over the whole length of a fiber amplifier. It would be also a welcome advance in the art to provide a method of designing such fiber amplifiers with net gain over the S- band as well as reliable narrowband and broadband light sources employing such fiber amplifiers that can be used for testing optical components, measuring the performance of optical components and generating signals in the S-band.

OBJECTS AND ADVANTAGES

It is a primary object of the present invention to provide a fiber amplifier that yields losses exceeding any high gains in a long wavelength band and at the same time yields losses substantially smaller than any positive gains in a short wavelength band. In particular, it is an object of the invention to provide an Er-doped fiber amplifier (EDFA) in which the long wavelength band is the C-band and L-band and the short wavelength band is the S-band. More specifically, the EDFA is to provide suppression of amplified spontaneous emission (ASE) near 1525 nm and above and ensure positive gains of at least 15 dB over the S-band.

It is an object of the invention to provide such fiber amplifier in a W-profile (or depressed cladding) fiber and use the fiber' s index profile to eliminate the need for external filters and reduce the required pump power by controlling a roll-off loss curve.

It is another object of the present invention to provide a fiber amplifier with distributed suppression of amplified spontaneous emissions (ASE) above a certain cutoff wavelength and suppression of cladding mode loss at wavelengths shorter than the cutoff wavelength. In particular, it is an object of the invention to provide an Erbium-doped fiber amplifier having these capabilities.

It is a further object of the invention to provide short-pass fibers that use a depressed cladding geometry to define a cutoff wavelength and an associated roll-off loss curve. In particular, the invention provides a reliable method for drawing fibers that contain various types of dopants, including active materials such as rare earth ions.

It is another object of the invention to provide reliable narrowband and broadband light sources in the S-band of wavelengths with Er-doped fibers or Erbium-doped fiber amplifiers (EDFAs) .

It is yet another object of the invention to provide a Thulium-doped silica fiber having its strongest gain at a range from about 1.6 μm to about 1.7 μm.

These and numerous other advantages of the present invention will become apparent upon reading the following description.

SUMMARY

The objects and advantages of the invention are achieved by a source generating light in an S-band of wavelengths using a W- profile fiber having a core doped with an active material such as Neodymium, Erbium or Thulium ions. The fiber core has a certain cross section and a refractive index n₀. An active material or lasant is doped into the core for amplifying light, e.g., any information-bearing light beam. The fiber's core is surrounded by a depressed cladding having a depressed cladding cross-section and a refractive index n_± . Furthermore, the fiber has a secondary cladding surrounding the depressed cladding. The secondary cladding has a secondary cladding cross-section and a refractive index n₂. In an embodiment, a pump source is provided for pumping the Erbium contained in the core to a high relative inversion D, such that the Erbium exhibits positive gains in the S-band and high gains in a long wavelength band longer than the S-band. The core cross-section, the depressed cladding cross-section, and the refractive indices n₀, n_{l f} and n₂ are selected to produce losses at least comparable to the high gains in the long wavelength band and losses substantially smaller than the positive gains in the S-band.

In another embodiment, the core cross-section, the depressed cladding cross-section and the refractive indices n₀, n_x, and n₂ are selected to obtain a roll-off loss curve about a cutoff wavelength λ_c. The roll-off loss curve yields losses at least comparable to the high gains in the long wavelength band and losses substantially smaller than the positive gains in the short wavelength band.

In order to obtain the desired roll-off loss curve the refractive index n₀ in the core is selected such that an effective index n_eff experienced by a mode of radiation which is guided, e.g., the fundamental mode at wavelength shorter than the cutoff wavelength, is large. In particular, refractive index n₀ is selected such that the slope of the effective index n_eff experienced by the confined mode is maximized, thereby maximizing a roll-off slope of the roll-off loss curve before the cutoff wavelength λ_c. Preferably, the refractive index n₀ is selected such that the slope of the effective index n_eff is in the range of .002/lOOnm to .008/1000nm. In another preferred embodiment, the refractive index n₀ of the core is chosen such that the roll-off slope of the roll-off loss curve is greater than or about equal to the maximum slope of the gain spectrum. In this embodiment, it is possible to select a cutoff wavelength such that the distributed loss exceeds the gain for all wavelengths in the long wavelength band, but that the gain exceeds the distributed loss for all wavelengths in the short wavelength band.

Depending on the design of the roll-off loss curve, the cutoff wavelength λ_c can be contained in the long wavelength band or in the short wavelength band, or between the short and long wavelength bands .

It is important that the selection of the cross-sections, i.e., the radii, and the selection of indices of refraction be not performed merely to establish a ratio of radii or refractive indices, but to fix absolute differences between them. Thus, it is preferable that the refractive index n₀ of the core differ from the refractive index n₂ of the secondary cladding by about 0.005 to about 0.03. Also, the refractive index ni of the depressed cladding should differ from the refractive index n₂ of the secondary cladding by about -0.004 to about -0.02.

In the preferred embodiment the fiber amplifier uses Er as the active material, i.e., it is an Er-doped fiber amplifier (EDFA) doped with a concentration of 0.1% wt. of Er. In this case it is further preferred that the short wavelength band is selected to be at least a portion of the S-band and the long wavelength band is selected to be at least a portion of the C- band and/or L-band. Further, it is advantageous to set the cutoff wavelength λ_c near 1525 nm in this embodiment. The host material used by the fiber amplifier is preferably a silicate-containing glass such as alumino-germanosilicate glass or phosphorus doped germanosilicate glass.

The pump source providing the pump radiation to invert the population in the Er ions can be any suitable pump source. For example, the pump source is a laser diode emitting pump radiation at about 980 nm. Alternative sources delivering pump radiation at about 980 nm can also be used. It is preferred that pumping is in-core pumping.

The fiber amplifier of the invention can be used in fibers of various cross-sectional profiles. For example, the core-cross section can have the shape of a circle, an ellipse, a polygon or another more complex shape. The same is true for the depressed cladding cross-section. The circular cross-sections can be used if no preferential polarization is to be amplified by the fiber amplifier. The eliptical cross-section can be used when a particular polarization is to be maintained during amplification over an orthogonal polarization.

For proper operation of the fiber amplifier it is important that the pump source provide pump radiation at a sufficient intensity to ensure a high relative inversion D, specifically D≥O .7. This is especially important in the preferred embodiment where the active material is Er.

Fiber amplifiers designed in accordance with the invention can be used in any situation where high gains are produced in a long wavelength band adjacent a short wavelength band in which the signal to be amplified is contained. In these situations the ASE from the long wavelength band will tend to prevent amplification of signals in the short wavelength band, especially when the positive gains in the short wavelength band are low in comparison to the high gains in the adjacent long wavelength band. The design is particularly useful in EDFAs to amplify signals in the short wavelength S-band. For this purpose the cutoff wavelength λ_c is preferably set at 1525 nm and the roll-off loss curve is selected to yield losses of at least 100 dB in the C-band and L-band to suppress ASE from the 1530 nm gain peak. Meanwhile, the roll-off loss curve is also adjusted to yield losses in the S-band which are smaller by at least 5 dB than the positive gains in the S-band to allow for signal amplification. This relationship will ensure at least a 5 dB amplification in the S-band.

In accordance with another embodiment of the invention several fiber amplifiers made according to the method can be used to amplify signals in the short wavelength band, e.g., the S- band. The length L of each of the fiber amplifiers can be varied to obtain the desired amount of gain for separate portions of the S-band.

In some embodiments the arrangement for suppressing coupling between the active core and the cladding is a material distributed in the cladding. The material can be a scattering material or an absorbing material. For example, a rare earth element can be used as the absorbing material.

Preferably, the cladding has a depressed cladding having a depressed cladding cross-section and a refractive index n_x and a secondary cladding having a secondary cladding cross-section and a refractive index n₂. The scattering or absorbing material is distributed in the secondary cladding. The radiation propagating in the active core occupies a mode having a mode diameter. The mode diameter extends from the active core into the cladding. It is important that the material be distributed outside the mode diameter of the radiation.

In some embodiments the arrangement for suppressing coupling between the active core and the cladding is a non-phase- matched length section in the fiber amplifier. The non-phase- matched length section is built such that coupling of the radiation between the active core and the cladding is not phase matched. In these embodiments the core has a core cross-section and a refractive index n₀ and the cladding has a cladding cross-section and a refractive index n_clad. The non- phase-matched length section is formed by a predetermined selection of the core cross-section, cladding cross-section and refractive indices n₀, n_clad. Preferably, the cladding has a depressed cladding having a depressed cladding cross-section and refractive index n_x, a secondary cladding having a secondary cladding cross-section and a refractive index n₂. The non-phase-matched length section is formed by a predetermined selection of the cross-sections and refractive indices n₀, n_{l r} n₂. Even more preferably, the cladding has an outer cladding having an outer cladding cross-section and a refractive index n₃ and n₃ is selected such that n₃<n₂.

The fiber amplifier can contain any suitable active medium in its active core. For example, the active core can be doped with Neodymium, Erbium, or Thulium ions. When using Erbium, the fiber amplifier is an EDFA and in one advantageous embodiment its cutoff wavelength λ_c is set near 1525 nm. Thus, the EDFA is pumped by a pump source delivering radiation at a pump wavelength near 980 nm. Under these conditions the EDFA can be used for amplifying signals in the short wavelength range falling within the S-band.

In another example, Thulium is doped into fused-silica fibers. Although the Thulium gain is typically thought to be at 1.9 microns, and indeed that is the peak of the gain, the wavelength range over which gain is possible stretches from 1.5 microns to 2.1 microns . The typical Thulium pump wavelength is 0.78 microns. However, it is also possible to pump Thulium at 1.48 microns, though very high intensities would be needed, possibly as high as 100 mW. lOOmW at 1.48 microns is easily obtainable with commercially available high quality diode pumps with about 500mW at 1480nm and nearby wavelengths. Another good pump wavelength is 1530nm where high power sources, up to Watts, are available.

The gain cross-section and the upper-laser-level lifetime of the Thulium ion are similar to those of the Erbium ion which is conventionally used to make 1.5 micron amplifiers. Thus the threshold for gain is similar - several milliwatts of pump power are required.

The Thulium ion could be used on the short-wavelength end of its gain region in exactly the same way as the Erbium ion. By pumping with an intense pump (30 mW or so) it is possible to reach inversion even at short wavelengths. However, before high gain is reached at a short wavelength such as 1.6 microns, there will be overwhelming superfluorescence near 1.9 microns.

A useful amplifier can be made at the shorter wavelength if the fiber is designed with a fundamental mode cut-off between 1.9 microns and the shorter wavelength of desired operation, and if the cut-off is such that the increase in loss at longer wavelengths exceeds the increase in gain due to the higher cross-section. This technique makes it possible to build useful amplifiers in the wavelength range between about 1.6 to 1.8 microns. Since telecommunication fiber is highly transmissive in this range, it is anticipated that amplifiers that work in this wavelength range will be highly desirable.

In accordance with the invention fiber amplifiers can be designed to suppress cladding mode loss. This is done in fibers where an appropriate index profile in the active core and cladding is established to set a cutoff wavelength λ_c. Cutoff wavelength λ_c is set such that the fiber amplifier exhibits positive gains in a short wavelength range below the cutoff wavelength λ_c. The coupling of radiation in the short wavelength range between the core and cladding is suppressed. This is achieved by distributing a material that scatters or absorbs the radiation in the cladding of the fiber amplifier. Preferably, the material is located outside the mode diameter of the radiation propagating through the active core. In another embodiment, the coupling is suppressed by preventing phase matching such that the coupling of radiation between the core and cladding is not phase matched. This can be achieved by engineering the cross-sections and refractive indices of the core and cladding in accordance with the invention.

When using the source as a narrowband source a wavelength selecting mechanism is provided for selecting an output wavelength of the light. This mechanism can be a feedback mechanism such as a fiber Bragg grating. In other embodiments the wavelength selecting mechanism is a filter selected from the group consisting of tilted etalons, strain-tuned fiber Bragg gratings, temperature-tuned fiber Bragg gratings, interferometers, arrays waveguide gratings, diffraction gratings and tunable coupled cavity reflectors. Alternatively, or in combination with the feedback mechanism or filter an additional pump source adjustment for tuning the high relative inversion D can be used to select the output wavelength. In yet another alternative, or in combination with the previous mechanism or mechanisms, a coiling diameter of the fiber can be used to select the output wavelength. The coiling diameter can be constant or variable, e.g., it can be continuously variable.

The fiber of the source can be placed within an optical cavity, e.g., in cases where it is desired that the fiber operate as a laser for producing light at a specific narrow output wavelength. Preferably the cavity is a ring cavity.

In one embodiment of the source, a master oscillator is used for seeding the fiber. The master oscillator can be any suitable optical source such as a distributed feedback laser, a Fabry-Perot laser, an external cavity diode laser, a distributed Bragg reflector laser, a vertical cavity surface emitting laser, a semiconductor laser, a fiber laser or a broadband source.

In a preferred embodiment, the fiber is broken up into two sections. The first section of the fiber has a first coiling diameter and the second section has a second coiling diameter larger than the first coiling diameter. The first section, whose emission spectrum is centered at a shorter wavelength, is positioned before the second section whose emission spectrum is centered at a longer wavelength. In this configuration the output from the first section is used to seed the second section. In some embodiments an isolator is installed between the two sections.

In another embodiment the first section is designed such that the core cross-section, the depressed cladding cross-section, and the refractive indices n₀, n_{l r} and n₂ produce a first cutoff wavelength λ_cl. Meanwhile, the core cross-section, the depressed cladding cross-section, and the refractive indices n₀, n_{l r} and n₂ in the second section are designed to produce a second cutoff wavelength λ_c2 that is longer than the first cutoff wavelength λ_cl. In this embodiment the first section produces an emission spectrum centered at a shorter wavelength and the second section produces an emission spectrum centered at a longer wavelength. Once again, the first section is positioned before the second section for seeding the second section. An isolator can be installed between the two sections in this embodiment.

The pump source for pumping the Erbium in the core of the fiber is preferably a laser diode. For example, one can use a laser diode providing pump light at about 980 nm. In accordance with the method of the instant invention it is preferable to use a counter-propagating pumping arrangement to pump the Erbium. In other words, the pump light is counter-propagating with respect to the output light.

The source of the invention can be used for testing and measuring purposes as well as for generating output light in the S-band. The source can be operated in a continuous mode or in a pulsed mode, as desired. The output light generated by the fiber can also be combined with light outside the S- band, e.g., with light in the C- and L-bands . A detailed description of the invention and the preferred and alternative embodiments is presented below in reference to the attached drawing figures .

BRIEF DESCRIPTION OF THE FIGURES

Fig. 1 is a diagram illustrating a W-profile fiber and guided and unguided modes according to the invention.

Fig. 2 is a graph illustrating a typical index profile in the fiber of Fig. 1. Fig. 3 is a graph illustrating the selection of appropriate core index n₀ to ensure that the effective index experienced by a guided mode in the short wavelength band of interest is maximized.

Fig. 4 is a graph illustrating appropriate selection of the core index to obtain a suitable roll-off loss curve in an Er-doped fiber amplifier (EDFA) in accordance with the invention.

Fig. 5 is a graph of the absorption and gain cross sections of Er ions in alumino-germanosilicate glass. Fig. 6 is an isometric view of an EDFA operated in accordance with the invention.

Fig. 7 are graphs of net gain in a 6 meter long alumino- germanosilicate EDFA doped at 0.1% wt. with a mode overlap factor T=0.5 at various inversion values D. Fig. 8 are graphs of net gain spectra in an alumino- germanosilicate EDFA at inversion values between D=0.4 and D=l for fiber lengths between 5 meters and 13 meters chosen to maintain 45 dB gain at 1530 nm.

Fig. 9 are graphs of gain spectra for a 15 meter long alumino-germanosilicate EDFA at inversion values between D=0.6 and D=l .

Fig. 10 is a diagram illustrating the use of three EDFA amplifiers to amplify three portions of the S-band. Fig. 11 is a graph illustrating the gain spectra for the three

EDFAs of Fig. 10 Fig. 12 illustrates the cross-section of another fiber amplifier with an elliptical core and depressed cladding.

Fig. 13 is a diagram illustrating a partial cross-section of a fiber amplifier in accordance with the invention and illustrating a core mode and a cladding mode. Fig. 14 is a graph illustrating a typical index profile in the fiber of Fig. 13.

Fig. 15 is a graph illustrating the effects of cladding mode losses in the fiber of Fig. 13. Fig. 16 are graphs illustrating the effects of an absorbing polymer material embedded in outer cladding of the fiber of Fig. 13.

Fig. 17 is a diagram illustrating a partial cross-section of another fiber amplifier according to the invention. Fig. 18 is a graph illustrating the phase-matching condition between core modes and cladding modes in the fiber amplifier of Fig. 17.

Fig. 19 are graphs of power levels of radiation in core mode and cladding mode. Figs. 20A&B are graphs illustrating the effective index n_eff experienced by the core mode and cladding modes . Figs. 21A&B are cross-sectional view of alternative fiber amplifiers in accordance with the invention. Fig. 22 is a diagram illustrating the use of an EDFA in a fixed narrowband source according to the invention. Fig. 23 is a graph illustrating the typical shaped of the ASE emission spectrum of the EDFA used in the source of

Fig. 22. Fig. 24 is a diagram illustrating the use of an EDFA in an alternative source according to the invention. Fig. 25 is a diagram illustrating a source using a single EDFA in a ring cavity. Fig. 26 is a diagram illustrating a source using two EDFAs in a parallel configuration in a ring cavity. Fig. 27 is a diagram illustrating a source using an EDFA' s coiling diameter for output wavelength tuning. Fig. 28 is a diagram illustrating a source using two fiber sections in accordance with the invention. Fig. 29 is a graph illustrating the effects of seeding EDFA having a longer wavelength emission spectrum by an

EDFA having a shorter wavelength emission spectrum. Fig. 30 is a graph illustrating the ASE emission spectra for

EDFAs at several coiling diameters. Fig. 31 is a graph illustrating the effect of using different pump power levels in two EDFA sections separated by an isolator on the total ASE emission spectrum. Fig. 32 is a diagram of a source with two EDFAs having different coiling diameters separated by an isolator. Fig. 33 is a diagram of a source with two EDFAs having different coiling diameters and employing a single pump source. Fig. 34 is a diagram illustrating an S-band source using a master oscillator. Fig. 35 is a diagram illustrating the use of an S-band source in a testing or measuring application in accordance with the invention. Fig. 36 is a diagram illustrating the pulling of a preform into a short-pass fiber with a depressed-profile. Fig. 37A is a graph illustrating the transverse portion of the refractive index profile in the preform of Fig. 36.

Fig. 37B is a graph illustrating the longitudinal portion of the refractive index profile in the preform of Fig. 36. Fig. 38 are graphs of exemplary roll-off loss curves obtained with the method of the invention. Fig. 39 shows the fluorescence spectrum of Thulium in fused silica.

DETAILED DESCRIPTION

The instant invention will be best understood by first reviewing the principles of generating a roll-off loss curve in a depressed profile or W-profile fiber 10 as illustrated in Figs. 1-4. Fig. 1 is a diagram illustrating a portion of a cross-section of a fiber 10 having a core 12 surrounded by a depressed cladding 14. Depressed cladding 14 is surrounded by a secondary cladding 16. Core 12 has a circular cross- section, as do depressed cladding 14 and secondary cladding 16. A region I associated with core 12 extends from 0<r≤r₀, depressed cladding 14 and secondary cladding 16 occupy regions II, III extending between r₀<r<r_! and r≥rn_.. Core 12 has an index of refraction n₀, depressed cladding 14 has an index of refraction n_x and secondary cladding 16 has an index of refraction n₂. The graph ^' positioned above the partial cross- section of fiber 10 illustrates an average index profile 20 defining a W-profile in fiber 10. In the present embodiment fiber 10 is a single mode fiber.

Fiber 10 has an active material 18 doped in core 12. Active material 18 is a lasing medium such as a rare earth ion or any other lasant which exhibits high gains in a long wavelength band and positive gains in a short wavelength band. Specifically, when pumped to a high relative inversion D, the high gains of active material 18 in the long wavelength band cause amplified spontaneous emissions (ASE) or lasing which reduces the population inversion of lasant 18 and thus reduces the positive gains in the short wavelength band, making it impossible to effectively amplify signals in the short wavelength band.

Fig. 2 illustrates a W-profile 20A as is obtained with normal manufacturing techniques . For the purposes of the invention it is sufficient that the radially varying index of core 12 have an average value equal to n₀. Likewise, it is sufficient that indices of depressed cladding 14 and secondary cladding 16 average out to the values n and n₂. The average index n₀ of core 12 is significantly higher than index n_x of depressed cladding 14 and index n₂ of secondary cladding 16. The selection of appropriate values of indices n₀, n_x, n₂ and radii r₀, r_x, r₂ is made to achieve certain guiding properties of fiber 10, as required by the instant invention. Specifically, profile 20 is engineered to have a fundamental mode cutoff wavelength λ_c such that light in the fundamental mode at wavelengths smaller than λ_c is retained in core 12 while light in fundamental mode at wavelength λ_c or longer wavelengths is lost to secondary cladding 16 over a short distance. This objective is accomplished by appropriately engineering W- profile 20A.

Fundamental mode cutoff wavelength λ_c of fiber 10 is a wavelength at which the fundamental mode (the LP₀ι mode) transitions from low-losses to high losses in core 12, i.e., is cut off from core 12. First, the fundamental mode cutoff wavelength λ_c for fiber 10 is set in accordance to selection rules for cross-sections and refractive indices n₀, n_x and n₂ of fiber 10 as derived from Maxwell's equations. In the weak guiding approximation (which is valid when the indices of refraction of core 12 and claddings 14, 16 are all relatively close to each other) , the Maxwell vector equations can be replaced with a scalar equation. The scalar ψ represents the strength of the transverse electric field in the fiber. For more information, see for example G. Agrawal, "Nonlinear Fiber Optics" (Academic, San Diego, 1995) , D. Marcuse, "Light Transmission Optics" (Van Nostrand, Princeton, 1972), and D. Marcuse, "Theory of Dielectric Optical Waveguides" (Academic, New York, 1974) .

For convenience, let us define the following parameters:

The scalar field ψ inside fiber 10 satisfies a wave equation whose solutions are Bessel functions and modified Bessel functions. For the fundamental mode supported by fiber 10, inside core 12 is thus:

ψ = J₀(κ r) , 0<r<r₀ (region I) (2)

where K is an eigenvalue that needs to be determined, and J₀ is the zeroth Bessel' s function.

Inside depressed cladding 14, the scalar field ψ is:

ψ = A K₀(β r) + B I₀(β r) , r₀<r<r_x (region II) (3)

where A and B are constants to be determined, β² = (u_Q ² + u ²)(2π I λ)² - κ² , and K₀ and I₀ are the modified Bessel' s functions. Here λ is the vacuum wavelength of the light.

In secondary cladding 16, we obtain:

ψ = C K₀(γ r) , r>rχ (region III) (4) Here C is another constant, and Y² = u_Q ²(2π /λ)² - κ² . A, B, C, and K are found using the boundary conditions, which require that ψ and its first derivative are both continuous at r₀ and

It can be shown that fundamental mode cutoff wavelength λ_c is a wavelength λ at which γ = 0. (See for example, Cohen et al., IEEE J. Quant. Electron. QE-18 (1982) 1467-1472.)

For additional convenience, let us define the following parameters :

Now, fundamental mode cutoff wavelength λ_c can be determined if parameter x is determined. That determination can be made with the aid of algebra known to a person skilled in the art, since parameter x is the root of the following equation:

p J₀(x) Kι(px) Iι(psx) - p J₀(x) Iι(px) Ki(psx)

- J_x(x) Kι(psx)I₀(px) - Jι(x) Iι(psx) K₀(px) = 0. (6)

Three observations should be made regarding the parameter x . First, x does not exist for all values of s and p. For example, for p = 1 and S ≤ J2 , there is no x that satisfies Eq. (6) . This means that all wavelengths are guided in core 12 in this regime. The criterion that Eq. (6) have a solution is:

s² > 1 + 1/p². (7) Second, for practical applications x cannot be too small. This is because, according to Eq. (5) , the parameter x is proportional to radius r₀ of core 12, and the radius has to be large enough that it is easy to couple light into and out of core 12. (A smaller core 12 also makes the nonlinear effects stronger, which is often a disadvantage.) Therefore, since x = 2πu_nr₀/λ_c, preferably x > 1. This implies that p > 0.224 or, in terms of the refractive indices (n -n²)/(n² -n²) ≥0.224.

Third, it is evident from Fig.7 that for larger values of s, the value of x only weakly depends on s . Thus it is advantageous to have a fiber in this region of parameter space, since a manufacturing flaw producing an error in s will have a small effect on the value of fundamental mode cutoff wavelength λ_c. Therefore, it is convenient to use the rule s > 1 + 1/p, or in terms of the refractive indices:

The selection of cross sections and refractive indices of core 12, depressed cladding 14 and outer cladding 16 is guided by the above rules in setting the appropriate fundamental mode cutoff wavelength λ_c. First, λ_c can be pre-selected, e.g. a wavelength close to 1530 nm, and then convenient values are selected for u₀ and r₀. Based on these choices x is computed from equation 5, and conveniently x≥l (otherwise the previous choices can be adjusted) . Then, suitable values of s and p are found using equation 6. A range of values for p and s will yield desired λ_c. Typically, all values of p are larger than 0.224. In addition, the rule of equation 8 is used to further narrow the range of suitable values of p and s. Finally, the values of s and p have an additional limitation. Namely, they must be selected so that core 12 of fiber 10 has a great enough loss, e.g., 5 dB/m or even 100 dB/m or more at a wavelength λ>λ_c. To find the loss at wavelength λ>λ_c, the fiber modes for light having wavelength λ>λ_c are required.

Equations (2), (3), and (4) specify the fundamental mode when λ<λ_c. When λ>λ_c, the function ψ is oscillatory, rather than exponentially decaying, in secondary cladding 16. Therefore when λ>λ_c, Eq. (4) is replaced by:

ψ = C J₀(qr) + D Nn(qr), r≥r_x (region III) (9)

where N₀ (also called Y₀) is the zeroth Neumann function, q — K - u₀ (2π I λ) _{r ancι} Q, and D are constants to be determined.

There are two key items to note regarding the modes for λ>λ_c.

First, there are five unknowns (A, B, C, D, and K) and four boundary conditions (continuity of ψ and dψ/dr at r₀ and r_x) . The equations are underconstrained: K may be chosen to be any value between 0 and (2πl )^u₀ ² - uf² . Thus, there is a continuum of states for each λ>λ_c, corresponding to the continuum of values that K may have. This situation is quite different from the case λ<λ_c, where four unknowns (A, B, C, and K) are fixed by the four boundary conditions, resulting in K being a discrete eigenvalue having a unique value at each λ<λ_c.

Second, the modes specified by Eqs . (2), (3), and (9) are eigenmodes of the fiber, e.g. a W-fiber; however, these modes do not correspond to the situation that is physically realized. This is a result of Eq. (9) containing both incoming and outgoing waves, whereas in practice only outgoing waves are present (the light at wavelength λ>λ_c originally propagating in core 12 radiates out) .

Nevertheless, the modes of Eqs . (2), (3), and (9) can be used to estimate the losses at wavelengths greater than λ_c. First, for a given wavelength λ, find the value of K that minimizes C² + D². This corresponds to the mode that is the most long- lived within the core. (An analogy can be made between the wave equation for the scalar ψ in the fiber and the quantum mechanical wave equation for a particle in a potential well. Then the quantum mechanical results can be borrowed. See for example David Boh , "Quantum Theory", Dover 1989, Chapter 12 §14 - 22.)

Second, once K is found in the above manner, the outgoing waves can be computed from Eq. (9) . These outgoing waves give a reasonable estimation of the loss from core 12 into secondary cladding 18, even when no incoming waves are present. These outgoing waves will cause beam at wavelength λ>λ_c propagating in core 12 to be attenuated along the length of the fiber. If the beam has power P, then the change in power P with distance z along fiber 10 is described by the equation: dJf

-AP az^~ (10)

The loss is given by the coefficient Λ, which is approximately: The loss Λ, having units of m ^l, can be converted to a loss β in units dB/m, using the relation:

β = 10 log₁₀(e) ^«Λ . (12)

Here the term "loss" refers to radiation that leaks out of core 12 into secondary cladding 16. In fact, the radiation may not be truly lost from fiber 10 itself, if it remains in secondary cladding 16. In some cases this will be sufficient. In other cases light from secondary cladding 16 can be out- coupled, as necessary.

Another method for calculating the losses involves calculating the complex propagation constant of the leaky fundamental mode of fiber 10. Leaky modes are discussed in, for example, D. Marcuse, "Theory of Dielectric Optical Waveguides" (Academic, New York, 1974) Chapter 1. The loss is related to the imaginary part of the complex propagation constant of the leaky mode. The complex propagation constant, or its equivalent that is the complex effective index of refraction, may be computed using commercially available software, such as that obtainable from Optiwave Corporation of Nepean, ON, Canada .

In some cases it may be preferable to numerically solve for the modes of a given fiber rather than use the Bessel function approach outlined above, since real fibers do not have the idealized step index profile indicated by profile 20 shown in Fig. 1, but have variations from the ideal as shown by graph 20A in Fig. 2 of the actual refractive index profile obtained in practice. In particular, the most common method of single- mode fiber manufacture today involves the MOCVD process, which typically leaves an index dip in the center of core 12. Numerical solutions can, more easily than the method described above, take into account the actual variations in refractive index as a function of radius. Such numerical calculations can again give fundamental mode cutoff wavelength λ_c and fiber losses as a function of fiber parameters including cross- sections and refractive indices, allowing fiber 10 to be designed to exhibit the desired features.

When Eq. (11) is used to estimate the loss, refractive indices n₀, n_{l r} and n₂ will in general be average indices of refraction of profile 20, since the actual indices of refraction will vary somewhat as a function of radius (see profile 20A) . Also, the index of refraction n is not necessarily radially symmetric. If the cross section of fiber 10 is described by polar coordinates r and θ the refractive index may depend upon the angle θ as well as the radius r. Thus, n = n(r,θ). Such an asymmetric fiber may be desirable for polarization maintenance, for example.

Here is the prerequisite for the fiber to have fundamental mode cutoff wavelength λ_c. Let R be a radius large enough that the index at radius R has substantially leveled off to the value n₂. Then fiber 10 will have fundamental mode cutoff wavelength λ_c if (see B. Simon, Ann. Phys. 97 (1976), pp. 279) :

rdr(n²(r,θ) - n ²) ≤ Q . (13)

Note that given the profile of Fig. 1, Eq. (13) becomes:

π r₀ u₀" π (r_x r₀' Ui < 0, (14) which is equivalent to Eq. (7) above.

Fundamental mode cutoff wavelength λ_c is the largest wavelength for which there is an eigenmode that is localized in region I. The losses for wavelengths above cutoff wavelength λ_c can be determined, for example, by (i) solving for the modes that are not localized but include incoming and outgoing waves, (ii) for each wavelength finding the mode with the smallest outgoing intensity, and (iii) using this outgoing intensity to estimate the loss. As discussed above, other methods are also available to a person skilled in the art for calculating losses. In general, fiber 10 with a desired fundamental mode cutoff wavelength λ_c and losses can therefore be designed by adjusting the profile n(r,θ), which is equivalent to adjusting the cross-sections and refractive indices of core 12, depressed cladding 14 and secondary cladding 16.

The rules presented above will enable a person skilled in the art can to set fundamental mode cutoff wavelength λ_c by making a selection of r₀, r_x, n₀, n_x and n₂. This selection of r₀, r_x, n₀, n_x and n₂ provide distributed ASE suppression over the length of the fiber 10 and result in a family of loss curves with different roll-offs (with respect to wavelength) . Therefore, additional constraints have to be placed on the selection of r₀, r_x, n₀, n_x and n₂ to achieve the objectives of the present invention, as discussed below.

Referring back to Fig. 1, superposed on average index profile 20 is an intensity distribution of a guided fundamental mode 22 at a first wavelength λ_x<λ_c. First wavelength λ_x is contained within a short wavelength band. A fundamental mode 24 which is no longer guided by fiber 10 is also superposed on index profile 20. Mode 24 is at cutoff wavelength λ₀. An intensity distribution of another mode 26 which is not guided by fiber 10 and exhibits an oscillating intensity distribution beyond core 12 and depressed cladding 14 is also shown. Radiation in mode 26 has a second wavelength λ₂, which is longer than cutoff wavelength λ_c<λ and is contained in a long wavelength band.

The graphs in Fig. 3 are plots of wavelength versus an effective index n_eff experienced by guided mode 22 whose wavelength λ_x is contained within a short wavelength band 42 and of non-guided mode 24 at cutoff wavelength λ_c for three choices of the value of index n₀ of core 12. Specifically, at a lowest value of index n_oX of core 12, the effective index ⁿ _eff experienced by mode 22 is described by graph 28. Graph 28 illustrates a relatively low value of effective index n_eff over short wavelength band 42, i.e., over the entire range of wavelengths λ_x at which mode 22 is guided. In addition, the value of n_eff remains very low in a region of interest 40 below cutoff wavelength λ_c. The choice of an intermediate value of index n_o2 of core 12 produces graph 30. In this graph n_eff is higher than in graph 28 over the entire short wavelength band 42. Still, the value of n_eff is low in region of interest 40. A choice of a large value of index n_o3 produces graph 32, which increases n_eff experienced by mode 22 over entire short wavelength band 42 including region of interest 40. Given such large value of refractive index n_o3 effective index n_eff exhibits a large negative slope right before cutoff wavelength λ_c in region of interest 40. Preferably, the value of refractive index n_o3 is large enough such that this roll-off slope is in the range of .002/1000 nm to .008/1000 nm. In a preferred embodiment, the refractive index n₀ of the core is at least 0.5% larger than the refractive index n₂ of the secondary cladding. Of course, a person skilled in the art will realize that index n₀ of core 12 can not be made arbitrarily large to continue increasing the negative slope of n_eff before λ_c due to material constraints.

Fig. 4 illustrates a gain profile 44 of active material 18 when pumped to a high relative inversion D. Short wavelength band is designated by reference 42, as in Fig. 3, and long wavelength band is designated by reference 46. Gain profile 44 exhibits high gains in long wavelength band 46 and positive gains in short wavelength band 42. In particular, high gains in long wavelength band 46 include a peak 48 very close to short wavelength band 42.

In this embodiment the cross-sections or radii of core 12, depressed cladding 14 and refractive indices n_Q, n_x, and n₂ are selected to place cutoff wavelength λ_c right at peak 48. Additionally, the value of index n₀ of core 12 is selected to obtain a roll-off loss curve 38 about cutoff wavelength λ_c set at peak 48 of high gains in long wavelength band 46. More particularly, roll-off loss curve 38 is selected to yield losses at least comparable to the high gains in long wavelength band 46 while yielding losses substantially smaller than the positive gains in short wavelength band 42. Roll-off loss curve 38 drops below the positive gains indicated by profile 44 because of its rapid decrease or large positive slope to the left for wavelengths below cutoff wavelength λ_c. The gains thus exceed losses across entire short wavelength band 42, as better visualized by hatched area 50. Preferably, roll-off loss curve 38 is- such that the gains exceed the losses in short wavelength band 42 by at least 5 dB. Curve 38 is obtained when n_eff experienced by guided mode 22 is high and the slope of n_eff just below λ_c has a large negative slope. In other words, curve 38 is obtained by selecting index n_o3 for core 12. Roll-off loss curves obtained with lower indices n_o2 and n_oX in core 12 are indicated by references 36 and 34 respectively. Because n_eff and its slope below λ_c experienced by mode 22 can not be maximized by choosing indices lower than n_o3, the roll-off slope is smaller for curves 36 and 34 and thus the losses they introduce in short wavelength band 42 remain above the positive gains. As long as losses exceed gains no useful amplification can be produced by active material 18 in short wavelength band 42.

The W-profile fiber designed in accordance with the above rules finds its preferred embodiment when active material 18 is Er and the short wavelength band is the S-band or a select portion of the S-band while the long wavelength band covers the C-band and/or the L-band or a select portion or portions of these two bands. Preferably, the host material of fiber 10 is silicate-containing glass such as alumino-germanosilicate glass or phosphorus doped germanosilicate glass.

Fig. 5 shows the wavelength dependent absorption cross-section 60 and wavelength dependent emission cross section 62 of Er- doped alumino-germanosilicate glass. Other Er-doped glasses have qualitatively similar gain (emission) and absorption spectra. Note that the gain extends to wavelengths shorter than 1450 nm, but the absorption cross section is much greater than the emission cross section for all wavelengths with a short wavelength band 64, in this case the S-band extending from about 1425 nm to about 1525 nm. Specifically, absorption cross section is much above emission cross section near 1500 nm. This indicates that high levels of relative population inversion D is required for Er to yield substantial net gain in S-band 64. A long wavelength band 66, in this case the C- band and the L-band extend from 1525 nm to 1600 nm and beyond. The C- and L-bands exhibit high gains, especially in the C- band at a peak wavelength of about 1530 nm. The choice of alumino-germanosilicate glass or phosphorus doped germanosilicate glass is preferred because when Er is doped into these host materials the emission cross section is increased in comparison to standard glass fiber. Other glass compositions which boost the emission cross section in S-band 64 relative to emission cross section 62 at the emission peak near 1530 nm can also be used.

Fig. 6 shows an Er-doped fiber amplifier 68 (EDFA) using alumino-germanosilicate glass as the host material. EDFA 68 is doped with a concentration of 0.1% wt. of Er in a core 70 of index n₀. Core 70 is surrounded by a depressed cladding 72 of index n_x and a secondary cladding 74 of index n₂. EDFA 68 has a protective jacket 76 surrounding secondary cladding 74 to offer mechanical stability and to protect EDFA 68 against external influences.

A signal radiation 78 at a first wavelength λ_x contained within S-band 64 is delivered to EDFA 68 for amplification from a fiber 80. For example, signal radiation 78 can be an information-bearing signal requiring amplification.

Fiber 80 is coupled with a fiber 82 in a wavelength combiner 84. Fiber 82 is used to couple a pump radiation 88 from a pump source 86 to EDFA 68. Pump source 86, preferably a laser diode, provides pump radiation 88 at a pump wavelength λ_p of about 980 nm for pumping the Er ions in core 70 to achieve a high level of relative population inversion D. Parameter D varies from D=-l indicating no population inversion to D=l signifying complete population inversion. When D=0, exactly half of the Er ions are in the excited energy state or manifold of states, while half remain in the ground energy manifold. In this case, EDFA 68 is approximately transparent

(for wavelengths near the 3-level transition at 1530 nm) . For non-uniformly inverted EDFAs, parameter D is considered as the average value of inversion. In the present embodiment, the intensity of pump radiation 88 is determined such that it ensures a relative inversion of D≥0.7 in the Er ions.

Pump radiation 88 and signal radiation 78 are combined in combiner 84 and both delivered to EDFA 68 by fiber 90. More particularly, both signal and pump radiation 78, 88 are coupled into core 70 from fiber 90.

Core 70 and claddings 72, 74 all have circular cross sections in this embodiment. The cross sections and indices n_Q, n_x, n₂ are selected in accordance with the method of invention to set cutoff wavelength λ_c near 1525 nm (see Fig. 5) . In other words, cutoff wavelength λ_c is selected to be between short wavelength band 64 or the S-band and the long wavelength band 66 or the C-band and L-band.

It is important that index n₀ of core 70 be chosen to provide for a large negative slope in effective index n_eff, preferably about .008/1,000 nm, near cutoff wavelength λ_c. As a result, the roll-off loss curve exhibits a rapid decrease for wavelengths below cutoff wavelength λ_c ensuring that the losses in S-band 64 are lower than the positive gains. The losses produced by this roll-off loss curve increase rapidly for wavelengths larger than cutoff wavelength λ_c. Thus, the losses produced in the C- and L-bands 66 are at least comparable to the high gains.

Designing EDFA 68 in accordance with the invention will ensure that signal radiation 78 at λ_x is amplified while ASE at any wavelength λ₂ in the C- and L-bands 66, and especially at λ₂=1530 nm is rejected into cladding 74 as shown. Positive gains in S-band 64 will typically be on the order of 25 dB above the losses and thus, to obtain sufficient amplification of signal radiation 78, EDFA 68 requires a certain length L. The smaller the difference between the positive gains and losses in the S-band 64, the longer length L has to be to provide for sufficient amplification of signal radiation 78. In the present embodiment L is about 6 meters .

Fig. 7 shows the net gain (gain minus absorption) of EDFA 68 for L=6 meters and with a typical mode-overlap factor, 17=0.5 without the benefit of the roll-off loss curve. The family of curves represent various levels of inversion, from D=0.6 through D=l. Note that as the level of inversion is increased, the net gain increases for all wavelengths. For full inversion (D=l) , the S-band 64 net gain ranges from 5-25 dB over 1470-1520 nm, the C-band 66 net gain exceeds 30 dB, and the 1530 nm gain peak exhibits over 55 dB of net gain. This condition is, in practice, very difficult to achieve because lasing at 1530 nm, and/or significant amplified spontaneous emission (ASE) would occur at significantly lower values of net gain (about 45 dB or lower) , thereby limiting the achievable level of inversion. The middle curve (D=0.8, with 90% of Er ions in the excited energy manifold) corresponds approximately to this ASE-limited situation, with about 25 dB of net gain within the C-band 66 and only about 10 dB of net gain within the S-band 64. In prior art EDFAs this situation gets worse (for the S-band) when a C-band EDFA is optimized for efficiency (dB gain per unit pump power) . This optimization results in somewhat longer (or more highly doped) fibers which become ASE-limited (45 dB net gain at 1530 nm) with lower levels of inversion. In summary, most EDFAs in use today operate with incomplete inversion because of 1530 nm-ASE combined with the requirement for good overall efficiency.

The relationship between the level of inversion, D, and the net gain in the S-band 64 relative to the net gain in the C- band 66 is shown in Fig. 8. A family of curves representing the net gain spectra for EDFA 68 without the benefit of the roll-off loss curve at inversion levels between D=0.4 and D=l, and L between 5 meters and 13 meters is shown. Lengths L were chosen in order to maintain 45 dB of net gain at 1530 nm, as this situation corresponds approximately to the onset of ASE. Note that the higher levels of inversion D favor gain in S- band 64, while more moderate (D=0.4-0.6) levels of inversion result in minimal gain-slope within the C-band 66. In other words, an EDFA designed for use within the S-band 64 should have nearly complete inversion, unlike an EDFA optimized for use within the C-band 66. For this reason, in the preferred embodiment the invention is maintained in the range D≥O .7.

Referring still to Fig. 8, one observes that the gain in S- band 64 can not exceed ~5 dB at 1470 nm and -20 dB at 1520 nm if the 1530 nm gain is limited to 45 dB. To achieve higher gain the length L of EDFA 68 has to be increased, while maintaining a high level of inversion would to produce larger gain in S-band 64. Fig. 9 shows the net gain spectra for EDFA 68 at inversion levels between D=0.6 and D=l, when length L is increased to 15 meters. While gain in S-band 64 exceeds 20 dB for a bandwidth exceeding 30 nm, the 1530 nm gain is in excess of >100 dB for D>0.7. Now, with the aid of the roll-off loss curve engineered in EDFA 68 in accordance with the invention, the losses at 1530 nm can be comparable or larger than this gain, thus preventing ASE or lasing.

Fig. 10 illustrates an embodiment in which three EDFAs 102, 104, 106 doped with Er at 0.1% wt . all engineered in accordance with the invention are provided to amplify three portions of the S-band. Four wavelength combiners 108, 110, 112, 114 are used to connect EDFAs 102, 104, 106 in accordance with well-known splicing and wavelength combining procedures to separately amplify the three portions of the S-band. EDFA 102 has a length of 10 meters and a cutoff wavelength λ_c at 1520 nm, EDFA 104 has a length of 33 meters and a cutoff wavelength λ_c at 1490 nm, and EDFA 106 has a length of 143 meters with a cutoff wavelength λ_c at 1460 nm. EDFA 102 amplifies input in the 1490-1520 nm range, EDFA 104 amplifies input in the 1460-1485 nm range and EDFA 106 amplifies input in the 1435-1455 nm range. All EDFAs 102, 104, 106 are engineered for the largest possible slope of n_eff, i.e., .008/1000 nm, near their respective cutoff wavelengths and the indices of refraction are: n_o=+0.011 and n_x=-0.0053. Fig. 11 illustrates the net gain spectra for these three EDFAs when pumping is sufficiently strong to obtain an inversion D=0.9. Note that they cover about 80 nm of total bandwidth in the S- band and provide gain exceeding 15 dB over this 80 nm bandwidth .

It should be noted that cutoff wavelength in this embodiment is placed in the short wavelength band for EDFAs 104 and 106. In fact, cutoff wavelength can also be placed in the long wavelength band, if desired. The choice of exactly where to place the cutoff wavelength can be made by the designer once the slope of the roll-off is known and the amount of high gains in the long wavelength band to be matched or exceeded are known .

Fiber amplifiers according to the invention can be used in fibers whose cores and cladding layers have cross-sections other than circular. For example, Fig. 12 illustrates the cross-section of a fiber amplifier 120 engineered according to the invention and whose core 122 is elliptical. Depressed cladding 124 is also elliptical while secondary cladding 126 has a circular cross section. These elliptical cross sections are advantageous when radiation in one polarization rather than the other polarization is to be maintained during amplification.

Fig. 13 is a diagram illustrating a partial cross-section of a fiber amplifier 210 with a core mode and a cladding mode. The fiber amplifier 210 has an active core 212 surrounded by a depressed cladding 214, which is surrounded by a secondary cladding 216. Core 212 as a circular cross section, as do depressed cladding 214 and secondary cladding 216. In addition, an outer cladding 220 of circular cross-section surrounds secondary cladding 216.

A region I associated with core 212 extends from 0≤r≤r₀, while depressed cladding 214 and secondary cladding 216 occupy regions II, III extending between r₀≤r≤r_x and r_x≤r≤r₂. Outer cladding 220 is associated with a region IV extending from r>r₂. Core 212 has an index of refraction n₀, depressed cladding 214 has an index of refraction n_x and secondary cladding 216 has an index of refraction n₂. Outer cladding 220 has an index of refraction n₃. The graph positioned above the partial cross-section of fiber amplifier 210 illustrates an average index profile 222 defined in fiber amplifier 210. In the present embodiment fiber amplifier 210 is a single mode fiber amplifier.

Fiber amplifier 210 has an active material 218 doped in core 212. Active material 218 is a lasing medium such as a rare earth ion or any other lasant that exhibits high gains in a long wavelength band and positive gains in a short wavelength band. Specifically, when pumped to a high relative inversion D, the high gains of active material 218 in the long wavelength band cause amplified spontaneous emissions (ASE) or lasing which reduces the population inversion of lasant 218 and thus reduces the positive gains in the short wavelength band.

Superposed on average index profile 222 is an intensity distribution of radiation in a guided fundamental core mode 224 at a first wavelength λ_x where λ_x<λ_c. First wavelength λ_x is contained within a short wavelength band where active material 218 exhibits positive gains. An intensity distribution of radiation in a cladding mode 226 that exhibits an oscillating intensity distribution beyond core 212 and depressed cladding 214 is also shown. There is an overlap between core mode 224 and cladding mode 226 as indicated by hatched areas A. However, as with all modes of waveguide structures, these modes are orthogonal (cladding mode 226 is anti-symmetric in electric field) in the ideal case. Hence, ideally there is no coupling between core mode 224 and cladding mode 226. However, all real waveguides have imperfections, inhomogeneities, scattering centers and perturbations which break the orthogonality and enable coupling between core and cladding modes. In fact, the three main causes of coupling in fiber amplifier 210 are manufacturing defects, bending or coiling of fiber amplifier 210 as necessary for packaging purposes, and micro bends and stresses which are pre-existing (e.g., frozen in during manufacturing) or caused during packaging. Clearly, it is beneficial to reduce these causes for coupling as far as possible.

Fig. 14 illustrates a refractive index profile 222A as is obtained with normal manufacturing techniques . For the purposes of the invention it is sufficient that the radially varying index of core 212 have an average value equal to n₀. Likewise, it is sufficient that indices of depressed cladding 214, secondary cladding 216 and outer cladding 220 average out to the values n_x, n₂, n₃. The average index n₀ of core 212 is significantly higher than index n_x of depressed cladding 214 and index n₂ of secondary cladding 216. In this embodiment, the average index n₃ of outer cladding 220 is higher than all other indices, although this need not be so.

The selection of appropriate values of indices n₀, n_x, n₂ and radii r_Q, r_x, r₂ is made to achieve certain guiding properties of fiber amplifier 210, as required by the instant invention. In particular, index profile 222A is established in core 212 and in the first two cladding layers, i.e., depressed cladding layer 214 and secondary cladding layer 216 such that radiation in core 212 exhibits a loss above a cutoff wavelength λ_c and positive gains in a short wavelength range below the cutoff wavelength λ_c. In a preferred embodiment, index profile 222A is engineered to have a fundamental mode cutoff wavelength λ_c such that radiation in fundamental mode 224 at wavelengths smaller than λ_c is retained in core 212 while radiation in fundamental mode 224 at wavelength λ_c or longer wavelengths is lost to secondary cladding 216 over a short distance. An exemplary engineering method of the refractive index profile 222A will now be discussed.

In Fig. 13, the cutoff wavelength λ_c is set such that core 212 exhibits a loss above cutoff wavelength λ₀ and positive gains due to active material 218 in a short wavelength range below the cutoff wavelength λ_c. This selection of r₀, r_x, n₀, n_x and n₂ provides distributed ASE suppression at wavelengths longer than cutoff wavelength λ_c over the length of fiber amplifier 210. Superposed on average index profile 222 is the intensity distribution of radiation in guided fundamental core mode 224 at a first wavelength λ_x where λ_x<λ_c and the intensity of radiation in cladding mode 226. Radiation in core mode 224 and in cladding mode 226 propagates at first wavelength λ_x. In other words, single mode fiber amplifier 210 allows for discrete modes, such as mode 226 to propagate in secondary cladding 216. Substantial power can then be transferred from core mode 224 to cladding modes such as cladding mode 226 when the phase velocities of core mode 224 and cladding mode 226 become identical. For a theoretical teaching on the cladding mode coupling effect the reader is referred to Akira Tomita et al . , "Mode Coupling Loss in Single-Mode Fibers with Depressed Inner Cladding", Journal of Lightwave Technology, Vol. LT-1, No. 3, September 1983, pp. 449-452.

The transfer of power from core mode 224 to cladding mode 226 causes losses from core 212 at wavelength λ_x. Thus, a signal at λ_x within the short wavelength band is not able to take advantage of the full positive gains of active material 218 at λ_x. As used herein, these losses are referred to as cladding mode losses. In certain cases, some power is also transferred back from cladding mode 226 to core mode 224 when coupling exists between core mode 224 and cladding mode 226. As used herein, this condition is referred to as cladding mode resonance.

The general effect of cladding mode losses sustained by fiber amplifier 210 is shown in Fig. 15. In this example Erbium is used as active material 18 and the short wavelength band is within the S-band. Specifically, graph 228 shows the gains of Erbium around its peak 230 at about 1530 nm. The design of refractive index profile of fiber 210 sets cutoff wavelength λ_c just below 1530 nm, e.g., at 1525 nm and produces a loss curve 232. Loss curve 232 indicates that the losses above cutoff wavelength λ_c increase rapidly. Thus, any ASE due to the gains of Erbium at 1530 nm and at longer wavelengths is effectively suppressed. Meanwhile, in short wavelength band 234 below cutoff wavelength λ_c Erbium exhibits gains above the losses produced by loss curve 232. In other words, the Erbium has positive gains in short wavelength band 234 and is therefore able to amplify signals in short wavelength band 234.

Due to coupling between fundamental mode 224 and cladding mode 226 at wavelength λ_x there is a loss peak 236 in short wavelength band 234 centered at λ_x. The size of loss peak 236 is not drawn to scale and is indicated in dashed lines. It should be noted that in practice there can be a number of wavelengths within short wavelength band 234 at which coupling between core mode and cladding mode occurs producing

• corresponding loss peaks. Also, it should be noted that coupling between fundamental core modes and cladding modes at wavelengths longer than λ_c can take place as well. For example, core mode and cladding mode coupling occurs at λ₂. The corresponding cladding mode resonance 238 is indicated in dashed lines. Because ASE in the wavelength range spanning λ₂ is suppressed, this coupling is not as detrimental to the function of fiber amplifier 210. Still, in a preferred embodiment, cladding mode coupling at wavelengths longer than λ_c should also be avoided.

Clearly, loss peak 236 reduces the effectiveness of fiber amplifier 210 at wavelength λ_x. Therefore, in accordance with the invention, loss peak 236 is suppressed by suppressing cladding mode loss in fiber amplifier 210. In the general case, as well as in this embodiment, this object is achieved by providing an arrangement for suppressing the coupling of radiation in the short wavelength' range between active core 212 and secondary cladding 216. In the embodiment of Fig. 13, the arrangement for suppressing coupling employs a material 240 distributed in outer cladding 220.

Material 240 is a scattering material or an absorbing material. In either case, material 240 is embedded in outer cladding 220 at a distance where core mode 224 is negligibly small. In particular, core mode 224 has a mode diameter D extending from core 212 into the cladding, i.e., into depressed cladding 214 and secondary cladding 216. Material 240 is distributed outside the mode diameter of core mode 224. Thus, core mode 224 does not exhibit appreciable intensity in the region where material ^" 240 is deposited within outer cladding 220. This means that in single mode fiber amplifier 210 material 240 should be embedded several tens of microns away from core 212. It should be noted that outer cladding 220 can be made up entirely of material 240 if outer cladding 220 commences at a distance where core mode 224 is negligibly small . 03

In the embodiment where material 240 is an absorber, it can be a rare earth element doped into outer cladding 220. Suitable materials include Erbium, Cobalt, Samarium and other suitable absorbers. Material 240 can be embedded in outer cladding 220 using any suitable fabrication technique. For example, in a typical manufacturing process employing the "sleeving technique" a sleeve of pure silica that is to be pulled over secondary cladding 216 can be provided with a layer of doped material 240 prior to the sleeving process. Specifically, a layer of doped material 240 coated onto the inner surface prior to the sleeving process can be employed. Modified Chemical Vapor Deposition (MCVD) and solution doping, followed by sintering can be used to create the proper layer of absorbing material 240.

In another embodiment, material 240 is any suitable scattering material, such as an inhomogeneous acrylate layer or other material exhibiting rapid variations in the refractive index and/or geometry. Scattering material can employ two scattering effects. First, it can scatter radiation in cladding mode 226 that is phasematched with core mode 224 into an assortment of other cladding modes. Typically there will be a large number (usually hundreds) of other cladding modes into which radiation of cladding mode 226 can be scattered. This effect is substantially equivalent to absorption loss as far as cladding mode 226 is concerned. Alternatively, radiation in cladding mode 226 can be perturbed in phase in a random fashion by scattering material 240. This effect is substantially similar to preventing phase matching between core mode 224 and cladding mode 226. By preventing phase matching the accumulation of cladding mode loss over a long distance of fiber amplifier 210 is thus prevented. The effect of using material 240 in outer cladding 220 is illustrated in Fig. 15. Specifically, by using material 240 loss peak 236 at λ_x is reduced to a smaller loss peak 236' indicated in solid line. Fig. 16 illustrates the experimental results of using absorbing material 240 in the form of a polymer buffer in outer cladding 220 of fiber amplifier 210. In this case, the host material of fiber 210 is silicate- containing glass such as alumino-germanosilicate glass or phosphorus doped germanosilicate glass. Graph 242 indicates the gain experienced by a signal in fiber 210 without material 240 in outer cladding 220 and graph 244 indicates the gain obtained with material 240. In these cases both material 240 and outer cladding 220 are made of polymer materials with differing loss characteristics. Clearly, the dip in gain associated with loss peak 236 is removed with the aid of absorbing material 240. Thus, fiber amplifier 210 of present invention provides distributed suppression of amplified spontaneous emissions (ASE) above cutoff wavelength λ_c and suppresses cladding mode loss at wavelengths shorter than cutoff wavelength λ_c, i.e., wavelengths in short wavelength range 234 such as wavelength λ_x in particular. It should be noted that the presence of absorbing material 240 in outer cladding 220 also suppresses cladding mode effects at λ₂.

Fig. 17 illustrates a partial cross-section of another fiber amplifier 200 in accordance with the invention. Parts of fiber amplifier 200 corresponding to those of fiber amplifier 210 are referenced by the same reference numbers. In fiber amplifier 100 the arrangement for suppressing coupling between core mode 224 and cladding mode 226 is a non-phase-matched length section of fiber amplifier 200. In the non-phase- matched length section outer cladding 220 has a lower refractive index n₃ than all other indices. Most importantly, refractive index n₃ is lower than refractive index n₂ of secondary cladding 216, i.e., n₃<n₂. This condition ensures that radiation in core mode 224 and cladding mode 226 are not phase matched. Appropriate material for outer cladding 220 to ensure such low refractive index n₃ is silicone, Teflon, Fluorine-doped silica and other low-index materials such as those used in dual clad fibers well known to those skilled in the art.

Prevention of phase matching and the selection of the value of refractive index n₃ will be better understood by referring to the graphs in Fig. 18. Graph 2102 illustrates the normalized propagation constant of radiation in core mode 224 plotted versus inverse of the wavelength (i.e., optical frequency, which is also proportional to the k-vector) for n₃≥n₂. Graph 2104 illustrates the normalized propagation constant of radiation in cladding mode 226 also plotted versus inverse of the wavelength for n₃≥n₂. (The condition n₃≥n₂ is typical for telecommunications fibers which use acrylate as the typical outer cladding also referred to as buffer.) At l/λ_x graphs 2102 and 2104 intersect indicating phasematching and hence cladding mode loss.

Graphs 2106 and 2108 in Fig. 19 illustrate the power level of radiation normalized to the value 1 (100% power level) in core mode 224 and cladding mode 226, respectively. Graphs 2106 and 2108 are observed for the phasematched condition and are graphed as a function of length of fiber amplifier 200 assuming an ideal case in which no power is lost or gained (i.e., no amplification). The power level of core mode 224 represented by graph 2106 starts at the high power value of 1 and undergoes sinusoidal oscillations between 1 and 0. In contrast, the power level of cladding mode 226 starts at the low power value of 0 and undergoes sinusoidal oscillation between 0 and 1. Clearly, power is transferred from core mode 224 to cladding mode 226 during the first part of the oscillation and back from the cladding mode 226 to core mode 224 during the second part of the oscillation.

In practice, outer cladding 220 has a loss of a finite value per unit length of fiber amplifier 200 while the loss in core 212 is negligible. Therefore, the power in core mode 224 will not manage to be coupled completely into cladding mode 226. Under these conditions, the power level in core mode 224 will follow a graph 2106' and the power level in cladding mode 226 will follow a graph 2108' as shown for an intermediate value of α. At a large value of the power levels will follow graphs 2106" and 2108". The cladding mode loss prevents appreciable power from building up in cladding mode 226, thereby reducing the coupling of power from core mode 224 to cladding mode 226. In fact, the loss of power γ from core mode 224 to cladding mode 226 can be described by the following equation:

8.7c² γ= , (15)

where c² is the speed of light squared. From this equation it is evident that increasing the loss α experienced by cladding mode 226 decreases the loss experienced by core mode 224. For a detailed derivation of the equation the reader is referred to Akira Tomita et al . , "Mode Coupling Loss in Single-Mode Fibers with Depressed Inner Cladding", Journal of Lightwave Technology, Vol. LT-1, No. 3, September 1983, pp. 449-452. Now, changing the refractive index n₃ of outer cladding 220 has the effect of shifting the phasematching wavelength λ_x and can be used to eliminate coupling of radiation from core mode 224 to cladding mode 226 in accordance with the invention. Graphs 2110 and 2110' in Figs. 20A and 20B illustrate the effective index n_eff experienced by core mode 224 when n₃>n₂ or n₃<n₂, respectively. Because a change in n₃ does not affect core mode 224 appreciably, graphs 2110 and 2110' are almost identical. The effective indices of a number of cladding modes, including cladding mode 226 are indicated by lines 2112 and 2112', respectively.

In Fig. 21A the condition n₃>n₂ dictates that the effective indices of cladding modes can exceed n₂. In fact, the effective index of core mode 224 intersects with the effective index of cladding mode 226 at intersection point 2114 in the short wavelength range below cutoff wavelength λ_c. Furthermore, effective index of core mode 224 also intersects with the effective indices of two additional cladding modes in this case. Therefore, cladding mode losses due to coupling between core mode 224 and cladding mode 226 as well as coupling between core mode 224 and the two additional cladding modes exist. The coupling behavior is as indicated by graphs 2106', 2106" and 2108', 2108" in Fig. 19 (depending on the value of cladding loss ) and causes the undesired cladding mode loss.

On the other hand, when n₂>n₃ the effective indices of cladding modes cannot exceed n₂, as shown in Fig. 20B. Thus, the effective index of core mode 224 does not intersect with any cladding modes below cutoff wavelength λ_c. Therefore, there is no coupling between core mode 224 and cladding mode 226 or any other cladding mode below cutoff wavelength λ_c. In fact, the intersection point 2114' between core mode 224 and cladding mode 226 occurs above cutoff wavelength λ_c in the long wavelength range in which ASE is being suppressed by the design of fiber amplifier 200, as discussed above. The same is true for coupling from core mode 224 to the other cladding modes .

The phasematching principle is used in accordance with the invention by introducing a non-phase-matched length section L of fiber amplifier 200 in which n₃<n₂ to suppress cladding mode loss. Referring to Fig. 6, in this embodiment, fiber amplifier 68 is similarly designed as fiber amplifier 200. Fiber amplifier 68 is used in a system 1200 to amplify a signal 78 at wavelength λ_x propagating through a fiber 80. System 1200 has a pump source 86 providing a pump radiation 88 at wavelength λ_p. Pump radiation 88 is coupled from source 86 into a fiber 82.

A fiber coupler 84 receives fibers 80 and 84 and couples them into a single output fiber 90. Output fiber 90 is connected to fiber amplifier 68.

During operation, signal 78 and pump radiation 88 are combined in coupler 84 and launched together through output fiber 90. Fiber 90 delivers signal 78 and radiation 88 to active core 70 of fiber amplifier 68. In accordance with the above-described principles, signal 78 is amplified in core 70. Meanwhile, pump radiation 88 is depleted in passing through core 70, as indicated. In fact, at the end of non-phase matched section L there may be little pump radiation remaining in fiber amplifier 68. ASE radiation at a wavelength λ₂ is generated as a by-product of pumping active core 70. Wavelength λ₂ is longer than cutoff wavelength λ_c of fiber amplifier 68 and is therefore lost into outer cladding 76. At the same time, some of signal 78, which travels in core mode, is also lost into outer cladding 76 because of cladding mode losses. However, since non phase-matched length section L has an index n₃ lower than n₂, the amount of loss of signal 78 to outer cladding 76 is minimized.

System 1200 using non-phase-matched length section L of fiber amplifier 68 is thus capable of suppressing mode loss at wavelengths shorter than the cutoff wavelength. In fact, fiber amplifier 68 can be effectively employed in various optical systems.

In another alternative embodiment, the use of a non-phase- matched length section and the use of an absorbing or scattering materials can be combined in one fiber amplifier. For example, the scattering or absorbing material may constitute a part of the outer cladding or the entire outer cladding in such alternative embodiments.

Yet another embodiment in accordance with the invention employs a non-phase-matched length section L which prevents phase matching between core and cladding modes by varying the cross-sectional profile of a fiber amplifier 2150 as shown in Figs. 21A and 21B. Fig. 21A shows the cross-section of fiber amplifier 2150 at a position L=x_x. Fiber amplifier 2150 has an active core 2152 surrounded by a cladding 2154 having a varying cladding index n_clad. A minimum value of n_{c ad} is indicated by line 2156. A graph of index profile 2158 showing the variation of n as a function of radius r is shown above fiber amplifier 2150. A person skilled in the art will appreciate that, in general, n_cι_ad can vary as a function of radius r and azimuthal angle θ, i.e., (^r/θ) •

At position L=x₂ the cross section of fiber amplifier 2150 is different, as shown in Fig. 21B. In particular, index profile 2158' remains the same as index profile 2158 in and near active core 2152 to ensure the same cutoff wavelength λ_c and loss curve for longer wavelengths are the same at positions x_x and x₂. However, the portion of index profile 2158' further away from core 2152 within cladding 2154 exhibits a different curvature and minimum value than index profile 2158. Specifically, the location of the new minimum value of n_{c ad} i-ⁿ index profile 2158' is indicated by line 2156' . Because of this variation of index profile from 2158 at x_x to 2158' at x₂, the wavelength for which cladding mode loss is phasematched at position x_x is different from the wavelength for which cladding mode loss is phasematched at position x₂. Therefore, phase matching between core mode and cladding modes in fiber amplifier 2150 is prevented.

As mentioned heretofore, the fiber amplifier of the present invention can contain any suitable active medium in its active core. For example, the active core can be doped with Neodymium, Erbium, or Thulium ions. When using Erbium, the fiber amplifier is an EDFA and in one advantageous embodiment its cutoff wavelength λ_c is set near 1525 nm. Specifically, Erbium 18 acts as a lasing medium and exhibits high gains in a long wavelength band including the C- and L-bands . Erbium 18 also has positive gains in a short or S-band of wavelengths shorter than the wavelengths in the C- and L-bands . When pumped to a high relative inversion D, the high gains of Erbium 18 in the long wavelength band cause amplified spontaneous emissions (ASE) or lasing which reduces the population inversion of Erbium 18 and thus reduces the positive gains in the S-band. As discussed before, by selecting the core cross-section, the depressed cladding cross-section, and the refractive indices n_σ, n_x, and n₂ to produce losses at least comparable to the high gains in the long wavelength band and losses substantially smaller than the positive gains in said S-band, the W-index profile of the inventive fiber nevertheless enables the fiber to effectively amplifying signals in the S-band.

In another example, Thulium is doped into fused-silica fibers. Although the Thulium gain is typically thought to be at 1.9 microns, and indeed that is the peak of the gain, the wavelength range over which gain is possible stretches from 1.5 microns to 2.1 microns. The typical Thulium pump wavelength is 0.78 microns. However, it is also possible to pump Thulium at 1.48 microns or about 1.5 microns, though very high intensities would be needed, possibly as high as 100 mW.

Graphs A and B in Fig. 39 show that the Thulium has fluorescent emission from 1.6 to 2 μm. The shape of the fluorescence spectrum is very similar to that of the gain spectrum, except that the gain will be at a slightly longer wavelength than the fluorescence. If Thulium acts as an ideal ion, as do Erbium and Ytterbium, then gain should be possible to stretch from 1.5 μm to 2.1 μm. The peak of the gain will be between 1.8 and 1.9 microns. The gain cross-section and the upper-laser-level lifetime of the Thulium ion are similar to those of the Erbium ion. Thus, the threshold for gain is similar - several milliwatts of pump power are required. The Thulium 3+ ion could be used on the short-wavelength end of its gain region in exactly the same way as the Erbium ion. By pumping with an intense pump (30 mW or so) it is possible to reach inversion even at short wavelengths. However, before high gain is reached at a short wavelength such as 1.6 microns, there will be overwhelming superfluorescence near 1.9 microns .

A useful amplifier can be made at the shorter wavelength if the fiber is designed with a fundamental mode cut-off between 1.9 microns and the shorter wavelength of desired operation, and if the cut-off is such that the increase in loss at longer wavelengths exceeds the increase in gain due to the higher cross-section. In an embodiment, the long wavelength band is about 1.7 to 2.1 microns, the short wavelength band is the L- band, which is roughly 1.6 to 1.8 microns, the cut-off wavelength is about 1.7 to 1.9 microns, and the pump wavelength is about 1.48 to 1.5 microns. The cut-off wavelength is selected such that the increase in loss at longer wavelengths exceeds the increase in gain due to the higher cross-section. This technique makes it possible to build useful amplifiers in the wavelength range between about 1.6 to 1.8 microns. Since telecommunication fiber is highly transmissive in this range, it is anticipated that amplifiers that work in this wavelength range will be highly desirable.

Fig. 22 illustrates a source 300 of light in the S-band employing a fiber 302 doped with Erbium 306 and constructed to form an EDFA in accordance with the above principles . Specifically, fiber 302 has a core 304 doped with Erbium 306, a depressed cladding 308 surrounding core 304 and a secondary cladding 310 surrounding depressed cladding 308. Source 300 has a pump source 312 for providing a pump light 314. Pump source 312 is preferably a diode laser emitting pump light 314 at a wavelength of about 980 nm. An optic 316 in the form of a lens is provided for coupling pump light 314 into a fiber 318. A coupler 320 is provided for coupling pump light 314 from fiber 318 into a fiber 324. Fiber 324 is joined to one end of fiber 302 in accordance with any suitable fiber splicing technique known to those skilled in the art such that fiber 324 delivers pump light 314 into core 304 of fiber 302.

Pump source 312 is controlled by a pump control 322 such that source 312 delivers pump light 314 for pumping Erbium 306 in core 304 to a high relative inversion D. The relative inversion D is sufficiently high when Erbium 306 exhibits positive gains in the S-band and high gains in the long wavelength band, i.e., the L- and C-bands . The cross-sections and refractive indices, n₀, n_x, n₂ of core 304, depressed cladding 308 and secondary cladding 310 are selected in accordance with the above rules. In particular, the cross- sections and refractive indices n₀, n_x, n₂ are selected to produce losses at least comparable to the high gains in the L- and C-bands and losses substantially smaller than the positive gains in the S-band.

Fiber 324 passes through coupler 320 and is terminated by a wavelength-selecting device 326. In the present embodiment device 326 is a wavelength-selecting feedback mechanism in the form of a fiber Bragg grating. Fiber Bragg grating 326 is a wavelength-selecting feedback mechanism because the portion of light that it is tuned to reflect propagates through fiber 324 back into fiber 302. Of course, other mechanisms can also be used. For example, another advantageous wavelength-selecting feedback mechanism is a tunable free-space diffraction grating configured to retro-reflect light at the desired output wavelength.

At its other end fiber 302 is joined with a fiber 328 that is terminated by an output coupler 330. Once again, any suitable fiber joining technique can be employed to join the end of fiber 302 to fiber 328. The junction is such that light propagating through core 304 of fiber 302 is freely coupled between fiber 302 and fiber 328. Output coupler 330 is any suitable optical coupling device for passing an output light 332. For example output coupler 330 can be a cleaved end of fiber 328, i.e., a cleaved output facet, a wavelength coupler, a free-space reflector, a fiber Bragg grating, a 2x2 fused fiber coupler used in conjunction with a broadband reflector. In fact, any output coupling device used to couple output light from a fiber laser can be used as output coupler 330 including a diffraction grating. In fact, as will be appreciated by a person skilled in the art, a diffraction grating can be used to serve the function of wavelength selecting device 326 and output coupler 330.

During operation pump laser control 322 is turned on to provide pump light 314 to fiber 302 such that Erbium 306 is pumped to a high relative inversion D. As a result, Erbium 306 exhibits positive gains in the S-band and high gains in the L- and C-bands. The selection of cross-sections and refractive indices n₀, n_x, n₂ of core 304, depressed cladding 308 and secondary cladding 310 in accordance with the invention cause losses at least comparable to the high gains in the L- and C-bands and losses substantially smaller than the positive gains in S-band 342. Therefore, fiber 302 exhibits a net optical gain spectrum that extends several tens of nanometers below fundamental mode cutoff wavelength λ_c within S-band 342.

Fig. 23 shows a shortest wavelength λ_short and a longest wavelength λ_long for which the gain is positive define a net gain bandwidth 390. Shortest and longest wavelengths λ_short, λi_ong a^re determined by design parameters of fiber 302 including a roll-off loss curve below cutoff wavelength λ_c, doping concentration, and distribution of Erbium 306 in core 304, and average degree of inversion D over the length of fiber 302. Changes in the length of fiber 302 do not impact shortest and longest wavelengths λ_short, λ_long for which the gain is positive as long as inversion D remains constant. Changes in the length of fiber 302, however, impact the amount of gain within net gain bandwidth 390 contained between shortest and longest wavelengths λ_short, λ_long. On the other hand, changes in the power of pump light 314 and its direction as well as single-end or dual-end pumping directly affect the average degree of inversion D in fiber 302. The present embodiment employs single-end pumping in which pump light 314 and output light 332 are co-propagating (propagate in the same direction) . Higher inversion D produces higher gain (or lower loss) at all wavelengths within S-band 342 and can also expand net gain bandwidth 390 between shortest and longest wavelengths λ_short, λ_long.

Even when fiber 302 does not receive a signal light for amplification (e.g., signal light 78 as illustrated in Fig. 6) it still creates an optical output. Unavoidable fluorescence also referred to as spontaneous emission (SE) occurs due to the natural radiative decay of excited (pumped) atoms of Erbium 306 back down to ground state. The spontaneous emission process happens in exact proportion to the spectrum of the "emission cross section" (often called the gain cross section, due to their correspondence) . In fact, even if population inversion has not been achieved, spontaneous emission still occurs. Some of this spontaneous emission generates light within S-band 342, and some of this light overlaps with a mode guided by fiber 302. More specifically, some of the light produced by spontaneous emission is trapped in core 304 of fiber 302 and travels along its core 304 in a guided mode. Of that trapped light the portion that overlaps with net gain bandwidth 390 of fiber 302 is amplified. Light outside net gain bandwidth 390 is generally not amplified and is lost by direct attenuation, absorption by non-inverted atoms of Erbium 306 and loss to secondary cladding 310 among other. In this case, ASE is guided in core 304 and amplified by fiber 302.

As will be appreciated by those skilled in the art, the spectral shape of the ASE is determined both by the spectral shape of the spontaneous emission (which is related to the emission cross section) and also by the spectral shape of the net gain bandwidth 390. Net gain bandwidth 390 is related to the emission cross section, absorption cross section, degree of inversion D and the spectral shape of the losses- dictated by roll-off loss curve produced by the selection of cross sections and refractive indices of fiber 302. However, the spectral shape of ASE is not merely the product of the spontaneous emission spectrum and the spectrum associated with net gain bandwidth 390, as would be expected if all of the spontaneous emission happened at one end of fiber 302 and all of the amplification occurred at a different location in fiber 302. Rather, the ASE output from fiber 302 is the superposition of the amplified bits of spontaneous emission originating at each and all locations within fiber 302. In general, wavelengths at which there are high gains and high losses exhibits higher ASE power than wavelengths with low gains and low losses, even if the net gain is the same. Typically, due to the shape of the emission cross section of Erbium 306, longer wavelengths within net gain bandwidth 390 exhibit higher gains than shorter wavelengths. Also, typically, longer wavelengths exhibit higher losses than shorter wavelengths. The higher losses are due to the shape of the absorption cross section of Erbium 306 and the shape of the roll-off loss curve. Hence, the ASE spectrum of S-band amplifier constituted by fiber 302 is often biased towards these longer wavelengths, even though the longest of these wavelengths may experience net loss. Typically, the shorter wavelengths of the ASE emission spectrum exhibit small positive net gains, through not much ASE power.

As a result of the above phenomena the following rules should be observed when constructing source 300. First, one should select a peak wavelength λ_peak within net gain bandwidth 390. Then, the cross sections and refractive indices of core 304, depressed cladding 308 and secondary cladding 310 should be selected to set cutoff wavelength λ_c about 10-20 nm above λ_eak- The exact distance between λ_peak and λ_c should be adjusted depending on the steepness of roll-off loss curve 38

(see Fig. 4) . In particular, when roll-off loss curve 38 is steep then λ_c should be set only about 10 nm above λ_peak. On the other hand, for a less steep roll-off loss curve a cutoff wavelength λ'_c should be set up to 20 nm above λ_peak._. The general shape of the ASE emission spectrum has the shape of the net gain spectrum within net gain bandwidth 390 as indicated by graph 392 for steep roll-off loss curve and by graph 392' for less steep roll-off loss curve. Next, one should determine the desired power level and bandwidth of source 300. To obtain output light 332 at a high power level fiber 302 is lengthened. The doping concentration of Erbium 306 in core 304 can be kept the same or even increased to further aid in increasing the power level of light 332. Then, the power level of pump light 314 is increased, e.g., to obtain 100-200 dB absorption of pump light 314 in fiber 302. For example, pump light 314 is delivered at a power level such that fiber 302 absorbs up to 90% of pump light 314. On the other hand, to obtain output light 332 spanning a wide bandwidth, fiber 302 is kept short and the power level of pump light 314 is decreased.

Thus, there exists a tradeoff between power and bandwidth. This is because for the high gains and wide amplification bandwidths that can be achieved in doped EDFAs the ASE process is quite efficient. The typical way of further increasing the power of an EDFA is to pump harder and/or lengthen the EDFA. This approach works well up to a point. However, the fiber length and pumping cannot be increased as much as desired due to the high efficiency of the ASE process. Once a significant ASE power builds up in an EDFA, e.g., up to net gains of 40 dB, the ASE process begins to rob the population of Erbium atoms in the excited state, thereby reducing the degree of inversion D. Reduced inversion D causes a reduction of spontaneous emission and a significantly reduced amount of net gain. The S-band EDFA is particularly sensitive to reductions in inversion D because of the unfavorable radio of emission cross section to absorption cross section within the S-band. This interplay between ASE and gain limits the available power and/or bandwidth of ASE within the S-band when a single EDFA section is used. Therefore, if sufficient power over the desired bandwidth cannot be achieved with fiber 302, then several fibers analogous to fiber 302 can be used in combination. Further details of such combinations are described below.

As fiber 302 is being pumped by pump light 314, source 300 generates ASE emission spectrum 392 centered about peak wavelength λ_peak. Lasing operation of source 300 is obtained with the aid of fiber Bragg grating 326. Specifically, fiber Bragg grating 326 is set to reflect an output wavelength λ_output within ASE emission spectrum 392. At the same time, output coupler 330 is set to pass a fraction of light 332 at wavelength λ_output. After many round trips between fiber Bragg grating 326 and output coupler 330, light at λ_output dominates over ASE emission spectrum 392. Therefore, source 300 emits output light 332 having a narrowband spectrum 334 centered at wavelength λ_output through output coupler 330. Pump source control 322 can operate in a continuous mode or in a pulsed mode. Therefore, output light 332 can be delivered in pulses or continuously, as desired.

Fig. 24 illustrates an alternative embodiment of a source 340 in which parts corresponding to those of source 300 are referenced by the same reference numerals. Source 340 differs from source 300 in that it has a wavelength selecting mechanism 342 and a control 344 for adjusting the wavelength reflected back to fiber 302 by mechanism 342. Wavelength selecting mechanism 342 is a wavelength filter such as a tilted etalon, a strain-tuned fiber Bragg grating, a temperature-tuned fiber Bragg grating, an interferometer, an array of waveguide gratings, a diffraction gratings or a tunable coupled cavity reflector. Correspondingly, control 344 is a mechanism for controlling stain, temperature, inclination angle or other required tuning parameter of filter 342, as will be appreciated by a person skilled in the art.

By controlling the wavelength band reflected by filter 342 an output wavelength λ_output of light 332 is selected as in source 300. Of course, output coupler 330 is adjusted to pass light 332 at the selected output wavelength λ_output. One can also select several output wavelengths within ASE emission spectrum 392 (see Fig. 23) .

Alternatively, or in combination with output wavelength selection performed with the aid of filer 342, pump source control 322 of source 340 can also be used to adjust the output wavelength of light 332 by tuning the level of relative inversion D. This is achieved by tuning the power delivered by control 322 to pump source 312. Changing the power level applied to pump source 312 adjusts the intensity of pump light 314, hence tuning the level of relative inversion D, as will be appreciated by a person skilled in the art.

Fig. 25 illustrates a preferred embodiment of a source 360 according to the invention using a single EDFA 364. Source 360 does not require the use of reflectors by virtue of having a fiber ring cavity 362 with an output coupler 366. In this embodiment, a wavelength filter 368 installed in ring cavity 362 serves as a wavelength selecting mechanism. Filter 368 can be an adjustable filter, preferably a diffraction grating used in conjunction with an optical circulator or a temperature controlled fiber Bragg grating with a suitable control mechanism (not shown) , an acousto-optic transmission filter (AOTF) or even a tunable etalon. Fiber ring cavity 362 also has an isolator 370 for controlling back-reflections and preventing output light 372 containing the light fraction at λo_utp_ut ^or the ASE from propagating in both directions around ring 362. During operation EDFA 364 is pumped by a pump source (not shown) and operated in accordance with the principles described above.

Fig. 26 illustrates a source 361 also using a fiber ring cavity 363. In order to obtain a broader ASE emission spectrum, source 361 employs two EDFAs 365, 367 connected in parallel between two couplers 371, 373. A third coupler 371 is employed for deriving output light 377 from ring cavity 363. The pump sources providing pump light to EDFAs 365, 367 are not shown in this embodiment for reasons of clarity.

EDFAs 365, 367 have different ASE emission spectra. These ASE emission spectra can be controlled by any of the above- discussed mechanisms, including different fiber parameters (cross sections, refractive indices and roll-off loss curves) , lengths and inversion levels set by the intensity of pump light (not shown) . Preferably, the ASE emission spectra of EDFAs 365, 367 are chosen to have their peak wavelengths at different locations within the S-band to thus span a wider total ASE emission spectrum. Thus, source 361 is able to provide a broader ASE emission spectrum and offers a wider range of wavelengths within which the output wavelength λ_output is selected by filter 369. Furthermore, source 361 also has an isolator 375 for controlling back-reflections and preventing output light 377 containing the light fraction at ^_outp_t or the ASE from propagating in both directions around ring cavity 361.

During operation wavelength filter 369 sets output wavelength ^_output of light 377 within the total ASE emission spectrum provided by EDFAs 365, 367. Light 377 is outcoupled from ring cavity 363 through output coupler 371, as shown. It should be noted that more than two EDFAs can be used to cover a still broader ASE emission spectrum. In fact, filter 369 can be left out completely in some embodiments to outcouple light 377 covering the wide bandwidth afforded by the parallel- configured EDFAs thus yielding a broadband source.

Source 361 can be easily adapted to cover more than just the S-band. For example, another EDFA covering the C- or L-band of wavelengths, or in fact several additional EDFAs, can be connected in parallel with EDFAs 365 and 367 and their outputs combined.

Fig. 27 illustrates yet another embodiment of a source 380 that uses a single EDFA 382. Source 380 has a pump source 384 for providing pump light 386. A lens 388 focuses pump light 386 into a fiber 390, which is coupled to EDFA 382 by a coupler 392.

EDFA 382 is coiled at a constant coiling diameter CD. To provide for mechanical stability, EDFA 382 can be coiled about a spool of diameter CD (not shown) . In fact, the strain introduced into EDFA 382 by coiling diameter CD serves as the wavelength-selecting mechanism in this embodiment. That is because coiling diameter CD produces a desired ASE emission spectrum in EDFA 382. Specifically, selecting a larger coiling diameter CD, e.g., CD' as indicated, shifts the maximum of the ASE emission spectrum of EDFA 382 to longer wavelengths within the S-band.

EDFA 382 is terminated by an angle cleaved facet 394 or other non-reflective termination that prevents back reflection for better stability of source 380. Thus, angle cleaved facet 394 ensures that a sufficient amount of stable and low-noise output light 402 is emitted by EDFA 382 to an output coupler 396. An isolator 398 is interposed between EDFA 382 and output coupler 396 to prevent back-coupling of light 402 into EDFA 382.

In this embodiment output coupler 396 has an additional tap 400 for deriving a small amount of output light 402, e.g. about 1%, for output monitoring. A photodetector 404, in this case a photodiode, is provided for measuring tapped output light 402.

Source 380 can be used as a fixed source or as a tunable source. In particular, source 380 can be rendered tunable by providing a mechanism for altering coiling diameter CD. Alternatively, source 380 can be rendered broadband by widening the ASE emission spectrum of EDFA 382, e.g., by selecting a less steep roll-off loss curve, as discussed above.

Source 380 employs a counter-propagating pumping geometry where pump light 386 is injected from a direction opposite to the direction in which output light 402 is derived from EDFA 382. This approach is preferred to co-pumping arrangements used in the above-described embodiments where the pump light is delivered along the same direction as the direction along which output light is derived.

A preferred embodiment of a source 410 is shown in Fig. 28. Source 410 uses two EDFA sections (which may or may not belong to the same piece of fiber) specifically a first section 412 and a second section 414. These two sections have different ASE emission spectra. In this case the ASE emission spectra are set by first and second coiling diameters CD1 and CD2 of sections 412, 414 respectively. Specifically, first section 412 has a smaller coiling diameter and second section 414 has a larger coiling diameter, CDKCD2. Thus, the maximum of ASE emission spectrum of first section 412 is at a shorter peak wavelength λ_peak than the maximum of ASE emission spectrum of second section 414.

As in the previous embodiment, an angle cleaved facet 416 prevents back reflection of output light 428. EDFA sections 412, 414 are pumped by pump light 418 delivered from a pump source 420 in a counter-propagating pumping arrangement. In particular, pump light 418 is focused by a lens 422 into a fiber 424 and a coupler 426 couples pump light 418 from fiber 424 into EDFA sections 412, 414.

An isolator 430 ensures that output light 428 is not coupled back into EDFA sections 412, 414. An output coupler 432 is provided for outcoupling output light 428. Output coupler 432 has a tap 434 for tapping a small portion of output light 428 and a photodetector 436 for monitoring the tapped portion of output light 428.

It is important to note that in source 410 first section 412 is positioned before second section 414 such that first section 412 seeds second section 414. In other words, the ASE from first section 412 propagates into second section 414 and output light 428 is derived from second section 414. The reasons for this arrangement is that second section 414 offers positive net gain for light at wavelengths generated by first section 412. First section 412, however, does not offer positive net gain and hence does not amplify light at wavelengths generated by second section 414. In other words, first section 412, which emits light centered around a shorter peak wavelength λ_peak can be used to seed second section 414 but not vice versa. Still differently put, the two-coil design of source 410 does not cause significant depletion of inversion D in second section 414, while reversing the order of sections 412 and 414 would and would hence degrade the operation of source 410.

Fig. 29 illustrates the ASE emission spectrum of first section 412 at first coiling diameter CD1=2.2 inches and of second section 414 at second coiling diameter CD2=2.9 inches. Fig. 29 also shows the total ASE emission spectrum obtained when section 412 seeds second section 414.

Based on the above principle, a number of EDFAs of different coiling diameters can be used in series from smallest diameter (shortest peak wavelength λ_peak) to largest diameter (longest peak wavelength λ_peak) to construct a still broader bandwidth source in accordance with the invention. Fig. 30 illustrates ASE emission spectra of five EDFAs having increasing coiling diameters ranging from 2.25 inches to 2.90 inches. Using these EDFAs in series makes it possible to construct a source spanning a wavelength range covering most of the S-band, i.e., from about 1460 nm to about 1525 nm.

Yet another method for broadening the ASE emission spectrum of an EDFA is by providing a continuously variable coiling diameter CD along the length of the EDFA. The coiling diameter should be increasing for seeding reasons, as explained above. A continuously variable coiling diameter can be produced, e.g., by winding the EDFA around a cone. Fig. 32 illustrates yet another embodiment of a source 440 employing an EDFA having a first section 442 and a second section 444. First section 442 has a smaller first coiling diameter and is used to seed second section 444 having a larger second coiling diameter. Source 440 has two separate pump sources 446, 448 with associated lenses 450, 452, fibers 454, 456 and couplers 458, 460 for delivering pump light 462 to first section 442 and pump light 464 to second section 444.

Source 440 has an angle cleaved facet 466 terminating first section 442. Source 440 employs an isolator 468 between first section 442 and second section 444 for stabilization. A tunable filter 470 installed after isolator 468 and before second section 444 is used to tune output wavelength λ_output of output light 472. Conveniently, coupler 460 is used as output coupler for light 472 in this embodiment.

Source 440 enables the operator to quickly and easily adjust the levels of pump power delivered by pump light 462 and 464 to sections 442 and 444 for tuning of output light 472. In fact, Fig. 31 illustrates how the use different levels of pump power in first and second sections 442, 444 tunes the total ASE emission spectrum for coiling diameters of first and second sections 442, 444 equal to 2.25 and 2.5 inches respectively.

Fig. 33 illustrates a source 480 employing a similar arrangement as source 440. Corresponding parts of source 480 are referenced by the same reference numerals . Source 480 uses a single pump source 482 for delivering pump light 484 to both sections 442, 444. This is done with the aid of lens 486, coupler 488 and fibers 490, 492 as shown. The coupling ratio of coupler 488 between fibers 490 and 492 can be adjusted to control the levels of pump power delivered by pump light 484 to section 442 and section 444. The methods to adjust this coupling ratio are well-known to those skilled in the art .

Of course, an EDFA in accordance with the invention can also be seeded by other means than a preceding EDFA . section. Fig. 34 illustrates in a simplified diagram a source 500 in which an EDFA 502 is seeded by a master oscillator 504. Master oscillator 504 can be any suitable source such as a distributed feedback laser, Fabry-Perot laser, external cavity diode laser, distributed Bragg reflector laser, vertical cavity surface emitting laser, semiconductor laser, a fiber laser or a broadband source. Input light 506 from master oscillator 504 is coupled into EDFA 502 by a lens 508. Output light 510 can be derived directly from EDFA 502 or with the aid of any suitable output coupling mechanism.

Alternatively, the sections of EDFA fiber in any of the preceding embodiments using coiling diameter to control the

ASE emission spectrum and the peak wavelength can take advantage of appropriate selection of core cross-section, depressed cladding cross-section, and refractive indices n₀, n_x, and n₂. Specifically, in the first section a first cutoff wavelength λ_cX is produced by appropriate selection of these parameters . In the second section a second cutoff wavelength λ_c2 longer than said first cutoff wavelength λ_cX is produced.

Then, the first section is positioned before the second section for seeding the second section in the same manner as discussed above. Preferably, an isolator is positioned between these two sections. Of course, an additional adjustment of the ASE emission spectrum of the two sections can be performed by coiling the first and second sections as necessary.

Fig. 35 illustrates the use of a source 520 according to the invention to test a device under test 522 (DUT) for performance characteristics in the S-band. An optical spectrum analyzer 524 is provided to measure the response of DUT 522. Source 520 generates test light 526 by using any of the above described configurations. Light 526 can span a wide band or be tuned to a particular output wavelength λ_outputf as required for testing DUT 522.

The method of producing short-pass fibers in accordance with the invention will be discussed with reference to Fig. 36, which shows a preform 600 for a depressed cladding fiber designed for pulling a short-pass fiber 620. Preform 600 has a core 612 surrounded by a depressed cladding 614. A secondary cladding 616 surrounds depressed cladding 614. Preform 600 is made of primary glass constituent Si0₂ and is manufactured by hydrolysis, oxidation, sol-gel or any other suitable method.

Core 612 has a core cross-section that is circular and is described by a core radius r_c. Depressed cladding 614 and secondary cladding 616 have corresponding circular cross- sections described by radii r_dc and r_sc, respectively. Core 612 has a refractive index n₀, depressed cladding 614 has a refractive index n_x and secondary cladding 616 has a refractive index n₂. Refractive index n_Q of core 612 is the highest, while refractive index n_x of depressed cladding 614 is the lowest. In the present embodiment, refractive index n₀ is attained by doping core 612 with index-raising dopant such as germanium or aluminum. Refractive index n_x is attained by doping depressed cladding 614 with an index-lowering dopant such as boron or fluorine. Secondary cladding 616 remains undoped and its refractive index n₂ is that of the primary glass constituent Si0₂. The incorporation of index-raising dopant ions in core 612 and index-lowering dopant ions in depressed cladding 614 is performed in accordance with the hydrolysis or oxidation processes.

Fig. 37A is a graph illustrating a typical refractive index profile 622 obtained in practice in preform 600 as a function of radius (r) , i.e., the transverse portion of index profile 622. The incorporation of index-raising dopant ions in core 612 and index-lowering dopant ions in depressed cladding 614 in either the hydrolysis or oxidation processes is controlled by the equilibria established during dopant reaction, deposition, and sintering. As a result, a depression 624 in refractive index is present in core 612 of preform 600. The equilibria further cause a sawtooth pattern 626 in refractive index to manifest in depressed cladding 614. Thus, refractive index n₀ of core 612 is in fact an average refractive index. Likewise, refractive index n_x of depressed cladding 614 is also an average refractive index. Meanwhile, refractive index n₂ of secondary cladding 616 is also an average refractive index. The actual value of the refractive index in secondary cladding 616 exhibits comparatively low variability as a function of radius because refractive index n₂ is not attained by doping.

In addition to exhibiting radial variation, actual refractive index profile 622 also varies as a function of position along an axis 627 of preform 600. In other words, profile 622 has a longitudinal portion varying along the length of preform 600. Preform 600 has a total length L and the variation of the refractive index at preselected radii as a function of length is illustrated in the graphs of Fig. 37B. Once again, refractive indices n₀ and n_x are average refractive indices while the actual refractive index values exhibit a large variation. Meanwhile, refractive index n₂ is also an average refractive index while the actual refractive index value remains relatively constant. Depending on the specifics of the manufacturing processes, the actual refractive index values in core 612 and depressed cladding 614 exhibit tolerance ranges TR_X and TR₂ that may approach up to 20% along the length of axis 627.

Fig. 36 also shows how short-pass fiber 620 is obtained by drawing or pulling preform 600 from an initial cross sectional area A₀ to a final total cross sectional area A_f. Initial and final cross sectional areas are equal to:

^Ao ^{= πr}X ^an

A , - πr²,

where r₂ is the radius of secondary cladding in pulled short- pass fiber 620. A drawing ratio DR is defined as the ratio of the radius of the fiber to the radius of the preform:

DR = -^ r sc

Since the refractive indices are nearly preserved during the pulling process, the average index n₀ of core 612 is significantly higher than the average index n_x of depressed cladding 614 and average index n₂ of secondary cladding 16 in pulled short-pass fiber 620. The drawing ratio DR by which preform 600 is to be pulled to obtain radii r₀, r_x, r₂ corresponding to core 612, depressed cladding 614 and secondary cladding 616 in pulled short-pass fiber 620 is made to achieve certain guiding properties in short-pass fiber 620. Specifically, the indices and radii are selected to produce a fundamental mode cutoff wavelength λ_c such that light in the fundamental mode at wavelengths smaller than λ_c is retained in core 612 while light in fundamental mode at wavelength λ_c or longer wavelengths is lost to secondary cladding 616 over a short distance. This objective is accomplished by ensuring that pulled short-pass fiber 620 exhibits the appropriate average refractive indices n₀, n_x, n₂ and cross-sections or radii r₀, r_x, r₂. In other words,- this goal is accomplished by appropriately engineering refractive index profile 622 and cross-sections of core 612, depressed cladding 614 and secondary cladding 616, or, still differently put, by obtaining the appropriate W-profile, such as the index profile 20 shown in Fig. 1, in short-pass fiber 620.

In any practical short-pass fiber 620 the depressed cladding cross-section has to be larger than the core cross-section. This is ensured by selecting the core cross-section A_c smaller than depressed cladding cross-section A_dc in preform 600. Specifically, in preform 600 core cross-section is equal to: X = πr² , (16)

while the depressed cladding cross section is equal to:

The aerial ratio established between core and depressed cladding cross-sections (A_c/A_dc) is preserved during the pulling of preform 600 into short-pass fiber 620. Likewise, the values of average refractive indices n₀, n_x, n₂ are nearly preserved during the pulling.

The values of r₀, r_x, n₀, n_x and n₂ in short-pass fiber 620 not only define fundamental mode cutoff wavelength λ_c but also define a roll-off loss curve with respect to wavelength. Fig. 38 illustrates an exemplary family of loss curves 640 for the same fundamental mode cutoff wavelength λ_c. It has been found that only the cutoff wavelength λ_c gets displaced during the pulling of short-pass fiber 620 from preform 600. In other words, the overall shapes of roll-off loss curves 640 are basically preserved.

Unfortunately, the actual fundamental cutoff wavelength will differ from point to point along axis 627 due to the variation in index profile 622 along axis 627. In fact, given that tolerances TR_X and TR₂ for refractive indices n₀ and n_x vary up to 20% (see Fig. 37B) , the actual cutoff wavelength can fluctuate by up to about 20%. Therefore, it is clearly not feasible to simply pull preform 600 at the computed drawing ratio DR to produce short-pass fiber 620 with the calculated fundamental mode cutoff wavelength λ_c.

Thus, in accordance with the method of invention, a minimum fundamental mode cutoff wavelength λ_m is set before pulling preform 600. Specifically, minimum cutoff wavelength λ_m is set to be the smallest possible value that cutoff wavelength λ_c can assume at any point along axis 627 in pulled short-pass fiber 620.

Furthermore, core cross-section A_c and depressed cladding cross-section A_dc are measured in preform 600 before pulling. In the present embodiment, where core 612 and depressed cladding 614 are circular this is done by measuring radii r_c, r_dc and using the equations given above. Preferably, the values of radii r_c, r_dc are measured at a number of locations along axis 627 to obtain average values.

The longitudinal portion of refractive index profile 622 in core 612 and depressed cladding 614 is measured along axis 627 of preform 600 as well. This is conveniently performed by taking measurements of actual values of refractive indices n₀, n_x at regular intervals along axis 627 and at a number of radii to thus obtain the average values of refractive indices n_σ, n_x. Such measurements can be performed by deflection tomography, which is well known in the art of optical fiber preform characterization. It is also convenient to plot the measurements of refractive indices n_σ, n_x in the form of a graph of average values at each point along axis 627, similar to the graph shown in Fig. 37A.

In accordance with the invention drawing ratio DR is derived from measured core cross-section A_c, depressed cladding cross- section A_c and the variation in indices n₀, n_x determined in preform 600. In particular, drawing ratio DR is set to achieve a final value of core cross-section A'_c. In this embodiment final value of core cross-section A' _c is defined by the final core radius r₀ to be obtained in short-pass fiber 620. This is done such that, given a final depressed cladding cross section A'_dc and indices n₀, n_x final core radius r_Q defines fundamental mode cutoff wavelength λ_c such that λ_c≥λ_m at all points along axis 627. Preferably, λ_m is set at least 5 nm below a lowest value of fundamental cutoff wavelength λ_c along axis 627. This is done as a precaution so that subsequent fine adjustment of fundamental mode cutoff wavelength λ_c in pulled short-pass fiber 620 is still possible by standard techniques, such as stressing or bending of the fiber.

Referring back to Fig. 36, in the next step preform 600 is pulled by drawing ratio DR determined in accordance with the above-defined rules. It is important to get as close as possible to the desired core radius r₀ during this pull. For example, when core radius r_Q is within 0.5% of the desired core radius, the error in cutoff wavelength λ_c is within 0.5%. This corresponds to a 5 nm error in cutoff wavelength λ_c when operating at a wavelength of 1.0 micron and an 8 nm error when operating at a wavelength of 1525 nm. This type of error is barely acceptable for short-pass . fibers used for S-band amplification with Er-doped fiber, and is more than adequate for short-pass fibers used for amplification at 980 nm with Nd-doped fiber.

In accordance with a preferred embodiment a short pilot section or test section 634 of preform 600 is pulled first by drawing ratio DR. The pulling of test section 34, sometimes also referred to as pilot draw, aids in eliminating systematical errors. That is because the process of pulling can modify index profile 622. For example, the pulling process tends to produce a smoothing of index profile 622 due to melting of the glass during the pulling process. Melting tends to shift actual fundamental mode cutoff wavelength λ_c to shorter or longer wavelengths depending on the details of the design of refractive index profile 622 of perform 600 and any index raising or lowering materials it uses. For example, index-lowering dopants consisting of small atoms such as Fluorine diffuse easily in softened silica glass. Thus, an index-lowering dopant such as Fluorine diffuses into core 612 and shifts cutoff wavelength λ_c to a shorter wavelength. This is problematic when depressed cladding 614 is deep and wide, so that significant diffusion into core 612 occurs without appreciably affecting the average refractive index of depressed cladding 614.^' Thus, the pilot draw is useful because the smoothing of profile 622 cannot be calculated or modeled with sufficient accuracy to determine its effect on fundamental mode cutoff wavelength λ_c.

After pulling of test section 634 fundamental mode cutoff wavelength λ_c is determined in pulled test section 634. This is preferably done at several points along axis 627. It is important to choose test section 634 long enough to be representative of preform 600 and hence of short-pass fiber 620 that will be pulled from preform 600. For this reason test section 634 should be chosen to be between a few percent and up to 20 percent of length L. The cutoff wavelength may be determined experimentally as the wavelength at which light is lost from the core at a significantly high rate, for example, at 10 dB/m or 40 dB/m.

Based on the deviation of fundamental mode cutoff wavelength λ_c measured in pulled test section 634 drawing ratio DR is adjusted to an adjusted drawing ratio DR' as follows:

DR = DR. ^{de red} measured λ„

Then the remainder of preform 600 is pulled by adjusted drawing ratio DR' to produce short-pass fiber 620.

This preferred embodiment of the method is especially useful in situations when preform 600 exhibits a sufficiently high uniformity such as about 0.5% for radii or indices. At this level of uniformity compensation for dopant diffusion and other systematic effects is very effective. However, even in cases where such uniformity is not present, it is still convenient to pull test section 634 and measure the deviation of fundamental mode cutoff wavelength λ_c in test section 634 to determine adjusted drawing ratio DR' for pulling the remainder of preform 600.

In an alternative embodiment, drawing ratio DR is varied as the preform is pulled to compensate for the variations in refractive index graphed in Fig. 37B. This variable drawing ratio DR(z) is used to obtain an approximately constant cutoff wavelength λ_c along the length of the fiber. As above, the variable drawing ratio DR(z) may be multiplied by a factor λ_c ( desired) /λ_c (measured) once the cutoff wavelength of the test section is measured, to compensate for systematic errors due to the pulling process.

In some embodiments of the method secondary cladding cross- section is adjusted before the pulling step. In the present embodiment this is done by increasing or decreasing secondary cladding radius r_sc. For example, radius r_sc of secondary cladding 616 is augmented by a rod-in-tube (also sometimes called "sleeving") technique or outside vapor deposition (OVD) . Alternatively, radius r_sc of secondary cladding 616 is reduced by a technique such as etching. For more information on these techniques the reader is referred to Erbium-Doped Fiber Amplifiers Fundamentals and Technology by P. C. Becker, N. A. Olsson, and J. R. Simpson, chapter 2 (Optical Fiber Fabrication), published by Academic Press, pp. 13-42. The necessity to augment or reduce secondary cladding cross- section before pulling it arises when the pulled fiber is supposed to have a certain, e.g., standard, outside diameter (OD) , such as 125 +/-1 microns or 80 +/-1 microns. It is important to maintain standard fiber OD when low loss splicing to standard single mode fiber is required. The remainder of the method is performed in accordance with the above-discussed principles for designing short-pass fiber 620.

The method of invention can be used for pulling short-pass fibers to obtain *5 nm control of fundamental mode cutoff wavelength λ_c in performs with random variations in index or cross sections of up to 20%. Without the method such variations cause >100 nm unpredictable shifts in fundamental mode cutoff wavelength λ_c. This advantage can be obtained even when systematic shifts are present.

Fundamental cutoff wavelength λ_c in pulled short-pass fiber 620 can be further adjusted by stressing or coiling fiber 620 in accordance with well-known principles. That is because the fundamental mode cutoff wavelength λ_c gets displaced during coiling of short-pass fiber 620 relative to the fundamental mode cutoff wavelength of short-pass fiber 620 when straight. Meanwhile, the overall shape of roll-off loss curves 640, as shown in Fig. 38 is basically preserved. Hence, one can use the coiling diameter of short-pass fiber 620 to make fine- tuning adjustments to fundamental mode cutoff wavelength λ_c after short-pass fiber 620 has been drawn from preform 600. This can be done to compensate for slight errors in selecting the correct drawing ratio DR, or to compensate for slight errors in pulling to an adjusted drawing ratio DR' . This can also be done to compensate for slight shifts in fundamental mode cutoff wavelength λ_c resulting from diffusion of dopants in short-pass fiber 620 during the pulling process, or to compensate for slight variations in the longitudinal portion of refractive index profile 622 of perform 600 along axis 627. Alternatively, it is also possible to determine drawing ratio DR with a particular coiling radius in mind. This is frequently the case when short-pass fiber 620 is to be packaged in a box of prescribed dimensions. The effect of coiling on cutoff wavelength λ_c is considered in determining drawing ratio DR in these situations. Specifically, since decreasing the coiling diameter (smaller coil) shifts cutoff wavelength λ_c to shorter wavelengths the amount of shift for the desired coiling diameter has to be added when setting minimum fundamental mode cutoff wavelength λ_m before drawing preform 600. For example, coiling a fiber at a diameter of 50 nm shifts fundamental mode cutoff wavelength λ_m by about 20 nm to 200 nm as compared with fundamental mode cutoff wavelength λ_m for the same fiber when straight. This shift increases approximately in proportion to the curvature (inverse of the diameter) of the fiber. The magnitude of this shift depends on the mode field diameter (MFD) of the fiber and also depends on the outside diameter (OD) of the fiber. In general, a fiber with a larger MFD is more sensitive to coiling (due to the increased stresses produced for a given bend diameter) . The sensitivity to bending of a particular fiber design (i.e., given MFD, OD, etc.) can be measured at the pilot draw stage.

In the embodiments discussed above the cross-sections described by radii r_c, r_dc and r_sc in preform 600 exhibit only small variation along the length of preform 600 or along axis 627 and hence do not cause significant variations of final cross-sections described by radius r₀ or radii r_x, r₂ in pulled short-pass fiber 620 along axis 627. In fact, when the variations in drawing ratio DR, radii and indices (i.e., the corresponding tolerances in DR, radii and indices) remain within .3% in preform 600 the resulting pulled fiber will have sufficient performance to amplify signals in the S-band. For other bands, such as the C- and L-bands the tolerances are even greater.

A person skilled in the art will realize that the method of invention can be employed for pulling any type of short-pass fiber. In particular, it is possible to pull fibers with active cores, e.g., Er or Tm doped cores. The same steps as described above can be used in pulling such fibers, and the additional effects on the refractive indices introduced by the active dopants will typically be automatically included in the measurements of refractive index profile and fundamental mode cutoff wavelength λ_c.

It will be clear to one skilled in the art that the above embodiments may be altered in many ways without departing from the scope of the invention. Accordingly, the scope of the invention should be determined by the following claims and their legal equivalents.

Claims

A fiber amplifier comprising: a) a core having a core cross-section and a refractive index n₀; b) an active material doped in said core; c) a depressed cladding surrounding said core, said depressed cladding having a depressed cladding cross-section and a refractive index n_x; d) a secondary cladding surrounding said depressed cladding, said secondary cladding having a secondary cladding cross-section and a refractive index n₂; e) a pump source for pumping said active material to a high relative inversion D, such that said active material exhibits positive gains in a short wavelength band and high gains in a long wavelength band; wherein said core cross-section, said depressed cladding cross-section, and said refractive indices n₀, n_x, and n₂ are selected to produce a roll-off loss curve about a cutoff wavelength λ_c, said roll-off loss curve yielding losses at least comparable to said high gains in said long wavelength band and losses substantially smaller than said positive gains in said short wavelength band.

The fiber amplifier of claim 1, wherein said refractive index n_Q is selected such that an effective index experienced by a mode of radiation confined in said core is selected to provide a roll-off slope of said roll-off loss curve before said cutoff wavelength λ_c that is greater than or about equal to the maximum slope of the gain spectrum in said long wavelength band.

3. The fiber amplifier of claim 2, wherein said refractive index n₀ is selected such that the slope of said effective index with respect to said cutoff wavelength λ_c is in the range of .002/1000 nm to .008/1000 nm.

4. The fiber amplifier of claim 2, wherein said refractive index n_Q is at least 0.5% larger than said refractive index n₂.

5. The fiber amplifier of claim 1, wherein said cutoff wavelength λ_c is contained in said long wavelength band.

6. The fiber amplifier of claim 1, wherein said cutoff wavelength λ_c is contained in said short wavelength band.

7. The fiber amplifier of claim 1, wherein said cutoff wavelength λ_c is between said short wavelength band and said long wavelength band.

8. The fiber amplifier of claim 1, wherein said active material is Erbium.

9. The fiber amplifier of claim 8, wherein said short wavelength band comprises at least a portion of the S- band and said long wavelength band comprises at least a portion of the C-band or L-band.

10. The fiber amplifier of claim 9, wherein said cutoff wavelength λ_c is set near 1525 nm.

11. The method of claim 9, wherein said roll-off loss curve is selected to yield losses in said S-band smaller by at least 5 dB than said positive gains. The fiber amplifier of claim 8, wherein said fiber comprises a silicate-containing glass.

The fiber amplifier of claim 12, wherein said silicate- containing glass is selected from the group of alumino- germanosilicate glass and phosphorus doped germanosilicate glass.

The fiber amplifier of claim 8, wherein said active material is Erbium with a concentration of about 0.1% wt in said core.

The fiber amplifier of claim 8, wherein said pump source is a laser diode providing pumping radiation at about 980 nm.

The fiber amplifier of claim 1, wherein said refractive index n₀ of said core differs from said refractive index n₂ of said secondary cladding by about 0.005 to about 0.03.

The fiber amplifier of claim 1, wherein said refractive index n_x of said depressed cladding differs from said refractive index n₂ of said secondary cladding by about -0.004 to about -0.02.

The fiber amplifier of claim 1, wherein said core cross- section and said depressed cladding cross-section are selected from the shapes consisting of circles, ellipses and polygons .

19. The fiber amplifier of claim 1, wherein said pump source provides pump radiation at an intensity sufficient to ensure that said high relative inversion D≥O .7.

20. The method of claim 1, wherein said roll-off loss curve is selected to yield losses of at least 100 dB in said long wavelength band.

21. A method for designing a fiber amplifier using an active material pumped to a high relative inversion D, said active material exhibiting positive gains in a short wavelength band and high gains in a long wavelength band, said method comprising: a) providing a core having a core cross-section and a refractive index n₀; b) doping said active material into said core; c) providing a depressed cladding around said core, said depressed cladding having a depressed cladding cross-section and a refractive index n_x; d) providing a secondary cladding around said depressed cladding, said secondary cladding having a secondary cladding cross-section and a refractive index n₂; e) selecting said core cross section, said depressed cladding cross-section, and said refractive indices n₀, n_x, and n₂ to produce a roll-off loss curve about a cutoff wavelength λ_c, said roll-off loss curve yielding losses at least comparable to said high gains in said long wavelength band and losses substantially smaller than said positive gains in said short wavelength band.

22. The method of claim 21, wherein said refractive index n₀ is selected such that an effective index experienced by a mode of radiation confined in said core is selected to provide a roll-off slope of said roll-off loss curve before said cutoff wavelength λ_c that is greater than or about equal to the maximum slope of the gain spectrum in said long wavelength band.

23. The method of claim 22, wherein said refractive index n₀ is selected such that the slope of said effective index with respect to said cutoff wavelength λ_c is in the range of .002/1000 nm to .008/1000 nm.

24. The method of claim 22, wherein said refractive index n_Q is at least 0.5% larger than said refractive index n₂.

25. The method of claim 21, wherein said cutoff wavelength λ_c is contained in said long wavelength band.

26. The method of claim 21, wherein said cutoff wavelength λ_c is contained in said short wavelength band.

27. The method of claim 21, wherein said cutoff wavelength λ_c is contained between said long wavelength band and said short wavelength band.

28. The method of claim 21, wherein said active material is Erbium, wherein said long wavelength band is at least a portion of the C-band and the L-band, and wherein said short wavelength band is at least a portion of the S- band.

29. The method of claim 28, wherein said roll-off loss curve is selected to yield losses of at least 100 dB in said long wavelength band. The method of claim 28, wherein said roll-off loss curve is selected to yield losses in said S-band smaller by at least 5 dB than said positive gains.

The method of claim 21, wherein said high relative inversion D is maintained at D≥O .7.

The method of claim 21, further comprising adjusting a length L of said fiber amplifier to yield a predetermined gain over said short wavelength band.

A method for pumping a- fiber amplifier in a W-profile fiber, said method comprising: a) providing a core having a core cross-section and a refractive index n₀; b) doping an active material into said core; c) providing a depressed cladding around said core, said depressed cladding having a depressed cladding cross- section and a refractive index n_x; d) providing a secondary cladding around said depressed cladding, said secondary cladding having a secondary cladding cross-section and a refractive index n₂; e) selecting said core cross section, said depressed cladding cross-section, and said refractive indices n₀, n_x, and n₂ to produce a roll-off loss curve about a cutoff wavelength λ_c; and f) pumping said active to a relative inversion D≥O.7, such that said active material exhibits positive gains in a short wavelength band and high gains in a long wavelength band.

34. The method of claim 33, wherein said active material is Erbium, and said roll-off loss curve yielding losses at least comparable to said high gains in said long wavelength band and losses substantially smaller than said positive gains in said short wavelength band, wherein said long wavelength band is at least a portion of the C-band or the L-band and said short wavelength band is at least a portion of the S-band.

35. The method of claim 34, wherein said refractive index n₀ is selected such that an effective index experienced by a mode of radiation confined in said core is selected to provide a roll-off slope of said roll-off loss curve before said cutoff wavelength λ_c that is greater than or about equal to the maximum slope of the gain spectrum in said long wavelength band.

36. The method of claim 35, wherein said refractive index n_Q is selected such that the slope of said effective index with respect to said cutoff wavelength λ_c is in the range of .002/1000 nm to .008/1000 nm.

37. The method of claim 34, wherein said cutoff wavelength λ_c is contained in said long wavelength band.

38. The method of claim 34, wherein said cutoff wavelength λ_c is contained between said long wavelength band and said short wavelength band.

39. The method of claim 34, wherein said cutoff wavelength λ_c is contained in said S-band.

40. The method of claim 34, wherein said refractive index n_σ is at least 0.5% larger than said refractive index n₂.

41. A fiber amplifier comprising: a) an active material-doped region wherein said active material is Erbium; b) a mechanism for providing a distributed loss by engineering an index profile in said fiber; and c) a pump source producing a high inversion, wherein the gain at a wavelength below 1525nm exceeds the distributed loss at said wavelength below 1525nm by at least 5dB, and wherein the distributed loss in a wavelength band longer than 1525nm exceeds the gain in said wavelength band longer than 1525nm.

42. A fiber amplifier comprising: a) an active material-doped region wherein said active material is Erbium; b) a mechanism for providing a distributed loss; and c) a pump source producing a high inversion, wherein the gain at a wavelength below 1525nm exceeds the distributed loss at said wavelength below 1525nm by at least 5dB, and wherein the distributed loss in a wavelength band longer than 1525nm exceeds the gain in said wavelength band longer than 1525nm.

43. The fiber of claim 42, wherein said distributed loss is by engineering an index profile in said fiber.

44. A fiber amplifier with suppressed cladding mode loss, said fiber amplifier comprising: a) an active core; b) a cladding surrounding said active core; c) an index profile established in said active core and in said cladding such that said active core exhibits a loss above a cutoff wavelength λ_c and positive gains in a short wavelength range below said cutoff wavelength λ_c; d) a means for suppressing coupling of a radiation in said short wavelength range between said active core and said cladding.

45. The fiber amplifier of claim 44, wherein said means for suppressing coupling comprises a material distributed in said cladding, said material being selected from the group consisting of scattering materials and absorbing materials .

46. The fiber amplifier of claim 45, wherein said cladding comprises a depressed cladding having a depressed cladding cross-section and a refractive index n_x, and a secondary cladding having a secondary cladding cross- section and a refractive index n₂, and said material is distributed in said secondary cladding.

47. The fiber amplifier of claim 45, wherein said radiation has a mode diameter extending from said active core into said cladding, and said material is distributed outside said mode diameter.

48. The fiber amplifier of claim 45, wherein said absorbing material comprises a rare earth element.

49. The fiber amplifier of claim 44, wherein said means for suppressing coupling comprises a non-phase-matched length section of said fiber amplifier, such that the coupling of said radiation is not phase matched between said core and said cladding.

50. The fiber amplifier of claim 49, wherein said core has a core cross-section and a refractive index n₀, said cladding has a cladding cross-section and a refractive index n_c, and said non-phase-matched length section is formed by a predetermined selection of said core cross- section, cladding cross-section and refractive indices no> ⁿclad-

51. The fiber amplifier of claim 49, wherein said cladding comprises a depressed cladding having a depressed cladding cross-section and a refractive index n_x, and a secondary cladding having a secondary cladding cross- section and a refractive index n₂.

52. The fiber amplifier of claim 51, wherein said core has a core cross-section and a refractive index n_Q, and said non-phase-matched length section is formed by a predetermined selection of said core cross-section, said depressed cladding cross-section, said secondary cladding cross section and refractive indices n₀, n_x, n₂.

53. The fiber amplifier of claim 52, wherein said cladding further comprises an outer cladding having an outer cladding cross-section and a refractive index n₃, where n₃<n₂.

54. The fiber amplifier of claim 44, wherein said active core comprises Erbium.

55. The fiber amplifier of claim 54, wherein said cutoff wavelength λ_c is set near 1525 nm.

56. The fiber amplifier of claim 54, further comprising a pump source for pumping said core with radiation at a pump wavelength near 980 nm.

57. A method for suppressing a cladding mode loss in a fiber amplifier having an active core and a cladding surrounding said active core, said method comprising: a) establishing an index profile in said active core and in said cladding such that said active core exhibits a loss above a cutoff wavelength λ_c and positive gains in a short wavelength range below said cutoff wavelength λ_c; and b) suppressing coupling of a radiation in said short wavelength range between said active core and said cladding.

58. The method of claim 57, wherein said step of suppressing coupling is performed by distributing a material in said cladding for scattering or absorbing said radiation.

59. The method of claim 58, wherein said radiation has a mode diameter extending from said active core into said cladding, and said material is distributed outside said mode diameter .

60. The method of claim 57, wherein said step of suppressing coupling is performed by preventing phase matching, such that the coupling of said radiation is not phase matched between said core and said cladding.

61. The method of claim 60, wherein phase matching is prevented by selecting a core cross-section and refractive index n_Q for said core, and by selecting a cladding cross section and refractive index n_cXad for said cladding.

62. The method of claim 60, wherein said core has a core cross section and a refractive index n₀, said cladding comprises a depressed cladding having a depressed cladding cross-section and a refractive index n_x, and a secondary cladding having a secondary cladding cross- section and a refractive index n₂, and wherein said phase matching is prevented by selecting said core cross- section, said depressed cladding cross-section, said secondary cladding cross section and refractive indices n₀, n_x, n₂.

63. The method of claim 62, wherein said cladding further comprises an outer cladding having an outer cladding cross section and a refractive index n₃, where n₃<n₂.

64. A source of light in an S-band of wavelengths comprising: a) a fiber having:

1) a core doped with Erbium and having a core cross-section and a refractive index n_Q;

2) a depressed cladding surrounding said core, said depressed cladding having a depressed cladding cross-section and a refractive index n_x; and

3) a secondary cladding surrounding said depressed cladding, said secondary cladding having a secondary cladding cross-section and a refractive index n₂; and b) a pump source for pumping said Erbium contained in said core to a high relative inversion D, such that said Erbium exhibits positive gains in said S-band and high gains in a long wavelength band longer than said S-band; wherein said core cross-section, said depressed cladding cross-section, and said refractive indices n₀, n_x, and n₂ are selected to produce losses at least comparable to said high gains in said long wavelength band and losses substantially smaller than said positive gains in said S- band.

65. The source of claim 64, further comprising a wavelength- selecting means for selecting an output wavelength of said light.

66. The source of claim 65, wherein said wavelength-selecting means comprises a wavelength-selecting feedback mechanism.

67. The source of claim 66, wherein said wavelength-selecting feedback mechanism comprises a fiber Bragg grating.

68. The source of claim 65, wherein said wavelength-selecting means consists of a filter selected from the group consisting of tilted etalons, strain-tuned fiber Bragg gratings, temperature-tuned fiber Bragg gratings, interferometers, arrays waveguide gratings, diffraction gratings and tunable coupled cavity reflectors.

69. The source of claim 65, wherein said wavelength-selecting means comprises a pump source adjustment for tuning said high relative inversion D.

70. The source of claim 65, wherein said wavelength-selecting means comprises a coiling diameter of said fiber.

71. The source of claim 70, wherein said coiling diameter is continuously variable.

72. The source of claim 64, further comprising a master oscillator for seeding said fiber.

73. The source of claim 72, wherein said master oscillator is an optical source selected from the group consisting of distributed feedback laser, Fabry-Perot laser, external cavity diode laser, distributed Bragg reflector laser, vertical cavity surface emitting laser, semiconductor laser, a fiber laser, a broadband source.

74. The source of claim 64, wherein said fiber comprises: a) a first section having a first coiling diameter; and b) a second section having a second coiling diameter larger than said first coiling diameter.

75. The source of claim 74, wherein said first section is positioned before said second section for seeding said second section.

76. The source of claim 75, further comprising an isolator installed between said first section and said second section.

77. The source of claim 64, wherein said fiber comprises: a) a first section wherein said core cross-section, said depressed cladding cross-section, and said refractive indices n_Q, n_x, and n₂ are selected to produce a first cutoff wavelength λ_cX; and b) a second section wherein said core cross-section, said depressed cladding cross-section, and said refractive indices n_D, n_x, and n₂ are selected to produce a second cutoff wavelength λ_c2 longer than said first cutoff wavelength λ_cX.

78. The source of claim 77, wherein said first section is positioned before said second section for seeding said second section.

79. The source of claim 78, further comprising an isolator installed between said first section and said second section.

80. The source of claim 64, wherein said pump source comprises a laser diode providing pump light at about 980 nm.

81. The source of claim 64, further comprising an optical cavity for containing said fiber.

82. The source of claim 81, wherein said optical cavity is a ring cavity.

83. A method for generating light in an S-band of wavelengths comprising: a) providing a fiber having a core doped with Erbium and having a core cross-section and a refractive index n_σ; b) surrounding said core with a depressed cladding having a depressed cladding cross-section and a refractive index n_x; T U 03/06971

c) surrounding said depressed cladding with a secondary cladding having a secondary cladding cross-section and a refractive index n₂; and d) pumping said active material contained in said core to a high relative inversion D, such that said active material exhibits positive gains in said S- band and high gains in a long wavelength band longer than said S-band; wherein said core cross-section, said depressed cladding cross-section, and said refractive indices n₀, n_x, and n₂ are selected to produce losses at least comparable to said high gains in said long wavelength band and losses substantially smaller than said positive gains in said S- band.

84. The method of claim 83, wherein said step of pumping comprises counter-propagating pumping.

85. The method of claim 83, further comprising seeding said fiber.

86. The method of claim 85, wherein said fiber comprises a first section and a second section, and said method comprises seeding said second section by said first section.

87. The method of claim 83, wherein said pumping is performed in a pulsed mode.

88. The method of claim 83, wherein said light in said S-band is combined with a light outside said S-band. fiber amplifier comprising: a) a core having a core cross-section and a refractive index n_c; b) an active material doped in said core, wherein said active material is Thulium; c) a depressed cladding surrounding said core, said depressed cladding having a depressed cladding cross-section and a refractive index n_x; d) a secondary cladding surrounding said depressed cladding, said secondary cladding having a secondary cladding cross-section and a refractive index n₂; and e) a pump source for pumping said active material to a high relative inversion D, such that said active material exhibits positive gains in a short wavelength band and high gains in a long wavelength band; wherein said core cross-section, said depressed cladding cross-section, and said refractive indices n₀, n_x, and n₂ are selected to produce a roll-off loss curve about a cutoff wavelength λ_c, said roll-off loss curve yielding losses at least comparable to said high gains in said long wavelength band and losses substantially smaller than said positive gains in said short wavelength band.

The fiber amplifier of claim 89, wherein said short wavelength band is the L-band.

The fiber amplifier of claim 89, wherein said short wavelength band is between 1.6 and 1.8 μm.

The fiber amplifier of claim 89, wherein said long wavelength band is between 1.7 and 2.1 μm.

93. The fiber amplifier of claim 89, wherein said cutoff wavelength is about 1.7 to 1.9 μm.

94. The fiber amplifier of claim 89, wherein said pump source provides pump radiation having an intensity of at least 30 mW.

95. The fiber amplifier of claim 89, wherein said pump source is a laser diode providing pumping radiation at about

1.48 to 1.5 μm.

96. The fiber amplifier of claim 95, wherein said pump source provides pump radiation having an intensity of at least 100 mW.

98. The fiber amplifier of claim 89, wherein said fiber comprises a silicate-containing glass.

99. The fiber amplifier of claim 98, wherein said silicate- containing glass is selected from the group of alumino- germanosilicate glass and phosphorus doped germanosilicate glass.

100. The fiber amplifier of claim 89, wherein said core cross- section and said depressed cladding cross-section are selected from the shapes consisting of circles, ellipses and polygons .