WO2002030014A1

WO2002030014A1 - Method of characterising optical amplifiers

Info

Publication number: WO2002030014A1
Application number: PCT/EP2001/011423
Authority: WO
Inventors: Evgeny Vanin; Gunnar Jacobsen; Ulf Persson
Original assignee: Telefonaktiebolaget L.M. Ericsson
Priority date: 2000-10-02
Filing date: 2001-10-02
Publication date: 2002-04-11
Also published as: AU2002223583A1

Abstract

The invention concerns a method of determining the spectral characteristics of optical amplifiers. Two methods are proposed for determining the spectral gain and the ASE spectral power density of an amplifier. Each method uses two spectral functions T(μ, μref), R(μ, μref) and TASE (μ, μref), RASE (μ, μref), respectively. The spectral functions are determined by calculation using two measured spectra of gain and ASE output power density, respectively, made at at least two different saturation states of an amplifier. The functions are independent of the operating conditions of the amplifier. This allows deviations in the calculated functions to be immediately identified and further enables the optimal area of application of the model to be located. A more accurate model of spectral gain includes a further function which takes account of the gain difference caused by spectral hole burning.

Description

Method of characterising optical amplifiers

Field of invention The invention relates to a method of characterising optical amplifiers, particularly active fibre and planar optical amplifiers.

Background art

Optical amplifiers are essential components of optical transmission systems. They provide efficient amplification of transmitted optical signals and are thus able to compensate for optical fibre losses over a broad wavelength range.

A good knowledge of the characteristics of optical amplifiers is important for the design of optical transmission systems. Ideally both the spectral gain and the noise figure of an optical amplifier should be known. These indicate the degree of amplification an optical signal at a certain wavelength will undergo and also how much noise, generally in the form of amplified spontaneous emission (ASE), will be added to a signal at the amplifier output, respectively. Such information is generally not available from manufacturers of amplifiers. When the amplifier is operated at specific set conditions, that is, with constant pumping power and a spectrally constant input signal, these characteristics can be measured using the input and output signals relatively easily. However, it is more complex to predict the spectral gain and noise figure of an amplifier operating at different conditions, for example with different values of pumping power and with input signals having different spectral content. This general information is nevertheless necessary and often invaluable for many applications, wavelength division multiplexed (WDM) transmission systems being just one of these.

Attempts have been made to present a model for optical fibre amplifiers. One method used to determine amplifier gain is described in a paper by D. Bonnedal "EDFA gain described with a black box model" presented at the Optical Amplifiers and Their Applications Topical Meeting (OA&A) in Montery, California, July 11-13, 1996 and published in the OS A publication 'Trends in Optics and Photonics Series', volume on OA&A, October 1996.

This paper describes a method of determining the spectral gain of a fibre amplifier by interpolation from two measured gain spectra. This model is developed further in G. Jacobsen et al. "Pump power dependent black box EDFA model" , Journal of Optical communications 21 (2000) 675. This reference extends the model to include a dependence of the modelled spectral gain on pump power. The predicted gain values are still determined from two measured reference spectra. In addition, this reference proposes a model for the prediction of the noise figure which is likewise derived by interpolation of two measured noise figure curves.

In both proposed methods the reference curves must be properly selected if the resulting derived gain and noise figures are to be accurate. However, there is no mechanism within the disclosed model for correctly selecting the curves. Moreover, if the selected reference curves can not provide an accurate model, there is no way of deteraύning this from the resulting values, nor is there any means of determining under which conditions the model is accurate for any particular amplifier type. The method proposed in the second paper for deriving the spectral noise figure is based on an empirical method and is very inaccurate.

A further model is proposed in "A black box model of EDFA's operating in WDM systems" , J Burgmeier et al., Jounal of Lightwave Technology, Vol. 16, No. 7,

July 1998. This paper discloses an analytical solution for characterising the effective spectral gain of compound optical fibre amplifiers. The described solution proposes a function Tλ_ref(λ), called the dynamic gain tilt function, which is defined in terms of two measured spectral gain characteristics.

While the dynamic tilt function goes some way towards characterising the amplifier spectral gain, a full accurate analytical model of the spectral gain is not suggested. Moreover, this reference makes no attempt to characterise the noise of an optical amplifier.

The above references start from the assumption that an optical amplifier is homogeneously broadened, i.e. that the same spectral gain profile can be obtained at different input signal powers and wavelengths when the amplifier is operated at fixed average population inversion. In practice, however, spectral gain manifests variations at and around an input signal wavelength due to inhomogeneous broadening. The resulting gain 'dip' in the location of a saturation input wavelength is known as spectral hole burning (SFIB). While the effect of spectral hole burning is small and for many applications negligible for single optical amplifiers, when amplifiers are used for WDM transmission or are cascaded the influence of spectral hole burning on gain is noticeable. The effect of spectral hole burning has also been the subject of literature. However, a model that can be used to characterise a closed amplifier package without knowledge of the exact composition or properties of the package is not available.

In the light of the prior art, it is an object of the present invention to propose a model for the spectral characteristics of an optical amplifier, which enables an amplifier to be accurately characterised on the basis of measured values.

SUMMARY OF INVENTION In accordance with a first aspect of the invention there is proposed a method of determining the spectral gain of an optical amplifier. The method includes using two spectral gain functions T(λ, λ_ref) and R(λ, λ_ref), which are each expressed in terms of at least two reference gain spectra measured in dB at different saturation states of the amplifier and a reference wavelength λ_ref. In addition to these two spectral gain functions, the saturated gain of the amplifier measured in dB at the reference wavelength G(λ_ref) is required. The spectral gain in dB is then fully characterised by the following expression: G (λ) = T(λ, λ_ref) ^• G (λ_ref) + R(λ A_ef).

This., method may be modified to obtain a more accurate model of spectral gain that takes account of the effect of spectral hole burning by adjusting the gain at any wavelength by a quantity U_SHB(λ) that represents the reduction in gain due to additional saturation around the input signal wavelength. In accordance with the present invention, this adjustment quantity, U_SHBM, may be deduced by determining the difference in gain at any wavelength when applying a saturating input signal at the wavelength and not applying a saturating input signal with the amplifier operated under the same saturation conditions.

In this modified method the spectral gain functions T(λ, λ_ref) and R(λ, λ_ref) are independent of spectral hole burning. These functions are preferably achieved by measuring at least one of the reference gain spectra applying saturating input signals at at least two different wavelengths and measuring spectral gain to obtain data representing two measurement curves. For each curve gain measurements are then extracted at areas not in the vicinity of the input signal wavelength to obtain data representing a single spectral gain curve. This composed spectral curve will not manifest the effects of spectral hole burning.

Preferably the quantity U_SHBW is calculated as a function of the gain compression of the optical amplifier for each wavelength. Gain compression is the absolute gain difference that occurs when the input signal, or channel wavelength for a WDM signal, is added or dropped under fixed pumping conditions.

With this method, the spectral gain of an amplifier can be described completely. When the spectral gain is characterised without taking account of spectral hole burning, the characterisation model is valid for all operation conditions of the characterised amplifier. When the additional adjustment term U_SHBW for spectral hole burning is used to determine spectral gain, an amplifier should be characterised for all input signal powers and wavelengths, as spectral gain will then be dependent on both input signal power and wavelength.

In accordance with a further aspect of the invention there is proposed a method of determining the amplified spontaneous emission (ASE) spectral output power density of an optical amplifier. This method includes using two spectral noise functions T_ASE ( ef) and R_AS_E (λ, λ_ref), both of which are expressed in terms of two reference amplifier output power density spectra in dB measured at different saturation states of the amplifier and a reference wavelength λ_ref . The method further requires the determination of measured ASE output power density of the saturated amplifier in dB at the reference wavelength S_AsE(λ_ref)- Using the two functions and the measured ASE power density in dB, the ASE output power density S_ASE (λ) in dB at any wavelength λ is calculated according to the expression: S_ASE (λ) = T_ASE (λ, λ_ref) ^•

SASE(λref) ⁺ ASE(λ,λ_ref).

This method allows the ASE spectral power density of an amplifier to be completely described.

The two spectral gain and ASE power density functions are determined by calculation using two measured spectra of gain and ASE output power density, respectively, made at two different saturation states of an amplifier. Moreover, one of the spectral gain functions is identical to the spectral ASE power density functions, so only three calculations are required to determine both the spectral gain and ASE spectral power density. The functions are independent of the operating conditions of the amplifier. This allows deviations in the calculated functions to be immediately identified and further enables the optimal area of application of the model to be located.

Using both expressions, the noise figure of the amplifier may also be calculated. Thus complete spectral amplifier characteristics are obtainable simply by measurement of signal powers at the input and output of the amplifier to determine three spectral functions. Moreover, other components that are contained in the amplifier module, such as isolators, filters, couplers and the like are likewise described by the model.

Advantageously, the above described model for spectral gain may be used in an algorithm to effect automatic gain control of an optical fibre amplifier used in a WDM system. To this end there is proposed an automatic gain control arrangement for an optical fibre amplifier arranged to receive multiple wavelength division multiplexed channels, including an input signal monitor arranged to monitor said channels, a gain flattening filter arranged to modify the output of the optical amplifier and a control unit for controlling the pump power to the amplifier and the filter. The control unit determines the spectral gain using the above described model on the basis of information from said monitor.

In accordance with a still further aspect of the present invention there is proposed a method of determining the spectral gain of an optical fibre amplifier that receives an input signal of known spectral power density.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects and advantages of the present invention will become apparent from the following description of the preferred embodiments that are given by way of example with reference to the accompanying drawings. In the figures:

Fig. 1 schematically illustrates an optical fibre amplifier;

Fig.2 shows a spectral gain function T(λ) calculated from experimental measurements for a first amplifier type;

Fig.3 shows a spectral gain function R(λ) calculated from experimental measurements for the first amplifier type;

Fig.4 shows a spectral noise function T_Asε(λ) calculated from experimental measurements for the first amplifier type;

Fig.5 shows a spectral noise function R_Asε(λ) calculated from experimental measurements for the first amplifier type;

Fig.6 shows a spectral gain function T(λ) calculated from experimental measurements for a second amplifier type;

Fig.7 shows a spectral gain function R(λ) calculated from experimental measurements for the second amplifier type;

Fig.8 shows a spectral noise function T_ASE(λ) calculated from experimental measurements for the second amplifier type;

Fig.9 shows a spectral noise function R_Asε(λ) calculated from experimental measurements for the second amplifier type; Fig.10 schematically illustrates an arrangement in an optical transmission system for controlling amplifier output power;

Fig. 11 shows a plot of spectral gain of an EDFA measured under different saturation conditions;

Fig. 12 shows a plot of spectral gain difference due to spectral hole burning;

Fig. 13 shows a plot of spectral gain difference due to spectral hole burning at different input signal powers;

Fig. 14 shows a plot illustrating the relationship between gain compression and both spectral hole depth and width; and

Fig. 15 schematically illustrates an arrangement for automatic gain control of an optical fibre amplifier.

DETAILED DESCRIPTION OF THE DRAWINGS Fig. 1 shows a schematic of a simple optical fibre amplifier. This amplifier includes a doped fibre 10, which typically consists of a glass fibre doped with rare earth ions. In the exemplary embodiment this fibre is doped with Erbium ions Er³⁺, and the whole is commonly referred to as an erbium doped fibre amplifier or EDFA. The doped or active fibre 10 is coupled to an input optical fibre 20 via an optical coupler 30. An optical signal source connected to the input fibre 20 provides the optical input signal to the amplifier. A source of optical pumping power 50 , which controls the gain of the amplifier is also connected to the active fibre 10 either via the same coupler 30, or via a separate non-illustrated coupler. The pumping source 50 includes a pumping laser driven with a suitable drive current. This drive current determines the power of the optical pumping signal fed to the active fibre 10. It will be appreciated that an amplifier may have several pumps, with the power or gain control of the amplifier being controlled by varying one or more of the pump lasers.

As shown in Fig. 1, an optical signal monitor 60 may also be provided to monitor the output signal power of the amplifier. This monitor is connected to an optical coupler 70 that extracts a defined proportion of the signal power from the active fibre output. This monitor 60 may include an opto-electric converter such as a photodetector, phototransistor or the like, and a suitably arranged current or voltage measuring device.

Other components may also be arranged in the amplifier circuit, such as filters, isolators and the like.

Throughout this document capital letters are used to designate quantities expressed in dB while the corresponding small case letters designate the same quantity expressed in linearly. Thus for example G is gain expressed in dB, while g is gain expressed in linear units. Similarly, S_Asε(λ) is used to designate the ASE spectral power density in dB while s_Asε(λ) is the ASE spectral power density in W/nm.

In accordance with a first embodiment of the present invention, a model is proposed that characterises the spectral gain of an active fibre amplifier. This model assumes that the amplifier is homogeneously broadened, i.e. that the gain of the amplifier is determined by the average distribution of the population inversion, which is maintained in the active fibre by a balance between resonance optical pumping and deactivation of rare-earth ions by laser emission. In this model, the spectral gain of an active fibre amplifier G expressed in dB at any wavelength λ, is characterised by the following equation, termed equation 1 :

G (λ) = T(λ, λ_ref) ^• G (λ_ref) + R(λ,λ_ref), (Equ. 1)

Where G (λ_ref) is the gain of the saturated amplifier in dB measured at a reference wavelength λ_ref. This reference wavelength λ_ref is preferably an input wavelength that differs from the input saturating wavelength. In this equation, two spectral gain functions T(λ,λ_ref) and R(λ,λ_ref) characterise a specific amplifier and are independent of the operating conditions of the amplifier. In other words the functions T(λ, λ_ref) and R(λ,λ_ref) are constant for different optical input signal and pumping powers. Thus when the spectral gain functions T(λ, λ_reI) and R(λ,λ_ref) are known, the spectral gain G(λ) of the amplifier for all operating conditions can be fully characterised using a measurement of gain at the reference wavelength G (λ_ref).

The gain functions T(λ, λ_ref) and R(λ,λ_ref) are defined in terms of the amplifier gain at the reference wavelength λ_ref as follows:

G_A(λ) ~G_B(λ)

T(λ,λ_ref) = Equ. 1.1

^G _A(λ_ref) -G_A(λ_ref)

and

G_A(λ_ref) - G_B(λ) - G_A (λ) - G_B(λ_ref) 2(A,^L,._e ) — G_A(λ_ref) -G_B(λ_ref) Equ. 1.2

where the two subscripts A and B to the gain G denote different saturation states of the amplifier. These two saturation states represent different average population inversion states of the amplifier. The saturation state of an amplifier is determined by the optical pumping and input signal powers to the amplifier. Thus G_A(λ) is the gain in dB measured at wavelength λ at the saturation state A defined by a first optical pump and saturating input signal power, while G_B(λ_ref) is the gain in dB measured at wavelength λ at the saturation state B defined by a second optical pump and saturating input signal wavelength power. These spectral functions can thus be calculated using the above expressions from two measured reference spectral gain curves for the two saturation states A and B. Preferably the two saturation states are selected such that the resulting spectral curves are sufficiently different to provide a usable value. It is apparent from the expression defining the functional form T(λ, λ_ref) that choosing saturation states G_A and G_B that are too close together will result in both a very small denominator and numerator which is likely to increase the proportion of error in the solution. Preferably the reference curves are measured in the limiting amplifier operation ranges. For example one curve could be the result of the amplifier operating close to the highest pump power and the lowest input signal power and the other being operated close to the lowest pump power and the highest input signal power. Alternatively, one curve may be measured close to the optimum gain conditions, that is under conditions at which the spectral gain curve is optimally flat. As mentioned before, the reference wavelength λ_ref is preferably not the saturating wavelength.

Similarly, the ASE spectral power density S_ASE(λ) expressed in dB generated in a homogeneously-broadened amplifier is defined as

^_ASE (λ) = T_ASE (λ, λ_κf ) ^• S_ASB (λ_ref ) + R_ASE (λ, λ_κf ), Equ. 2

Where S_ASE(λ_ref) is the ASE spectral power density expressed in dB at a reference wavelength λ_ref. This equation likewise uses two functions to characterise the amplifier, which are defined as spectral noise functions, T_Asε(λ, λ_ref) and R_Asε(λ, λ_ref). In a similar manner to the spectral gain functions these functions are defined as follows:

EqU. 2.2

The values S_ASEA(λ) and S_ASEβ(λ) are the ASE power density values expressed in dB measured at the output of the amplifier at a wavelength λ for two different saturation conditions A and B of the amplifier. As for the spectral gain functions T(λ, λ_ref) and R(λ,λ_ref) the different saturation states of the amplifier should be chosen such that the curves obtained after measuring S_AsEA(λ) and S_ASEβ(λ) at various wavelengths are sufficiently different to provide usable values for calculation of the spectral noise functional forms.

The spectral noise function T_ASE(λ,λ_ref) is actually identical to the spectral gain function T(λ, λ_ref) given in equation 1.1 above, thus

The spectral noise figure of the amplifier is defined by the equation

^EC1^U- ³

where h denotes Planck's constant and c the free space velocity of light. It should be noted that the spectral gain g(λ) is not in dB in this equation. Likewise the ASE spectral power density s_Asε(λ) is expressed in W/nm rather than dB. The relationship between the ASE spectral power density expressed in dB and that expressed in W/nm is defined by the following relationship:

S_ASE (λ) = \0\og(λ's_ASE(λ)lhc²) Equ. 4

From the above equations it is apparent that the spectral gain of an amplifier can be determined using two gain functions T(λ, λ_ref) and R(λ,λ_ref), while the spectral noise figure can be obtained using an additional spectral noise function R_As_E(λ, _ref), since the spectral noise function T_ASE(λ,λ_ref) is equivalent to the gain function T(λ, λ_ref).

It will be understood that complete characterisation of the spectral characteristics of an optical fibre amplifier require the relationship between gain at a reference wavelength G(λ_ref) for different input, i.e. saturating, wavelengths. The same is true for the ASE spectral power density S_ASE(λ_ref). However, this measurement is well known in the art and will not be described here.

As mentioned above, the analytical model described above assumes that the optical fibre amplifier is a homogeneously-broadened system. This implies that the saturation of the amplifier is determined entirely by the number of pump and input signal photons injected into the active fibre, and thus is independent on the wavelength of the saturating signals. This is a fairly accurate assumption particularly for EDFAs at least over the typically used C- band of wavelengths between about 1530nm to 1570nm. However, with the above model it is possible to identify under what conditions an amplifier is not homogeneously broadened, and, if necessary, to compensate for this behaviour. This is illustrated in the examples shown in Figs. 2 to 9.

Figs. 2 to 5 show the spectral gain functions T(λ) and R(λ) and the spectral noise functions T_ASε(λ) and R_Asε(λ) calculated for a single pumped EDFA.

The functions are calculated using measured data on the spectral gain and ASE spectral power density.

The measurements were made in a standard way using a probe input signal at a tuneable wavelength λ of known, low power relative to the signal power λ_s.

The gain was measured by filtering the extracted output signal to obtain the desired probe wavelength output power. The ASE spectral power density was measured at the output of the amplifier using a spectrum analyser. Each of the Figs. 2 to 5 shows a graph made up of 25 curves. Figs. 2 and 3 illustrate the spectral gain functions T(λ) and R(λ),. Respectively while Figs. 4 and 5 show the ASE spectral power density functions T_Asε(λ) and R_Asε(λ). Each of these curves is calculated from gain measurements in dB or power density measurements in W/nm subsequently converted to dB, respectively, taken at five different pumping laser diode currents, namely 48mA, 68mA, 97mA, 144mA and 220mA, and two sets of five different input signal powers with a signal wavelength λ_s (i.e. saturating wavelength) of 1550nm, for each saturation state A and B of the amplifier. In other words, measurements were taken over the wavelength band of interest for each of the five pumping laser diode currents at signal powers of 0.04dBm and -5.96dBm, 0.04dBm and -11.96dBm, 0.04dBm and -17.96dBm, 0.04dBm and -23.96dBm and finally for -5.96dBm and -11.96dBm.

It is apparent from the curves of the T and R functions in Figs. 2 to 5 that the calculated curves deviate from one another very little around the wavelength range between about 1535nm to 1570nm. This verifies the fact that the amplifier is a homogeneously broadened system at least in this wavelength band. It further shows the repeatability of the results. It should be noted that if the measured curves representing two different saturation states A and B of the amplifier were two close to one another resulting in an incorrect T or R curve, this would be immediately apparent when the calculated curves are compared to curves based on different measured reference spectra.

Figs. 6 to 9 show similar curves for the spectral gain Tand R functions as well as the spectral noise T_ASE and R_ASE functions calculated for a different amplifier. This amplifier has a built-in optical filter for reducing the ASE noise at around 1530nm. The spectral gain and noise functions of Figs. 2 to 5 and 6 to 9 differ from one another as is expected, since these functions are dependent on the amplifier type. Moreover, it is apparent that at least within the wavelength range of about 1535nm to 1570nm these spectral functions are independent of the amplifier operating conditions. Furthermore, when comparing the spectral gain and noise function curves in Figs. 2 and 4 and those of Figs. 6 and 8, that these functions are substantially the same for each amplifier. Moreover, the T-functions of both amplifiers are also substantially the same. This indicates that the amplifiers are fabricated from the same type of active fibre, since the T-function depends on the mode confinement factor and the cross-sections of resonance laser transitions, which will be the same for identical fibre types. The R-functions shown in Figs. 3, 5, 7 and 9 additionally depend on the length of the fibre and on the ASE filter characteristics. Any other components contained in the amplifier, such as isolators, couplers and the like, will affect the R-functions for a particular amplifier type.

It is apparent from the results shown in Figs. 2 to 9 that the proposed characterisation method is valid for EDFA's operating in the C-band, that is in the range of 1530nm to 1570nm. However, this model is also valid for other rare earth doped fibre amplifiers, including, but not limited to, Thulium doped fibre amplifiers, Erbium- Ytterbium doped fibre amplifiers, Praseodymium doped fibre amplifiers and Neodymium doped fibre amplifiers. The proposed characterisation method may also be valid for broader or even different wavelength ranges. For example, Thulium doped fibre amplifiers are particularly suitable for operation in the S-band communication window, that is wavelengths of between 1450nm to 1530nm, which would allow the use of the method over this range. Furthermore, the types of glass used to fabricate optical fibre amplifiers influences the operating wavelength range of the fibre amplifier and also affects other technical characteristics, such as the optimum pumping wavelength, efficiency, and the like. The tested Erbium doped fibre amplifiers are silica-based fibres. The proposed method could, however, be usefully applied to amplifiers made of other glass materials, such as fluoride, telluride, or the like.

Another class of amplifiers to which the characterisation method can be validly applied are the optical planar-glass-amplifiers, which are also termed waveguide optical amplifiers. This type of amplifier is also doped with rare earth elements such as those mentioned above.

Once the spectral functions T(λ), R(λ), T_Asε(λ) and R_Asε(λ) have been determined for a specific amplifier, this information can be used in designing optical transmission systems. Existing software tools presently used for this purpose may be modified to specifically include the T and R functions defined above to enable a more accurate modelling of a system as a whole, and thus facilitate the design process.

In a further example illustrated in Fig. 10, the model for spectral gain and noise figure may be used to actively control the output signal power from an optical amplifier in a wavelength division multiplexed optical transmission system. Fig 10 schematically shows an optical amplifier arrangement suitable for a node in an optical transmission system. The arrangement includes an optical amplifier 100 connected to an optical fibre carrying multiple channel wavelengths. A multiplexer 110 is connected to the same optical fibre upstream of the optical amplifier 100. Attenuators 120 tuned to each of the channel wavelengths are connected to the multiplexer input. Some form of feedback link is provided between the amplifier 100 and the attenuators and is illustrated in Fig. 10 by a dashed line 130. This feedback loop 130 provides information on the total output power of the amplifier 100, such as obtained with the optical signal monitor 60 shown in Fig. 1. It may also provide information on the output power of each channel wavelength, provided that the amplifier is equipped with the necessary filters.

It is assumed that the component referred to as the amplifier 100 is a closed module that may contain other passive or active elements, such as couplers, isolators filters and the like. It is further assumed that this amplifier module 100 has been characterised to determine the specific T and R functions as defined above such that the spectral gain and spectral noise performance over the wavelengths of interest are known. Optical amplifiers in optical transmission systems are typically operated in saturation. Thus with this knowledge of the amplifiers spectral properties it is possible to exactly control the gain of the amplifier, and therefore the output power by altering the input power. Two types of operation are possible. According to a first operation, the attenuators are adjusted to obtain constant total output signal power. In an alternative operation, the attenuators may be adjusted to maintain constant channel output power. As mentioned above, the attenuators 120 and demultiplexer 110 may be built into a node with an optical amplifier, in which case the input signal to the node would first be demultiplexed. In a point to point link, the attenuators may be connected at the beginning of a link. In this case they would be adjusted on the basis of the output signal power received at the end of the link to compensate for variations in the gain as a function of wavelength for the whole link.

As mentioned previously, the model for characterising spectral gain described in accordance with a first embodiment of the invention assumes that the amplifier has a homogeneous saturation behaviour, i.e. that the same spectral gain profile can be obtained at different input signal powers and wavelengths when the amplifier is operated at fixed average population inversion. While this assumption is reasonable in many cases, for certain applications and certain amplifier configurations it is less valid. For example, high power fibre amplifiers, i.e. amplifiers which propagate high power will demonstrate more inhomogeneous broadening than those operating at low powers. Inhomogeneous broadening of the optical fibre leads to the spectral gain of the amplifier experiencing a stronger saturation around the wavelength of the optical input signal. This effect is termed spectral-hole burning after the resulting dip in the spectral gain.

This effect is illustrated in Fig. 11. Fig. 11 is a graph of gain in dB on the y- axis against wavelength in nm on the x-axis and shows spectral gain curves in dB for an Erbium doped fibre amplifier operating in the C band under different saturating conditions A and B. A first curve denoted G_A(λ) is the small signal gain expressed in dB, i.e. obtained with a non-saturating input signal, measured with a probe signal. Two further curves denoted G_B(λ)ι and G_B(λ)₂ are gain curves obtained with saturating input signals. These two last gain curves are obtained with identical pumping conditions but with different saturating optical input signal wavelengths. Specifically, G_B(λ)ι is obtained with a saturating optical input signal at 1535nm while G_B(λ)₂ is obtained with a saturating optical input signal at 1555nm. It is apparent from Fig. 11 that both the latter gain curves G_B(λ)ι and G_B(λ)₂ are identical and overlap one another in all regions except for the areas around the input signal wavelengths. At wavelengths around 1535nm the gain curve G_B(λ)ι shows a dip and diverges from that of G_B(λ)₂; at wavelengths around 1555nm the gain curve G_B(λ)₂ shows a dip and diverges from that of G_B(λ)ι. Since the spectral functions T(λ, λ_ref), R(λ, λ_ref) are defined in equations 1.1 and 1.2 terms of gain curves at two different saturating conditions G_A(λ) and G_B(λ), the spectral functions will be influenced to a greater or lesser extent by the input signal wavelength used for the gain curve G_B(λ). For the purposes of the present invention it is assumed that the small signal gain G_A(λ) is substantially unaffected by spectral-hole burning as spectral-hole burning from amplified spontaneous emission is negligible.

In accordance with a further embodiment of the invention, a model for spectral gain of an optical fibre amplifier G λ) is proposed which takes account of the effects of spectral hole burning. In accordance with this embodiment, the spectral functions T(λ, λ_ref) and R(λ, λ_ref) are determined as in equations 1.1 and 1.2 above without the influence of spectral hole burning. A third term, Us_Hβ(λ), which represents the influence of spectral hole burning is then added to the model for spectral gain G(λ) given in equation 1. This modified definition of spectral gain G'(λ) is given in equation 5 below :

G λ) = T(λ,λ_ref) • G(λ_ref) + R(λ,λ_ref) + U_SHB(λ) Equ. 5

In order to determine the spectral functions T(λ, λ^ and R(λ, λ_ref) in the absence of spectral hole burning, the gain curve G_B(λ) for a saturating input signal is obtained by combining at least two saturated gain profiles obtained with identical pumping conditions but different saturating input signal wavelengths. The gain profile G_B(λ) is composed of those parts of the different gain curves that are not in the vicinity of the input signal wavelength. Taking the curves G_B(λ)ι and G_B(λ)₂ shown in Fig. 11 as an example, the gain profile G_B(λ) will be equal to G_B(λ)j for signal wavelengths greater than around 1542nm and to G_B(λ)₂ for signal wavelengths less than 1542nm. The n saturated gain curves G_B(λ)_n used for generating the saturated gain curve G_B(λ) that is unaffected by spectral hole burning should be identical to one another except in the regions of the input signal wavelengths, so that when superimposed on one another they overlap in all but these regions.

The third term, U_SHBW, of the adjusted spectral gain model that accounts for the effect of spectral hole burning (SHB) is obtained by calculating the gain difference ΔG_SHB(λ,λ,) induced by the input signal wavelength λ^ i.e. the gain difference due to spectral hole burning. If the optical fibre amplifier is to be used for transmitting wavelength division multiplexed (WDM) signals, the gain difference is calculated for each channel wavelength that is or may be used and the contribution from each channel wavelength summed to generate the total gain difference U_SHβ(λ) defined by equation 5.1

M

U_SHBW = ∑ΔG^! _s//β( ,/t₁), Equ. 5.1

where λi is the wavelength of the i-th channel, and M the number of wavelength channels in the WDM input signal.

The gain difference ΔGs_HB(λAι) for each channel wavelength can be extracted from experimental data by subtracting the gain curves saturated at different wavelengths, such as the curves G_B(λ)ι and G_B(λ)₂ illustrated in Fig. 11. The gain difference ΔG_SHB(λ,λι) may also be obtained by subtracting the spectral gain saturated at the wavelength of interest from the spectral gain G(λ) calculated using equation 1 above with the spectral functions T(λ, λ_ref) and R(λ, λr_ef) obtained as described above. Experimental data representing the gain difference ΔG_SHB(λ,λι) for different saturating input signal wavelengths between 1530nm to 1570nm is shown in Fig. 12. Fig. 12 is a graph of gain difference in dB due to spectral hole burning (SHB) against wavelength in nm and shows plots for several different input signal wavelengths represented by arrows on the x-axis. It can be seen from the curves represented in Fig. 12 that the gain dip or spectral hole representing the gain difference for each input wavelength has a certain depth, D, in dB and width, Δλ, in nm depending on the wavelength of the optical input signal or channel λi. The dependencies of depth D(λι) and width Δλ(λj) on the input signal wavelength λi may be extracted from the experimental data and interpolated to form an approximation of the gain difference ΔGs_Hβ(λ,λι). This is given in the following equation 5.2.

Turning now to Fig. 13 a further set of curves of spectral gain difference in dB are illustrated for two different input signal wavelengths of 1535 nm and 1555 nm with different optical input signal powers for a C-band EDFA. For each curve the spectral gain is set close to the optimum gain profile, i.e. with minimum gain ripple, by adjusting the input signal power at different pumping powers. From the curves in Fig. 13 it is apparent that the spectral hole depth D and to a certain extent also the spectral hole width Δλ depend also on the input signal power. In particular, with increasing input signal power, the spectral hole depth also increases.

The dependence of the spectral hole depth D and width Δλ on the input signal power can be represented as a function of gain compression. Gain compression is the absolute gain difference that occurs when the input signal, i.e. the channel wavelength, is added or dropped under fixed pumping conditions. The gain compression is proportional to the optical power of the input signal. The relationship between spectral hole depth and width with gain compression is illustrated in Fig. 14. Fig. 14 shows a plot of the spectral hole depth (on the left-hand vertical axis) represented by circles and spectral hole width (on the right hand vertical axis) represented by squares against gain compression in dB. Filled circles and squares correspond to a spectral hole burned by a 1535 nm saturating signal, and open circles and squares correspond to a spectral hole burned at 1555 nm. The lines are a least square linear approximation of the experimental data.

The illustrated relationship between spectral hole depth D and width Δλ, respectively with gain compression ΔG(λ) can be expressed in analytical form as follows:

∑ Λ = a(λ )- ΔG(λ ) Equ. 5.3

Δλ(λ_l) = Δλ₀(λ_l) + β(λ_i) - G(λ_l), _Equ. _5>4

Where the gain compression ΔG(λ is taken at the input signal or WDM channel wavelength λj, and α(λ,), β(λj) and Δλ(λι) are fixed parameters obtained by interpolating experimental data, such as that shown in Fig. 14, for each wavelength of the input optical signal or WDM channel.

Since the gain compression for any input signal wavelength is a quantity that may be easily obtained, the spectral hole depth and width can be approximated for any input signal wavelength and power using equations 5.3 and 5.4 and so used to obtain the gain difference. When determining the spectral gain G'(λ) in accordance with equation 5 of an optical amplifier that is to be used for WDM, the gain difference term ΔGs_HB( ,λj) for wavelength λ_\ must be determined for each input channel wavelength and the total summed to obtain the total gain difference U_SHβ(λ). Since this term is also dependent on the input signal power, it must be determined for all signal powers to obtain complete characterisation of the amplifier spectral gain.

For the purposes of the present invention, it is assumed that the spectral density of the ASE noise of the amplifier is unaffected by spectral hole burning. However, the spectral noise figure as defined by equation 3 may be adjusted to take account of the more accurate spectral gain model by substituting the modified spectral gain calculated using equation 5 and converted to linear units as the denominator of equation 3.

The application of the model for determining the spectral gain will now be illustrated by means of an example for calculating the gain of an optical amplifier in WDM operation.

It is assumed that the WDM input signal, described by spectral power density

Sw_DM(λ) measured in mW/nm, is injected into the optical fibre amplifier under constant optical pumping conditions.

The first step in the characterisation method is to calculate the spectral gain G(λ) that does not take account of spectral hole burning, the gain at a reference wavelength G(λ_ref) and the equivalent input signal power in mW at the reference wavelength p_s(λ_ref) by solving the following three equations 6 to 8:

J- ^• W ^• (g(λ) - \)dλ = λ_ref ^• _Ps(λre_f) ^• (g λ_ref) - 1).

Equ. 6

G(λ) = T(λ,λ_ref) ■ G(λ_ref) + R(λ,λ_ref) Equ. ₈

In the equations 6 to 8, g(λ) is the spectral gain in linear units, i.e. iθ^{0 1G(λ)}, P_s(λ_ref) is the input optical signal power (measured in mW) at a reference wavelength λ_ref and go, pij_m, / and α are fitting parameters that are derivable from experimental data.

The gain compression (in dB) at the i-th wavelength channel of the WDM signal is then found using the following equation:

AG(A,) = G₍(A₍) - G(^), Equ. 9

Where the gain G(λj) at the channel wavelength λ; was calculated at the previous step. Gj(λj) is the gain when the i-th channel in the WDM input signal is eliminated. This value is also calculated by using the set of equations 6 to 8. in terms of the spectral power density of the input signal, it corresponds to the following substitution in equation 6:

^SWDM ( ) ^{→ S}WDM W ~ ^S _t ( ),

where s;(λ) is the spectral power density in mW/nm of the i-th WDM channel.

In the next step, the spectral hole depth D(λj) and width Δλ(λj) are found for the i-th WDM channel using equations 5.3 and 5.4.

The spectral gain difference ΔGs_Hβ(λ,λi) is then also calculated for the i-th channel using equation 5.2. The gain difference due to spectral hole burning resulting from all WDM channels U_SHβ(λ) is then added to the spectral gain profile obtained in the first step of the calculation as follows:

σ(λ) = G(λ) + ∑AG_s λ,λ_i) = t=\

M

T(λ,λ_ref) • G(λ_ref) + R(λ,λ_ref) + ∑ΔG_srø ( )

/=!

The spectral noise figure is then calculated from equation 3 using the modified spectral gain G'(λ) in place of the spectral gain G(λ) as denominator.

As for the simplified model of spectral gain G(λ), which ignores the effect of spectral hole burning, the modified spectral gain G'(λ) can likewise be determined for different amplifier types. The T(λ,λ_reι) and R(λ,λ_ref) functions once determined for an amplifier type are valid for all operating and pumping conditions. The final term representing the gain difference resulting from spectral hole burning, U_SHβ(λ), must be determined for different signal powers and wavelengths.

The model for determining spectral gain taking account of the spectral hole burning may be used in an algorithm for automatic gain control in a WDM system. A schematic arrangement for implementing such an arrangement is illustrated in Fig. 15. Fig. 15 schematically illustrates an optical fibre amplifier 100. The amplifier 100 includes a rare earth doped active fibre and a source of optical pumping energy, such as illustrated in Fig. 1. It also includes appropriate control electronics for controlling the optical pumping source. An input signal monitor 110 is arranged to detect information concerning the WDM channels that are activated. In the illustrated embodiment, this information is carried on a supervisory or control channel multiplexed with the payload channels on the input optical fibre to the amplifier. The monitor 110 includes a filter for extracting the control channel. Alternatively, the a drop coupler may be connected to the input of the optical amplifier 100 for extracting the control channel information. The control information need not be transmitted with the payload channels. In an alternative embodiment, the monitor may not be connected to the input fibre but instead receive information through a separate dedicated supervisory channel transmitted through a cable or separate optical fibre. In a still further embodiment, the monitor 110 may determine itself which WDM channels are active and to this end contain an optical photodiode array and receive information coupled from the input optical fibre. A filter module 120 is arranged at the output of the optical amplifier 100. This filter 120 is preferably a dynamic gain flattening filter. The transmittance of this filter is controlled by a control unit 130, which also controls the pumping power to the active fibre of the amplifier 100 in response to information received from the monitor 110. The control unit 130 contains a processor and has access to a memory. The memory contains the functional forms T(λ, λ_ref) and R(λ, λ_ref) for each channel wavelength and also values of the gain difference U_SHB(λ) for each channel wavelength and for different channel input powers arranged in a database or lookup table. Using these stored terms, and information regarding which channels are contained in the input signal to the optical amplifier 100 from the monitor 110, the control unit 130 is able to determine the desired gain for each channel, and adjust the gain by controlling the amplifier pump power and the transmittance of the gain flattening filter 120.

Claims

Claims:

1. A method of determining the spectral gain of an optical amplifier, including the steps of: using a first spectral gain function T(λ, λ_ref) expressed in terms of at least two reference gain spectra measured at different saturation states of the amplifier and a reference wavelength λ_ref, using a second spectral gain function R(λ, λ_ref) expressed in terms said at least two reference gain spectra and said reference wavelength, determining a measured gain of the saturated amplifier at said reference wavelength G(λ_ref) expressed in dB, and calculating the gain expressed in dB at any wavelength λ according to the expression

G (λ) = T(λ, λref) ^• G ( ref) + R( ref).

2. A method as claimed in claim 1, characterised by adjusting said gain at any wavelength by a quantity U_SHβ(λ) representative of a difference in gain due to additional saturation around said input signal wavelength to obtain spectral gain G'(λ) adjusted for the effect of spectral hole burning.

3. A method as claimed in claim 3, characterised in that said adjustment quantity U_SHβ(λ) represents a difference in gain obtained with said amplifier under saturation conditions when applying a saturating input signal at said wavelength and not applying a saturating input signal at said wavelength.

4. A method as claimed in claim 2 or 3, further characterised by the step of calculating said quantity Us_Hβ(λ) as a function of gain compression of said optical amplifier for each wavelength.

5. A method as claimed in claim 4, characterised by calculating said quantity Us_Hβ(λ) for each wavelength using the following expression>

α( ,) -ΔG( l,) -exp _ _41n2f

where α(λι), β(λι) and Δλ(λι) are fixed parameters for said wavelength λi and ΔG(λj) is the gain compression at wavelength λi.

6. A method as claimed in any one of claims 2 to 5, characterised by the step of determining said quantity Us_Hβ(λ) for each input signal power.

7. A method as claimed in any previous claim, characterised by determining said first spectral gain function T(λ, λ_ref) by measuring the gain of the amplifier as a function of wavelength for a first saturation state of an amplifier to obtain at least one first reference gain spectra, G_A(λ) in dB, measuring the gain of the amplifier as a function of wavelength at a second saturation state of an amplifier to obtain at least a second reference gain spectra G_B(λ) in dB, calculating said first spectral gain function using said first and second measured gain spectra in accordance with the following expression> T(λ, λref) = (G_A(λ) - G_B(λ)) / (G_A(λ_ref) - G_B(λ_ref).

8. A method as claimed in any previous claim, characterised by determining said second spectral gain function R(λ, λ_ref) by measuring the gain of an amplifier as a function of wavelength for a first saturation state of an amplifier to obtain at least a first reference gain spectra G_A(λ) in dB, measuring the gain of an amplifier as a function of wavelength at a second -saturation state of an amplifier to obtain at least a second reference gain spectra G_B(λ) in dB, calculating said second spectral gain function using said first and second measured gain spectra in accordance with the following expression

R(λ, λref) = (G_A(λ_ref) X G_B(λ) - G_A(λ) X G_B(λ_ref) / (G_A(λ_ref) - G_B(λ_ref).

9. A method as claimed in claim 7 or 8, wherein at least one of said first and second reference gain spectra are measured by applying saturating input signals at at least two different wavelengths and measuring spectral gain to obtain data representing two measurement curves, for each curve extracting gain measurements at areas not in the vicinity of the input signal wavelength to obtain data representing a single spectral gain curve.

10. A method of characterising the amplified spontaneous emission spectral power density of an optical amplifier including the steps of: using a first spectral noise function T _SE (λ, λ_ref) expressed in terms of two reference amplifier output power density spectra measured at different saturation states of the amplifier and expressed in dB, and a reference wavelength λ_ref , using a second spectral noise function R_As_E(λ, λ_ref) expressed in terms of said two reference gain spectra and a said reference wavelength, determining a measured ASE output power density of the saturated amplifier at said reference wavelength S_ASE(λ_ref) expressed in dB, and calculating the ASE output power density S_ASE (λ) expressed in dB at any wavelength λ according to the expression

S_ASE (λ) = T_ASE (λ, λ_ref) ' S_ASE(λ_ref) + R_ASE(λ,λ_ref).

11. A method as claimed in claim 10, characterised by determining said first spectral noise function T_ASE (λ, λ_reι) by measuring the output spectral power density S_ASE of the amplifier as a function of wavelength λ for a first saturation state of an amplifier to obtain a first reference noise spectra S_{ASE A}(λ) expressed in dB, measuring the output spectral power density S_ASE of the amplifier as a function of wavelength λ at a second saturation state of an amplifier to obtain a second reference noise spectra S _SE β(λ) expressed in dB, calculating said first spectral noise function using said first and second noise spectra in accordance with the following expression

T_ASE (λ, λ_ref) ⁼ (S_ASE λ(λ) - S_ASE β(λ)) / (S_ASE A(λref) - $_ASE B^ref)-

12. A method as claimed in claim 10 or 11, characterised by determining said second spectral noise function R_ASE (λ, λ_ref) by measuring the output spectral power density S_ASE of the amplifier as a function of wavelength λ for a first saturation state of an amplifier to obtain a first reference noise spectra S_{ASE A}(λ) expressed in dB, measuring the output spectral power density S_ASE of the amplifier as a function of wavelength λ at a second saturation state of an amplifier to obtain a second reference noise spectra S _SE β(λ) expressed in dB, calculating said second spectral noise function using said first and second noise spectra in accordance with the following expression:

13. A method as claimed in claim 10, characterised by determining said first spectral noise function T_ASE (λ, λ_ref) by measuring gain of the amplifier as a function of wavelength for a first saturation state of an amplifier to obtain a first reference gain spectra G_A(λ) in dB, measuring the gain of the amplifier as a function of wavelength at a second saturation state of an amplifier to obtain a second reference gain spectra G_B(λ) in dB, calculating said first spectral gain function using said first and second measured gain spectra in accordance with the following expression

T_ASE (λ, λr_ef) ⁼ (G_A(λ) - G_B(λ)) / (G_A(λ_ref) - G_B(λ_ref).

14. A method as claimed in any previous claim, characterised by determining the noise figure of the amplifier for any wavelength using said calculated spectral gain and spectral power density.

15. The use of a method as claimed in any previous claim for rare earth doped fibre amplifiers.

16. The use of a method as claimed in any one of claims 1 to 14 for optical planar glass amplifiers.

17. The use of a method as claimed in any one of claims 1 to 14 for erbium doped fibre amplifiers (EDFA).

18. The use of the method as claimed in claim 17, wherein said erbium doped fibre amplifiers operate in the wavelength band between 1530nm and 1570nm.

19. An automatic gain control arrangement for an optical fibre amplifier arranged to receive multiple wavelength division multiplexed channels, including an input signal monitor (110) arranged to monitor said input channels, a gain flattening filter (120) arranged to modify the output of the optical amplifier and a control unit (130) for controlling the pump power to said amplifier and said filter, wherein said control unit is arranged to determine the spectral gain of the amplifier using a predetermined relationship as defined in any one of claims 1 to 8 in response to information from said monitor.

20. A method of determining the spectral gain of an optical fibre amplifier, including the steps of : injecting a broadband optical signal with known spectral power density into said optical fibre amplifier under constant optical pumping conditions, determining a first approximation of spectral gain, the gain of the amplifier at a reference wavelength and the input signal power at said reference wavelength, for each wavelength in said broadband optical signal, determining gain compression of said optical amplifier for each wavelength determining a spectral hole depth and width, using said spectral hole depth and width values determining the spectral gain difference for each wavelength, adjusting said first approximation of spectral gain using said spectral gain difference.

21. A method as claimed in claim 20, further including the step of calculating the spectral noise figure using said adjusted spectral gain.