JP5135067B2 - Optical device design method - Google Patents

Description

  The present invention relates to a method for designing an optical device that can be used in a chromatic dispersion compensator for compensating chromatic dispersion of an optical fiber. This device can be used in fiber optic communication networks.

In optical communication, broadband and high-speed transmission of high-density wavelength division multiplexing (DWDM) transmission is being promoted. In order to perform high-speed transmission, it is desirable to use, as these transmission lines, optical fibers whose chromatic dispersion is as small as possible in the transmission band and whose chromatic dispersion is not zero in order to suppress nonlinear effects.
In addition, many of the optical fibers already laid in a wide range are used in a wavelength region where the dispersion is large. For example, a standard single-mode fiber (S-SMF) having zero dispersion near a wavelength of 1.3 μm is used for an erbium-doped optical fiber amplifier, and has a wavelength of 1.53 to 1.63 μm. Used in obi. Further, a dispersion shifted fiber (DSF) in which the zero dispersion is shifted to around 1.55 μm may be used not only in the C band but also in the S band and the L band. In addition, there are various non-zero dispersion shifted fibers (NZ-DSF) that do not become zero dispersion at 1.55 μm. When these fibers are used in DWDM, compensation techniques for residual dispersion over a wide wavelength range are important.

  Various techniques are used for dispersion compensation. A dispersion compensation fiber (DCF: Dispersion Compensation Fiber) is the most practical technology (see, for example, Patent Documents 1 and 2). DCF is realized by controlling the refractive index distribution of the fiber so as to obtain a desired dispersion compensation amount. However, the DCF usually requires the same length as the fiber to be compensated, and when this is modularized, not only a large space is required, but also propagation loss cannot be ignored. In addition, DCF requires accurate control of the refractive index distribution, which is not only difficult to manufacture, but also often makes it difficult to satisfy the dispersion compensation amount required in a wide band.

  Fiber Bragg Grating (FBG) is also one of the techniques often used for dispersion compensation (see, for example, Patent Document 3). The FBG performs dispersion compensation by irradiating the fiber with UV light, thereby changing the refractive index of the fiber core and forming a grating due to the different refractive index. Thereby, a small device can be realized. However, since it is difficult to control the change in refractive index and there is a limit to the change in the refractive index of the fiber, there is a limit to the dispersion compensation characteristics that can be realized. There are also limits to device miniaturization and mass production.

  There has also been proposed a structure in which a region where dispersion compensation is performed is divided for each channel, and chirped FBGs for which dispersion compensation is performed in each channel are superposed at one place (see, for example, Patent Document 4). By using this, the required fiber length is shortened. However, since this proposal is designed to simply superimpose a plurality of FBGs, the structure of each channel approaches and affects each channel characteristic, so there is a limit to the characteristics that can be realized. In addition, since a change in refractive index required for superimposing FBGs cannot be obtained by UV irradiation, some structures cannot be realized.

  An optical planar circuit (PLC: Planar Lightwave Circuit) can perform dispersion compensation by using an optical circuit constructed in a plane. Lattice type PLC is one example (see, for example, Non-Patent Document 1). However, the lattice type PLC controls the dispersion by cascading coupled resonators and is based on the principle of a digital IIR (Infinite Impulse Response) filter, so that the amount of dispersion to be realized is limited.

  It is also possible to demultiplex wavelength-multiplexed signal light with an arrayed waveguide grating (AWG), add an optical path difference for each channel, adjust the delay time, and then combine the light again with a collimator lens (for example, , See Patent Document 5). However, not only is the structure complicated and difficult to fabricate, it also requires a large amount of space.

A VIPA (Virtually Imaged Array) type dispersion compensator is a dispersion compensation device composed of a wavelength dispersion element (VIPA plate) in which a reflection film is coated on both surfaces of a thin plate, and a reflection mirror (for example, see Patent Document 6). . This device adjusts dispersion with a three-dimensional structure, is structurally complex, and requires extremely high accuracy in manufacturing.
Japanese Patent No. 3857211 Japanese Patent No. 3819264 JP 2004-325549 A International Publication No. 03/010586 Japanese Patent No. 3852409 JP-A-2005-275101 K. Takiguchi, et al., "Dispersion Slope Equalizer for Dispersion Shifted Fiber Using a Lattice-Form Programmable Optical Filter on a Planar Lightwave Circuit", Journal of Lightwave Technology, 1998 years, Vol. 16, No. 9, p. 1647-1656

The problems in the prior art described above are as follows.
(1) The DCF requires a large space due to the use of a long fiber and is difficult to downsize. In addition, there is a limit to the dispersion compensation characteristics that can be realized.
(2) A device in which FBGs and FBGs are overlapped has a limit in the characteristics that can be realized.
(3) Lattice type PLC has a small amount of dispersion compensation that can be realized.
(4) The PLC using AWG has a complicated structure, is difficult to manufacture, and increases the cost. In addition, the required space is large and it is difficult to reduce the size of the device.
(5) VIPA has a complicated structure, is difficult to manufacture, and is expensive.

  Recently, the present inventors have proposed a dispersion compensation device (an unpublished application by the present applicant, such as Japanese Patent Application No. 2007-33004) using a planar waveguide (NPWG: Non-uniform Planar WaveGide) having a non-uniform width. Yes. This dispersion compensation device performs dispersion compensation by controlling the reflection spectrum by making the optical waveguide non-uniform. This device has a planar structure and can be easily manufactured in large quantities in the manufacturing process. However, the distance between peaks where the width changing along the traveling direction of the NPWG waveguide becomes maximum or minimum may conventionally be about 1/10 of the wavelength used. In order to realize such a fine structure, extremely high manufacturing accuracy is required. For example, in an L-band device, when a waveguide is made of a material having a center wavelength of 1590 nm and a refractive index of about 2.3, a manufacturing accuracy of about 70 nm is required, which cannot be achieved by the current process.

  The present invention has been made in view of the above circumstances, and the fabrication accuracy of an optical device composed of an optical waveguide in which the equivalent refractive index of the core varies nonuniformly in the light propagation direction by changing the physical dimensions of the core. It is an object of the present invention to provide a method for designing an optical device that can alleviate the above.

In order to solve the above-described problems, the present invention provides a design of an optical device composed of an optical waveguide in which the equivalent refractive index of the core varies non-uniformly in the light propagation direction by changing the physical dimensions of the core embedded in the cladding. A first dimension derivation step of designing a physical dimension of a waveguide based on reflection spectrum data indicated by an optical device to be obtained, and obtaining a distribution of the physical dimension; calculated averaging section width of the light propagation direction on the basis of the distribution of the physical dimensions possess an averaging step of averaging for each of the interval width, wherein in the first dimension deriving step, the reflected spectrum data The potential function for realizing the reflection spectrum data is obtained by solving the Zakharov-Shabat equation as an inverse scattering problem that numerically derives the potential function from The average dimension width is 0.2 to 0.4 times the length of one wavelength at which the signal propagates in the waveguide at the central wavelength used in the device. Or (0.1 + 0.5j to 0.4 + 0.5j) times (where j is an integer of 1 or more) .
In the optical waveguide designed by the design method, the physical dimensions of the core are uniform within the range of the section width in the light propagation direction.

  Preferably, the physical dimension of the core is a core width, and the optical waveguide is a planar optical waveguide in which the core width is unevenly distributed in the light propagation direction.

  The Zakharov-Shabat equation is derived from a wave equation that introduces a variable of power wave amplitude propagating forward and backward of the optical waveguide, and has a potential function derived from a logarithmic derivative of the equivalent refractive index of the waveguide. The Shabat equation is preferred.

  According to the method for designing an optical device of the present invention, the requirement for manufacturing accuracy of the NPWG is eased, the change in the physical dimension of the core of the waveguide is reduced, and the manufacturing process can be facilitated.

Hereinafter, an embodiment of a design method of an NPWG device of the present invention will be described with reference to the drawings.
When designing an optical device composed of an optical waveguide in which the equivalent refractive index of the core varies nonuniformly in the light propagation direction by changing the physical dimensions of the core embedded in the cladding, The minimum dimensions to be designed are relaxed in consideration of limitations. In particular, when the equivalent refractive index of the core is due to a change in the core width, that is, a device using a non-uniform planar wave guide (NPWG) (hereinafter also referred to as “NPWG device”). The case is preferred. That is, the accuracy required for device fabrication was eased by making the width of the waveguide constant within a predetermined distance in the traveling direction of the waveguide.

  The design procedure is as follows. First, the device is designed by a normal method. Therefore, an averaging process is performed on the obtained width distribution, and the averaged portion has a uniform width.

<Structure of optical waveguide>
FIG. 1 is a schematic perspective view showing an embodiment of an optical waveguide which is a main component of a dispersion compensation device using an NPWG of this embodiment. The optical waveguide provided in the device of this embodiment is a planar waveguide having a non-uniform width obtained by changing the width w of the core in the longitudinal direction (z) as a means for changing the equivalent refractive index of the core non-uniformly in the light propagation direction. It is a waveguide (NPWG). In FIG. 1, reference numeral 10 is an NPWG, 11 is a core, and 12 is a cladding.

The NPWG 10 of this embodiment has a structure having a core 11 formed in a clad 12. The core 11 has a constant (fixed) height h ₃ , but its width w varies non-uniformly in the longitudinal direction (z direction), thereby changing the local equivalent refractive index of the propagation mode of the waveguide. Thus, a reflection type chromatic dispersion compensation function can be provided. The width distribution w (z) of the waveguide core can be determined by solving the inverse scattering problem for the desired reflection characteristics.

The operational principle of the NPWG 10 is similar to the FBG grating at first glance. However, the FBG changes the refractive index of the core medium by UV light irradiation or the like with respect to the change of the equivalent refractive index. In the NPWG 10, the equivalent refractive index is changed by changing the width of the core 11 along the longitudinal direction. Thus, the two are completely different with respect to changes in the equivalent refractive index.
The variation rate of the equivalent refractive index obtained by changing the width of the core 11 along the longitudinal direction is larger than that of the FBG, and fine and accurate control is easy. In addition, since the structure of the device is planar, it can be easily manufactured in large quantities by the manufacturing process.

  A material constituting the core 11 and the clad 12 is not particularly limited, such as a dielectric or a semiconductor. Specific examples include quartz-based materials, resin-based materials, and silicon-based materials. When a quartz material is used for the waveguide, for example, pure quartz may be used for the clad, and a quartz material to which germanium is added to increase the refractive index as the core may be used. Also, a resin material can be used. In addition, when a silicon-based material is used, for example, if a voltage application control is performed with an electrode attached, a variable device can be realized. Further, if the temperature of the device is controlled, the waveguide length becomes longer due to the thermal expansion of the material, so that the wavelength for performing desired chromatic dispersion compensation can be shifted to the longer wavelength side. By utilizing this characteristic, a variable device by controlling heat becomes possible (see Maekawa et al., Japanese Patent Application Laid-Open No. 2001-330741 (Japanese Patent Application No. 2000-147960)). Different types of materials (for example, one is quartz and the other is resin) may be used for the core 11 and the clad 12. Different materials may be used for the upper cladding and the lower cladding.

  Some NPWG dispersion compensators that have been proposed so far use a method in which a wavelength region to be compensated is divided into a plurality of channels and dispersion compensation is performed in each channel. By using this method, not only the required waveguide length is shortened and the device is reduced, but also the loss of the waveguide can be reduced.

<Device design method>
In designing an NPWG device, a method of an inverse scattering problem is used to obtain a necessary width distribution from a desired reflection spectrum. By using this method, there is an advantage that interference between channels that occurs in the method of superimposing FBGs (Patent Document 4) does not occur because it is considered in the design method. The waveguide obtained by the design used here has a structure different from that of Patent Document 4.

Next, an NPWG device design method using the inverse scattering problem method will be described.
First, the electromagnetic field propagating in the waveguide is formulated as follows (JE Shipe, L. Polarian, and C. Martijn de Starke, “Propagation through non-uniform forming structures”, J. Opt. Soc. Soc. A, 1994, Vol. 11, No. 4, pp. 1307-1320).

  Assuming that the time variation of the electromagnetic field is exp (−iωt), the following equations (1) and (2) are obtained according to the Maxwell equation.

Here, E and H represent the complex amplitudes of the electric field and the magnetic field, respectively, and n represents the refractive index of the waveguide. Here, the power wave amplitude A ₊ (z) propagating in front of z and the power wave amplitude A ₋ (z) propagating in the rear of z defined by the following formulas (3) and (4) are introduced.

However, Z ₀ = √ (μ ₀ / ε ₀ ) represents the impedance in vacuum, and n ₀ represents the reference refractive index. These variables satisfy the following expressions (5) and (6).

Here, c represents the speed of light in vacuum.
These equations (5) and (6) are reduced to the Zakharov-Shabat equation by the variable transformation represented by equation (7).

However, ω ₀ represents the reference angular frequency.
The Zakharov-Shabat equation obtained by the variable conversion is expressed by the following equations (8) and (9).

  The Zakharov-Shabat equation can be solved as an inverse scattering problem. First, the spectral data of the reflection coefficient is defined by the following formula (10).

Then, the potential function u (x) can be derived numerically from the spectral data of the reflection coefficient defined by the equation (10) (P. V. Francos and DL Jaggard, “A Numerical Solution to the Zakharov”. -See Shabat Inverse Scattering Problem ", IEEE Transactions on Antennas and Propagation, 1991, Vol. 39, No. 1, pp. 74-79). If this is applied to the above problem, a potential for realizing a desired reflection spectrum can be obtained.
Here, the reflection spectrum refers to complex reflection data obtained from the group delay amount and the reflectance with respect to the wavelength. Furthermore, non-uniform means that the physical dimension changes with the location of the waveguide in the traveling direction.
When an NPWG is designed for the purpose of chromatic dispersion compensation, this reflection spectrum is set so as to compensate the chromatic dispersion of an optical fiber having a predetermined length in a limited wavelength band. In this case, the necessary reflection characteristics can be set as appropriate. For example, in the wavelength band consisting of one or a plurality of channels where the center wavelength λ _c is 1280 nm ≦ λ _c ≦ 1320 nm or 1490 nm ≦ λ _c ≦ 1613 nm and the operating band ΔBW is 0.1 nm ≦ ΔBW ≦ 60 nm, the dispersion D of the optical waveguide There -3000ps / nm ≦ D ≦ 3000ps / nm, the ratio RDS dispersion slope for the dispersion is exemplified in the -0.1nm ^-1 ≦ RDS ≦ 0.1nm ^-1.

  If the potential u (x) is obtained, the local equivalent refractive index can be obtained by the following equation (11).

However, n (0) is the value of n (x) at x = 0.
Furthermore, the core width w (x) with respect to the variable x is obtained from the relationship with the equivalent refractive index to the core width, which is obtained from the core thickness, the core refractive index, and the cladding refractive index in the waveguide to be actually manufactured. Can be sought.

  In the present invention, the obtained width distribution is corrected by an averaging method as shown in FIG. That is, the original width distribution with respect to x in the figure is averaged within the range of a certain length Δx as shown in the following equation (12), and the width of the section is replaced with the average constant value.

However, w _a (x) represents an averaged width distribution in a section from x to x + Δx. w _a (x) takes a constant value within a section from x to x + Δx.
This Δx is determined according to the production accuracy that can be realized. That is, according to the first expression of Expression (7), Δx is expressed as the following Expression (13) using the section width Δz in the light propagation direction.

However, n _a (z) represents an average refractive index in a section defined by the following formula (14) from z to z + Δz.

Also, λ ₀ represents the guide wavelength at the center wavelength defined by the following formula (15).

Therefore, the section width Δx used for averaging can be determined based on the fabrication accuracy that can realize the width change interval Δz in the light propagation direction of the waveguide. It should be noted that n _a (z) / n ₀ can be regarded as approximately 1 as shown in the examples described later (particularly, refer to the graph of the normalized normalized refractive index distribution averaged). If it is constant, Δx can be regarded as substantially constant.

Δz is 0.2 to 0.4 times the length of one wavelength (inner tube wavelength) λ ₀ at which the signal propagates in the waveguide at the center wavelength used in the device, or (0.1 + 0.5j to 0.4 + 0) .5j) times (where j is an integer of 1 or more). For example, 0.2λ _{0 to} 0.4λ ₀ , 0.6λ _{0 to} 0.9λ ₀ , 1.1λ _{0 to} 1.4λ ₀ , and the like.
Further, when approximated as Δx≈Δz / λ ₀ from Expression (13), Δx is 0.2 to 0.4, or 0.1 + 0.5j to 0.4 + 0.5j (where j is an integer of 1 or more) ) Is preferably within the range. For example, 0.2 to 0.4, 0.6 to 0.9, 1.1 to 1.4, and the like.

<Dispersion compensation device>
NPWG10 is obtained by taking into consideration the wavelength, bandwidth and length of the compensated fiber, creating spectral data so as to be opposite to the fiber dispersion, solving the inverse problem using the above design method, and averaging. Can be designed. If the NPWG 10 is manufactured based on the design, a small and high-performance dispersion compensation device can be realized.

In the above embodiment, in the cladding 12, the height (thickness) is width h ₃ is constant is exemplified NPWG10 uneven varying core 11 is buried structure over the longitudinal direction, the light used in the present invention The waveguide is not limited to this example, and various modifications can be made.
For example, as shown in FIG. 1, the width distribution of the core 11 includes a structure in which the width of the core is non-uniformly distributed over the light propagation direction so that both sides of the width direction are symmetrical from the central axis. Alternatively, a structure in which both sides in the width direction are asymmetrically distributed in the light propagation direction so as to be asymmetrical may be used. Here, the asymmetric width distribution may be a case where one side in the width direction of the core is parallel to the central axis (that is, does not change non-uniformly) and the other side changes non-uniformly, or the width of the core It may be a case where both sides in the direction have different and nonuniform changes.
Further, as shown in FIG. 1, the core 11 may have a structure in which the center axis is provided in a meandering manner in addition to a structure in which the central axis is provided linearly along the longitudinal direction (z) of the NPWG 10. Thus, by providing a meandering core and having a structure in which the light propagation direction is alternately folded on the substrate, the NPWG 10 can be further downsized.

FIG. 3 is a configuration diagram illustrating an example of a usage pattern of the dispersion compensation device according to the present embodiment. The dispersion compensation device 20 includes the above-described NPWG 10 and a circulator 15 connected to the start end 13 side thereof, and a non-reflective terminal 16 is provided at the tip 14 of the NPWG 10. The circulator 15 is connected to a compensated optical fiber (not shown) on the input side (input), and an optical fiber on the downstream side is also connected to the output side (output), and is used in the optical transmission line. The NPWG 10 used in the dispersion compensation device 20 is a reflection type device, and an optical signal input to the input side of the circulator 15 from the compensated optical fiber enters the NPWG 10 and is reflected, and the reflected wave is output through the circulator 15. It has come to be.
The output of the reflected wave can be realized not only by the circulator 15 but also through directional coupling. Further, instead of attaching a non-reflective terminal 16 as a separate member to the tip 14 of the NPWG 10, the tip 14 of the NPWG 10 may be subjected to a non-reflective treatment.

  As described above, the NPWG 10 of the dispersion compensation device 20 has reflectivity characteristics that can compensate for the chromatic dispersion of the compensated optical fiber. Therefore, the optical signal output from the compensated optical fiber is reflected by the NPWG 10. In this case, the chromatic dispersion of the optical signal is corrected and output. The optical signal output from the dispersion compensation device 20 is input to the downstream optical fiber connected to the output side of the circulator 15 and propagates through the fiber.

The NPWG 10 that is a main component of the dispersion compensation device 20 of the present invention is manufactured, for example, as shown in the following (a) to (d).
(A) First, a lower cladding layer of the NPWG 10 is provided.
(B) Next, a core layer having a refractive index larger than that of the lower cladding layer is provided on the lower cladding layer.
(C) Next, the core layer 11 is processed by leaving a predetermined core shape designed so that the equivalent refractive index of the core varies nonuniformly in the light propagation direction, and removing the other portions. Form.
(D) Next, the cladding 12 covering the core 11 is provided, and the NPWG 10 is manufactured.

  In the dispersion compensation device 20 using the NPWG 10, after the NPWG 10 is manufactured as described above, the end 14 of the NPWG 10 is terminated with a non-reflection termination 16 or subjected to a non-reflection treatment. It can be manufactured by connecting a coupler.

  When the core 11 of the NPWG 10 is formed, the core 11 is formed by a photolithography method using a mask having a predetermined core shape designed so that the equivalent refractive index of the core 11 varies nonuniformly in the light propagation direction. It is preferable. The material and procedure used for this photolithography method can be implemented using the material and procedure used for the photolithography method well-known in the semiconductor manufacturing field etc. Moreover, the film-forming method of a clad layer or a core layer can be implemented using the well-known film-forming technique currently used in manufacture of a general optical waveguide.

Example 1
In the wavelength region [1570.01 nm, 1612.22 nm] (where [a, b] represents a closed section from a to b; the same applies hereinafter), the dispersion amount D = −236 ps / nm, the ratio of the dispersion slope to the dispersion A dispersion compensator was designed to realize chromatic dispersion such that RDS = 0.018 nm ⁻¹ . However, the wavelength region is divided into 50 channels where the frequency f satisfies (188.45 + 0.1n THz ≦ f ≦ 188.45 + 0.1n THz), and dispersion compensation is performed in each channel. Here, n represents an integer satisfying −25 ≦ n ≦ 24. These channels satisfy the ITU grid interval.

This dispersion compensator is an L-band dispersion-shifted fiber (DSF) having a length of 80 km (with a transmission loss of 0.02 dB / km, a dispersion at a wavelength of 1590 nm of 2.95 ps / nm / km, and a dispersion slope of The residual dispersion of the ratio (0.018 nm ⁻¹ ) can be compensated.

  FIG. 4 represents the potential when the averaging of the width distribution is not considered. The horizontal axis in the figure represents a location standardized at a center wavelength of 1590.83 nm. When this potential is used, the group delay shown in FIG. 5 and the reflectance shown in FIG. 6 are obtained. Both figures show the spectrum data (designed) used in the design and the obtained spectrum data (rearized).

When a waveguide structure is used in which a core having a height of h ₃ = 6 μm and a relative refractive index difference Δ = 0.6% is embedded in a clad made of quartz, FIG. 5 and FIG. The width distribution of the waveguide to be realized is shown in FIG. The distribution of the equivalent refractive index of the waveguide at that time is shown in FIG.

  The material for the core and cladding is not limited to quartz, but other materials such as silicon and polymer can also be used. If a material having a high refractive index is used, the device can be further reduced and the transmission loss can be reduced.

An enlarged view of a part of FIG. 8 is shown in FIG. However, the vertical axis is normalized by the central refractive index (reference refractive index n _{0 at the} central wavelength). This distribution cannot be realized due to the limitation of the minimum dimensions that can be realized in the fabrication process.
So, averaging the original distribution as Delta] z = 0.2? ₀ a minimum interval as shown in Figure 10. Here, λ ₀ represents an in-tube wavelength when a signal having a wavelength of 1590.83 nm passes through the waveguide.

Potential when the original distribution averaged as Delta] z = 0.2? ₀ is as shown in Figure 11. As shown in the figure, it is understood that the potential amplitude is reduced by averaging. As a result, the change in the width of the waveguide is reduced, and the waveguide becomes easier to make.

FIG. 12 shows the width distribution of the waveguide when a waveguide structure in which a core having a height of h ₃ = 6 μm and a relative refractive index difference Δ = 0.6% is embedded in a clad made of quartz is used. .
The group delay and reflectance at that time are shown in FIGS. 13 and 14, respectively. Both figures show the data used for the design (designed), the data before averaging (original), and the data after averaging (averaged). As shown in the figure, the shape of the group delay is preserved even when averaged, but only the reflectance is lowered.

  In order to confirm the effect of the dispersion compensator, the propagation characteristics of the 40 G / s NRZ signal shown in FIG. 15 were examined. FIG. 16 shows an eye pattern when the signal passes through the DSF of 80 km using a channel having a wavelength λ of 1590.41 nm ≦ λ ≦ 1591.26 nm. The eye pattern when the original dispersion compensator is used is shown in FIG.

Further, the eye pattern in the case of using the dispersion compensator averaged in Delta] z = 0.2? ₀ is shown in Figure 18. Compared to FIG. 17, the amplitude is small, but it can be seen that the effect of dispersion compensation can be maintained.

(Example 2)
In the original design in Example 1, except that the average of the original distribution as Δz = 0.3λ ₀ the minimum interval as shown in FIG. 19 in the same manner as in Example 1, designed dispersion compensator for L-band did.
Potential when the original distribution averaged as Δz = 0.3λ ₀ is as shown in Figure 20. As shown in the figure, it is understood that the potential amplitude is reduced by averaging. As a result, the change in the width of the waveguide is reduced, and the waveguide becomes easier to make.

FIG. 21 shows a waveguide width distribution when a waveguide structure in which a core having a height of h ₃ = 6 μm and a relative refractive index difference Δ = 0.6% is embedded in a clad made of quartz is used. .
The group delay and reflectance at that time are shown in FIGS. 22 and 23, respectively. As shown in the figure, the shape of the group delay is preserved even when averaged, but only the reflectance is lowered.
Further, the eye pattern in the case of using the dispersion compensator averaged with Δz = 0.3λ ₀ is shown in Figure 24. Compared to FIG. 17, the amplitude is small, but it can be seen that the effect of dispersion compensation can be maintained.

(Example 3)
In the original design in Example 1, except that the original distribution averaged as Δz = 0.4λ ₀ the minimum interval as shown in Figure 25 in the same manner as in Example 1, designed dispersion compensator for L-band did.
Potential when the original distribution averaged as Δz = 0.4λ ₀ is as shown in Figure 26. As shown in the figure, it is understood that the potential amplitude is reduced by averaging. As a result, the change in the width of the waveguide is reduced, and the waveguide becomes easier to make.

FIG. 27 shows the width distribution of the waveguide when a waveguide structure in which a core having a height of h ₃ = 6 μm and a relative refractive index difference Δ = 0.6% is embedded in a clad made of quartz is used. .
The group delay and reflectance at that time are shown in FIGS. 28 and 29, respectively. As shown in the figure, the shape of the group delay is preserved even when averaged, but only the reflectance is lowered.
Further, the eye pattern in the case of using the dispersion compensator averaged with Δz = 0.4λ ₀ is shown in Figure 30. Compared to FIG. 17, the amplitude is small, but it can be seen that the effect of dispersion compensation can be maintained.

Example 4
In the original design in Example 1, except that the average of the original distribution as Δz = 0.6λ ₀ the minimum interval as shown in Figure 31 in the same manner as in Example 1, designed dispersion compensator for L-band did.
Potential when the original distribution averaged as Δz = 0.6λ ₀ is as shown in Figure 32. As shown in the figure, it is understood that the potential amplitude is reduced by averaging. As a result, the change in the width of the waveguide is reduced, and the waveguide becomes easier to make.

FIG. 33 shows the width distribution of a waveguide when a waveguide structure in which a core having a height of h ₃ = 6 μm and a relative refractive index difference Δ = 0.6% is embedded in a cladding made of quartz is used. .
The group delay and reflectance at that time are shown in FIGS. 34 and 35, respectively. As shown in the figure, the shape of the group delay is preserved even when averaged, but only the reflectance is lowered.
Further, the eye pattern in the case of using the dispersion compensator averaged with Δz = 0.6λ ₀ is shown in Figure 36. Compared to FIG. 17, the amplitude is small, but it can be seen that the effect of dispersion compensation can be maintained.

(Example 5)
In the original design in the first embodiment, an L-band dispersion compensator is designed in the same manner as in the first embodiment except that the original distribution is averaged by setting the minimum interval to Δz = 0.9λ ₀ as shown in FIG. did.
Potential when the original distribution averaged as Δz = 0.9λ ₀ is as shown in Figure 38. As shown in the figure, it is understood that the potential amplitude is reduced by averaging. As a result, the change in the width of the waveguide is reduced, and the waveguide becomes easier to make.

FIG. 39 shows the width distribution of the waveguide when a waveguide structure in which a core having a height of h ₃ = 6 μm and a relative refractive index difference Δ = 0.6% is embedded in a cladding made of quartz is used. .
The group delay and reflectance at that time are shown in FIGS. 40 and 41, respectively. As shown in the figure, the shape of the group delay is preserved even when averaged, but only the reflectance is lowered.
Further, the eye pattern in the case of using the dispersion compensator averaged with Δz = 0.9λ ₀ is shown in Figure 42. Compared to FIG. 17, the amplitude is small, but it can be seen that the effect of dispersion compensation can be maintained.

( Comparative Example 1 )
In the original design in the first embodiment, an L-band dispersion compensator is designed in the same manner as in the first embodiment except that the original distribution is averaged by setting the minimum interval to Δz = 0.5λ ₀ as shown in FIG. did. In this case, the averaged equivalent refractive index distribution is almost constant, and fluctuations are almost eliminated. Its cause is hit to the period of the refractive index distribution of Delta] z = 0.5 [lambda ₀ is just source, averaging is in place and which has been offset the variation.
Potential when the original distribution averaged as Delta] z = 0.5 [lambda ₀ is as shown in Figure 44. As shown in the figure, it can be seen that the potential amplitude becomes very small by averaging.

FIG. 45 shows the width distribution of the waveguide when a waveguide structure in which the core having a height of h ₃ = 6 μm and a relative refractive index difference Δ = 0.6% is embedded in a clad made of quartz is used. . In that case, there is almost no fluctuation in the waveguide width, reflecting that the fluctuation in potential is too small.
Further, the reflectance at that time is shown in FIG. As shown in the figure, the reflectivity becomes very small and it does not operate as a dispersion compensator.
This phenomenon occurs when Δz is an integral multiple of 0.5λ _0.

(Example 6 )
In the wavelength region [1530.33 nm, 1570.42 nm], the dispersion compensator was designed so as to realize chromatic dispersion such that the dispersion amount D = −1700 ps / nm and the ratio of dispersion slope to dispersion RDS = 0.0036 nm ⁻¹ . However, the wavelength region is divided into 50 channels satisfying the frequency f (193.4 + 0.1n THz ≦ f ≦ 193.5 + 0.1n THz), and dispersion compensation is performed in each channel. Here, n represents an integer satisfying −25 ≦ n ≦ 24. These channels satisfy the ITU grid interval.

This dispersion compensator is a C-band standard single-mode fiber (S-SMF) with a length of 100 km (transmission loss is 0.02 dB / km, dispersion at a wavelength of 1550 nm is 17 ps / nm / km, It is possible to compensate for the residual dispersion of the dispersion slope ratio of 0.0034 nm ⁻¹ .

  FIG. 47 shows the potential when the averaging of the width distribution is not considered. The horizontal axis in the figure represents a location standardized at a center wavelength of 1550.12 nm. When this potential is used, the group delay shown in FIG. 48 and the reflectance shown in FIG. 49 are obtained. Both figures show the spectrum data (designed) used in the design and the obtained spectrum data (rearized).

When a waveguide having a height h ₃ = 6 μm and a core having a relative refractive index difference Δ = 0.6% is embedded in a clad made of quartz, FIGS. 48 and 49 are used. The width distribution of the waveguide to be realized is shown in FIG. The distribution of the equivalent refractive index of the waveguide at that time is shown in FIG.

FIG. 52 shows an enlarged part of FIG. However, the vertical axis is normalized by the central refractive index (reference refractive index n _{0 at the} central wavelength). This distribution cannot be realized due to the limitation of the minimum dimensions that can be realized in the fabrication process.
So, averaging the original distribution as Δz = 0.3λ ₀ the minimum interval as shown in Figure 53. Here, λ ₀ represents an in-tube wavelength when a signal having a wavelength of 1550.12 nm passes through the waveguide.

Potential when the original distribution averaged as Δz = 0.3λ ₀ is as shown in Figure 54. As shown in the figure, it is understood that the potential amplitude is reduced by averaging. As a result, the change in the width of the waveguide is reduced, and the waveguide becomes easier to make.

FIG. 55 shows the width distribution of the waveguide when a waveguide structure in which a core having a height of h ₃ = 6 μm and a relative refractive index difference Δ = 0.6% is embedded in a clad made of quartz is used. .
The group delay and reflectance at that time are shown in FIGS. 56 and 57, respectively. As shown in the figure, the shape of the group delay is preserved even when averaged, but only the reflectance is lowered.

  In order to confirm the effect of the dispersion compensator, the propagation characteristics of the 10 G / s NRZ signal shown in FIG. 58 were examined. FIG. 59 shows an eye pattern when this signal passes through the S-SMF of 100 km using a channel having a wavelength λ of 1533.47 nm ≦ λ ≦ 153.25 nm. The eye pattern when the original dispersion compensator is used is shown in FIG.

Further, the eye pattern in the case of using the dispersion compensator averaged with Δz = 0.3λ ₀ is shown in Figure 61. Compared to FIG. 60, the amplitude is small, but it can be seen that the effect of dispersion compensation can be maintained.

It is a schematic perspective view which shows an example of the structure of a non-uniform planar optical waveguide (NPWG). It is a graph explaining the averaging method for correction of width distribution. It is a block diagram which shows one Embodiment of a dispersion compensation device. 3 is a graph showing an original potential distribution of Example 1. 3 is a graph showing original group delay characteristics of Example 1. 4 is a graph showing original reflectance characteristics of Example 1. 6 is a graph showing the width distribution of the original waveguide of Example 1. 6 is a graph showing the distribution of the original equivalent refractive index of Example 1. It is a graph which shows the partial expansion of FIG. Is a graph showing the averaged normalized equivalent refractive index distribution in Delta] z = 0.2? ₀ of Example 1 (part). Is a graph showing a potential distribution (part) when averaged over Delta] z = 0.2? ₀ of Example 1. Is a graph showing the width distribution of the waveguide when averaged over Delta] z = 0.2? ₀ of Example 1. Is a graph showing the group delay characteristics (part) when averaged over Delta] z = 0.2? ₀ of Example 1. Is a graph showing reflectance characteristics (a part) in the case of averaging by Delta] z = 0.2? ₀ of Example 1. It is a graph which shows the eye pattern of NRZ initial stage pulse of 40 G / s. It is a graph which shows the eye pattern of 40 G / s pulse after passing 80 km DSF. It is a graph which shows the eye pattern of 40 G / s pulse after passing an original compensator. It is a graph which shows the eye pattern of 40 G / s pulse after passing through the compensator averaged by (DELTA) z = 0.2 (lambda) ₀ of Example 1. FIG. It is a graph showing the averaged normalized equivalent refractive index distribution in Δz = 0.3λ ₀ Example 2 (part). It is a graph showing a potential distribution (part) when averaged over Δz = 0.3λ ₀ Example 2. Is a graph showing the width distribution of the waveguide when averaged over Δz = 0.3λ ₀ Example 2. It is a graph showing the group delay characteristics (part) when averaged over Δz = 0.3λ ₀ Example 2. It is a graph showing reflectance characteristics (a part) in the case of averaging by Δz = 0.3λ ₀ Example 2. It is a graph which shows the eye pattern of 40 G / s pulse after passing through the compensator averaged by (DELTA) z = 0.3 (lambda) ₀ of Example 2. FIG. It is a graph showing the averaged normalized equivalent refractive index distribution in Δz = 0.4λ ₀ Example 3 (part). It is a graph showing a potential distribution (part) when averaged over Δz = 0.4λ ₀ Example 3. Is a graph showing the width distribution of the waveguide when averaged over Δz = 0.4λ ₀ Example 3. It is a graph showing the group delay characteristics (part) when averaged over Δz = 0.4λ ₀ Example 3. It is a graph showing reflectance characteristics (a part) in the case of averaging by Δz = 0.4λ ₀ Example 3. It is a graph which shows the eye pattern of the 40 G / s pulse after passing the compensator averaged by (DELTA) z = 0.4 (lambda) ₀ of Example 3. FIG. It is a graph showing the averaged normalized equivalent refractive index distribution in Δz = 0.6λ ₀ Example 4 (part). It is a graph which shows potential distribution (a part) at the time of averaging by (DELTA) z = 0.6 (lambda) ₀ of Example 4. FIG. Is a graph showing the width distribution of the waveguide when averaged over Δz = 0.6λ ₀ Example 4. It is a graph showing the group delay characteristics (part) when averaged over Δz = 0.6λ ₀ Example 4. It is a graph which shows the reflectance characteristic (partial) at the time of averaging by (DELTA) z = 0.6 (lambda) ₀ of Example 4. FIG. It is a graph which shows the eye pattern of 40 G / s pulse after passing the compensator averaged by (DELTA) z = 0.6 (lambda) ₀ of Example 4. FIG. It is a graph showing the averaged normalized equivalent refractive index distribution in Δz = 0.9λ ₀ Example 5 (part). It is a graph showing a potential distribution (part) when averaged over Δz = 0.9λ ₀ Example 5. Is a graph showing the width distribution of the waveguide when averaged over Δz = 0.9λ ₀ Example 5. It is a graph showing the group delay characteristics (part) when averaged over Δz = 0.9λ ₀ Example 5. It is a graph showing reflectance characteristics (a part) in the case of averaging by Δz = 0.9λ ₀ Example 5. It is a graph which shows the eye pattern of 40 G / s pulse after passing through the compensator averaged by (DELTA) z = 0.9 (lambda) ₀ of Example 5. FIG. It averaged normalized equivalent refractive index distribution in Delta] z = 0.5 [lambda ₀ of Comparative Example 1 is a graph showing (a part). Potential distribution when averaged over Delta] z = 0.5 [lambda ₀ of Comparative Example 1 is a graph showing (a part). Is a graph showing the width distribution of the waveguide when averaged over Delta] z = 0.5 [lambda ₀ of Comparative Example 1. Reflectance characteristic when averaged over Delta] z = 0.5 [lambda ₀ of Comparative Example 1 is a graph showing (a part). 10 is a graph showing an original potential distribution of Example 6 . 10 is a graph showing original group delay characteristics of Example 6 . 10 is a graph showing original reflectance characteristics of Example 6 . 10 is a graph showing the width distribution of the original waveguide of Example 6 . 10 is a graph showing an original equivalent refractive index distribution of Example 6 . It is a graph which shows the partial expansion of FIG. It is a graph showing the averaged normalized equivalent refractive index distribution in Δz = 0.3λ ₀ Example 6 (part). It is a graph which shows potential distribution (a part) at the time of averaging by (DELTA) z = 0.3 (lambda) ₀ of Example 6. FIG. It is a graph which shows the width distribution of the waveguide at the time of averaging by (DELTA) z = 0.3 (lambda) ₀ of Example 6. FIG. It is a graph showing the group delay characteristics (part) when averaged over Δz = 0.3λ ₀ Example 6. It is a graph which shows the reflectance characteristic at the time of averaging by (DELTA) z = 0.3 (lambda) ₀ of Example 6. FIG. It is a graph which shows the eye pattern of a NRZ initial pulse of 10 G / s. It is a graph which shows the eye pattern of a 10 G / s pulse after passing S-SMF of 100 km. It is a graph which shows the eye pattern of 10 G / s pulse after passing an original compensator. It is a graph which shows the eye pattern of 10 G / s pulse after passing through the compensator averaged by (DELTA) z = 0.3 (lambda) ₀ of Example 6. FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 ... NPWG (non-uniform planar waveguide), 11 ... core, 12 ... cladding, 13 ... start end, 14 ... tip, 15 ... circulator, 16 ... non-reflection end, 20 ... dispersion compensation device.

Claims (4)

An optical device design method comprising an optical waveguide in which the equivalent refractive index of the core varies nonuniformly in the light propagation direction by changing the physical dimensions of the core embedded in the cladding,
Designing a physical dimension of a waveguide based on reflection spectrum data indicated by an optical device to be obtained, and obtaining a distribution of the physical dimension;
An average step of obtaining an average section width in the light propagation direction based on the fabrication accuracy of the waveguide, and averaging the distribution of the physical dimensions for each section width;
I have a,
In the first dimension deriving step, by solving a Zakharov-Shabat equation as an inverse scattering problem that numerically derives a potential function from the reflection spectrum data, a design method for obtaining a potential function for realizing the reflection spectrum data is used. Obtaining a distribution of the physical dimensions;
The averaging interval width is 0.2 to 0.4 times the length of one wavelength at which the signal propagates in the waveguide at the center wavelength used in the device, or (0.1 + 0.5j to 0.4 + 0.5j). ) A method for designing an optical device, wherein j is in a range (where j is an integer of 1 or more) .   The optical device design method according to claim 1, wherein the optical waveguide designed by the design method has a uniform physical dimension of the core within a range of a section width in the light propagation direction. 3. The light according to claim 1, wherein the physical dimension of the core is a width of the core, and the optical waveguide is a planar optical waveguide in which the width of the core is unevenly distributed in the light propagation direction. How to design the device. The Zakharov-Shabat equation is derived from a wave equation that introduces a variable of power wave amplitude propagating forward and backward of the optical waveguide, and has a potential function derived from a logarithmic derivative of the equivalent refractive index of the waveguide. The optical device design method according to claim 1, wherein the method is a Shabat equation.

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