Patent Publication Number: US-7212335-B2

Title: Apparatus and method for amplification medium performance simulation, and optical amplifier

Description:
This application is a continuation application, filed under 35 USC 111(a), of International Application PCT/JP2003/008219, filed Jun. 27, 2003. 

   TECHNICAL FIELD 
   The present invention relates to an apparatus and a method for amplification medium performance simulation, and an optical amplifier. 
   On the basis of a rapid increase in data communication traffic with a recent rapid spread of the Internet, focused is a technique relating to a wavelength division multiplexing transmission technique which is a technique for increasing the speed and capacity of the network, and a photonic network which is a network in which each wavelength transmitted by means of the wavelength division multiplexing transmission technique is supposed to be one communication path. 
   The present invention relates to an apparatus and a method for amplification medium performance simulation suitable for use in simulation of performance of an amplification medium applied when a photonic network is configured, and an optical amplifier made on the basis of a result of simulation obtained by this apparatus. 
   BACKGROUND ART 
   Because of expectation for realization of an optical network (photonic network) having high flexibility, it is required for a node configuring the network to cope with a large change in the number of wavelengths, which are supposed to be a communication path. Particularly, an optical amplifier which is a constitutional element of a node is required to cope with a large change in allocation and the number of wavelengths to stabilize the amplification characteristic. 
   The wavelength characteristic of an amplification medium such as an EDFA (Erbium Doped Fiber Amplifier) used in a known optical network system, in which allocation and the number of the wavelengths are assumed not to be largely changed, can be presupposed to depend upon only population inversion by a single band approximation (refer to non-patent document 1). Namely, the wavelength characteristic can be approximated and grasped according to the value of the population inversion rate, with the whole amplification band of the EDFA being one unit. 
   In concrete, as shown in  FIG. 24 , a pattern of relative gain coefficients as being the wavelength characteristic over the whole range of the amplification bandwidth (wavelengths from 1500 to 1580 nm of an input signal light in the drawing) of the EDFA can be grasped for each population inversion rate. Accordingly, wavelength flatness of the EDF in C band (Conventional Band) is realized by combining the automatic gain control by which the population inversion is controlled to be constant, and the gain equalizer according to the relative gain coefficient distribution corresponding to the population inversion that is controlled to be constant. 
     FIG. 25  shows an example of the structure of an optical repeater  100  used in a known optical network system in which wavelength allocation and the number of wavelengths are not largely changed. The optical repeater  100  shown in  FIG. 25  is configured by inserting an optical attenuator (VOA: Variable Optical Attenuator)  102  between two EDFA amplifying units  101 - 1  and  101 - 2  serially connected. 
   Each of the EDFA amplifying units  101 - 1  and  101 - 2  comprises branching couplers  101   a  and  101   b , an EDFA  101   c , photodiodes (PD: Photo Diode)  101   d  and  101   e , and a control circuit  101   f . In each of the EDFA amplifying units  101 - 1  and  101 - 2 , the input/output powers are monitored by the respective photodiodes  101   d  and  101   e , and an optical signal amplified by the EDFA  101   c  under the automatic gain control by the control circuit  101   f  is outputted. 
   As shown in  FIG. 26 , for example, when the input power of the optical repeater  100  is changed from the first level to the second level, the output power of the optical repeater  100  is made constant by adjusting the quantity of loss in the variable optical attenuator  102  while keeping the gain in each of the EDFA amplifying units  101 - 1  and  101 - 2  constant. 
   If the amplification characteristic of the EDFA  101   c  in each of the EDFA amplifying units  101 - 1  and  101 - 2  is assumed to be an optical network that can be approximated to a single band, the gain wavelength characteristic can be always kept constant by keeping the gain of each of the EDFA  101   c  constant. Accordingly, it becomes possible to make the gain wavelength characteristic of the optical repeater  100  flat irrespective of the input power, by disposing a gain equalizer whose loss characteristic is appropriately designed in the following stage of the EDFA amplifying units  101 - 1  and  101 - 2 . 
   Namely, since it is supposed that the known optical repeater is applied to an optical network in which wavelength allocation and the number of wavelengths are not largely changed, the gain equalizer arranged in the following stage of the EDFA amplifying units  101 - 1  and  101 - 2  is designed on the assumption that the wavelength characteristic of an amplifying medium as above is approximated to a single band. 
   However, in an optical network recently demanded in which wavelength allocation and the number of wavelengths are largely changed, the gain deviation due to an effect of spectral hole burning (SHB: Spectral-Hole Burning) which is a local gain saturation effect in the wavelength region cannot be ignored when the selected wavelengths are arranged to be particularly gathered in a narrow band. Since the effect of this SHB differs according to wavelength allocation supposed in the optical network, it is necessary to analyze the gain deviation caused by SHB according to the wavelength allocation beforehand supposed when the apparatus is designed. 
     FIG. 27  shows gain deviation characteristic due to SHB of an EDFA. When a gain wavelength characteristic A in the saturated state where a saturation signal at 1540 nm (signal saturating the gain of the EDFA) is compared with a gain wavelength characteristic B in the non-saturated state where no saturation signal is inputted, it can be confirmed that, in the saturated state, the gain in the vicinity of the saturation signal wavelength and 1530 nm is decreased (refer to a gain difference C between the characteristics A and B) to make holes. 
   This phenomenon occurs due to a local gain saturation phenomenon of a gain medium having inhomogeneous broadening. In the known single band approximation, this local change in gain wavelength characteristic is ignored. 
   As a model of EDFA in which SHB is considered, there have been reported a model (refer to non-patent document 2) which separately deals with the absorption/emission process and the saturation process between energy levels formed by the inhomogeneous broadening, and a model which adds the quantity of gain fluctuation due to SHB derived from a result obtained by separately measuring the gain wavelength characteristic obtained by means of single band approximation (refer to non-patent document 3). 
   As techniques relating to the present invention, there are also techniques described in Patent Document 1 and Patent Document 2 shown below. 
   However, the technique described in Non-Patent Document 2 provides a very complex calculation formula for analyzing the gain deviation, thus has a disadvantage that the process requires a long time. The technique described in Non-Patent Document 3 considers only the neighborhood of the signal wavelength, thus has a disadvantage that the gain fluctuation in the vicinity of 1530 nm cannot be modeled. 
   As a method of measuring the amplification characteristic of an amplification medium, there is a method (hardware simulation) for measuring the amplification characteristic from an actually formed optical amplifier other than the method of calculating through numerical value calculation described above. However, some sorts of hardware simulation take a long time or require much labor to measure entirely the wide operation conditions of an optical repeater. 
   In the light of the above problems, an object of the present invention is to provide an apparatus and a method for amplification medium performance simulation, and an optical amplifier, which introduce a simple approximate expression, thereby modeling gain fluctuation in a range other than the neighborhood of the signal wave within a short time. 
   Non-Patent Document 1: C. R. Giles, et al., “Modeling Erbium Doped Fiber Amplifiers,” IEEE J. of Lightwave Tchnol., pp. 271–283, vol. 9, no. 2, Feb., 1991; 
   Non-Patent Document 2: E. Desurvire, “ERBIUM-DOPED FIBER AMPLIFIERS Principles and Applications,” John Wiley &amp; Sons, Inc., Chapter 4, 1994; 
   Non-Patent Document 3: T. Aizawa, et al., “Effect of Spectral-Hole Burning on Multi Channel EDFA Gain Profile,” OFC&#39;99, WG1, 1999; 
   Patent Document 1: Japanese Patent Application Laid-Open No. 2000-261078; and 
   Patent Document 2: Japanese Patent Application Laid-Open No. 2000-261079. 
   DISCLOSURE OF INVENTION 
   To attain the above object, the present invention provides an amplification medium performance simulation apparatus for simulating performance of an amplification medium excited by a pump beam from a pumping source to amplify a signal beam comprising a basic data retaining unit for retaining basic data of the amplification medium, an input signal beam information retaining unit for retaining a total power and a power at each wavelength of an input signal beam as information on the input signal beam to be inputted to an amplification medium to be simulated, and a simulation executing unit for reckoning a fluctuation in ion population at a metastable energy level in the amplification medium caused by input of the input signal beam, and approximating and calculating an output signal beam power at each signal beam wavelength outputted from the amplification medium, by using contents retained in the basic data retaining unit and the input signal beam retaining unit, and outputting a result of the calculation as a result of simulation of the performance of the amplification medium. 
   The simulation executing unit may comprise a population inversion rate calculating unit for calculating a population inversion rate on the basis of a signal beam power according to a position with a coordinate in the longitudinal direction of the amplification medium, a population inversion rate change quantity calculating unit for calculating a quantity of a change in population inversion rate which may occur due to a fluctuation in ion population at the metastable energy level of the amplification medium caused by input of the input signal beam, as a function of a wavelength of the input signal beam and a position in the longitudinal direction of the amplification medium, by using the population inversion rate calculated by the population inversion rate calculating unit and contents retained in the basic data retaining unit and the input signal beam information retaining unit, a signal beam power change calculating unit for performing calculation of a change in optical power of the signal beam propagating through the amplification medium from a signal beam input end in the amplification medium in each of minute propagation ranges started from the signal beam input end and terminated at a signal beam output end, by using a differential equation defined by the quantity of a change in population inversion rate calculated by the population inversion rate change quantity calculating unit and the contents retained in the basic data retaining unit and the input signal beam information retaining unit, a signal beam power calculating unit for adding, in order, changes in optical power in the minute propagation ranges from a change in optical power in the minute propagation range at the signal input end as a starting point to a change in optical power in the minute range at the signal output end as a terminating point calculated by the signal beam power change calculating unit to the power value of the input signal beam retained in the input signal beam information retaining unit, to calculate a signal beam power according to a position with a coordinate in the longitudinal direction of the signal beam propagating in the amplification medium including the fluctuation in ion population at the metastable energy level in the amplification medium caused by input of the input signal beam, and an outputting process unit for outputting a result of calculation of the power of the signal beam outputted from the signal beam output end calculated by the signal beam power calculating unit as a result of simulation of the performance of the amplification medium. 
   Preferably, the population inversion rate change quantity calculating unit uses at least one or more Gaussian functions as functions for calculating the quantity of a change in the population inversion rate. 
   The population inversion rate change quantity calculating unit for calculating a quantity of a change in the population inversion rate may comprise a first function operating unit for operating a first function having a first wavelength band in a gain saturation state as a center, a second function operating unit for operating a second function comprised of a function having a second wavelength band characteristic of the amplification medium as a center, and an adding unit for adding results of the operations from the first function operating unit and the second function operating unit. 
   Preferably, the first function operated by the first function operating unit is composed of a total of Gaussian functions given according to respective wavelengths of the input signal beam, and the second function operated by the second function operating unit is composed of a total of a plurality of Gaussian functions. 
   In this case, the Gaussian function given according to each wavelength of the input signal beam in the first function is determined as a value expressed in terms of a center wavelength which is a wavelength of the input signal beam and a full width half maximum according to the amplification medium, each of the Gaussian functions in the second function is determined as a value expressed in terms of a center wavelength which is in a second wavelength band characteristic of the amplification medium and a full width half maximum according to the amplification medium, and the full width half maximum of each of the Gaussian functions in the first function and the second function is retained in the basic data retaining unit. 
   A depth of each of the Gaussian functions in the first function or the second function may be defined by a depth function which increases as a total power of the input signal beam increases, and saturates above a predetermined value. 
   In this case, the depth function of each Gaussian function given according to each wavelength of the input signal beam in the first function may be defined by a function having a wavelength λ i  of the input signal beam, an optical power P i (z) at a position with a coordinate z in the longitudinal direction of the amplification medium at the wavelength λ i  of the input signal beam and a total power P total (z) of the input signal beam at a position with a coordinate z in the longitudinal direction of the amplification medium as variables, the depth function of each Gaussian function in the second function may be defined by a function having a wavelength λ i  in the second wavelength band, a total power P total (z) of the input signal beam at a position with the coordinate z in the longitudinal direction of the amplification medium and a population inversion rate n(z) of the amplification medium as variables, and coefficients defining the depth functions of the Gaussian functions in the first function and the second function may be retained in the basic data retaining unit. 
   The basic data retaining unit may retain, as the basic data of the amplification medium, at least an overall length of the amplification medium, a gain coefficient g(λ), an absorption coefficient α(λ) and a loss l(λ) expressed as functional equations with respect to each input signal beam wavelength, and a population inversion rate n(z) not added thereto the fluctuation in ion population at the metastable energy level in the amplification medium, the signal beam power change calculating unit may calculate the population inversion rate n(z) from a signal beam power according to a position with a coordinate in the longitudinal direction of the signal beam propagating in the amplification medium calculated by the signal beam power calculating unit, and calculate a minute change in optical power of the signal beam propagating at a position with the coordinate z in the longitudinal direction of the amplification medium, by using a change in optical power in each minute unit of the length in the longitudinal direction of the amplification medium
 
 dP ( z )/ dz ={( g (λ)+α(λ))( n ( z )+Δ n   SHB (λ,  z ))−(α(λ)+1(λ))}· P ( z )
 
using the population inversion rate n(z), the change quantity Δn SHB (λ,z) of the population inversion rate calculated by the population inversion rate change quantity calculating unit and the basic data retained in the basic data retaining unit.
 
   Preferably, the simulation executing unit approximates and calculates gain deviation among signal beam wavelengths caused by spectral hole burning. 
   The present invention further provides an amplification medium performance simulation method for simulating performance of an amplification medium excited by a pump beam from a pumping source to amplify a signal beam, comprising a population inversion rate change quantity calculating step of calculating a quantity of a change in population inversion rate which may occur due to a fluctuation in ion population at a metastable energy level of the amplification medium caused by input of the signal beam, an optical power change calculating step of performing calculation of a change in optical power of the signal beam propagating in the amplification medium from a signal beam input end of the amplification medium in each of minute propagation ranges started from the signal beam input end and terminated at a signal beam output end, by using a propagation equation of the amplification medium on the basis of a corrected population inversion rate corrected with the quantity of a change in population inversion rate calculated at the population inversion rate change quantity calculating unit, an output signal beam power calculating step of performing successive addition of each change in optical power in the minute propagation range calculated at the optical power change calculating step to the power value of the input signal beam between the signal beam input end and the signal beam output end, to calculate an output signal beam power outputted from the amplification medium including the fluctuation in ion population at the metastable energy level in the amplification medium due to input of the input signal beam, and an outputting process step of outputting a result of calculation calculated at the output signal beam power calculating step as a result of simulation of the performance of the amplification medium. 
   The present invention still further provides an optical amplifier comprising a pumping source for outputting a pump beam, a signal beam amplification medium excited by the pump beam from the pumping source to amplify an input signal beam, and a gain equalizer for equalizing a gain of an output signal beam outputted from the signal beam amplification medium, wherein the gain equalizer has a gain equalization characteristic so that it compensates gain deviation due to a fluctuation in ion population at a metastable energy level in the amplification medium caused by input of the input signal beam, on the basis of a result of simulation outputted from an amplification medium performance simulation apparatus for simulating the performance of the amplification medium excited by the pump beam from the pumping source to amplify the signal beam, the amplification medium performance simulation apparatus comprising a basic data retaining unit for retaining basic data of the amplification medium, an input signal beam information retaining unit for retaining a total power and a power at each wavelength of the input signal beam as information on the input signal beam to be inputted to the amplification medium to be simulated, and a simulation executing unit for reckoning a fluctuation in ion population at a metastable energy level in the amplification medium caused by input of the input signal beam, and approximating and calculating an output signal beam power at each signal beam wavelength outputted from the amplification medium, by using contents retained in the basic data retaining unit and the input signal beam information retaining unit, and outputting a result of calculation as a result of simulation of the performance of the amplification medium. 
   The present invention still further provides an optical amplifier comprising a pumping source for outputting a pump beam, a signal beam amplification medium excited by the pump beam from the pumping source to amplify an input signal beam, and a pumping source controlling unit for controlling the pumping source, the pumping source controlling unit controlling the pumping source so that it compensates gain deviation due to a fluctuation in ion population at a metastable energy level in the amplification medium caused by input of the input signal beam, on the basis of a result of simulation outputted from an amplification medium performance simulation apparatus for simulating the performance of the amplification medium excited by the pump beam from the pumping source to amplify the signal beam, the amplification medium performance simulation apparatus comprising a basic data retaining unit for retaining basic data of the amplification medium, an input signal beam information retaining unit for retaining a total power and a power at each wavelength of the input signal beam as information on the input signal beam to be inputted to the amplification medium to be simulated, and a simulation executing unit for reckoning a fluctuation in ion population at a metastable energy level in the amplification medium caused by input of the input signal beam, and approximating and calculating an output signal beam power at each signal beam wavelength outputted from the amplification medium, by using contents retained in the basic data retaining unit and the input signal beam information retaining unit, and outputting a result of calculation as a result of simulation of the performance of the amplification medium. 
   In this case, the pumping source controlling unit may comprise a first power monitor for monitoring powers of the input signal beam and the output signal beam, a wavelength allocation information obtaining unit for obtaining wavelength allocation information on a signal beam propagating in the amplification medium, an automatic gain control unit for outputting a signal for controlling the pumping source obtained on the basis of the powers of the input signal beam and the output signal beam monitored by the first power monitor so that a gain of the optical signal amplification medium is constant, and a correcting unit for correcting a control quantity for the pumping source in the automatic gain control unit on the basis of the wavelength allocation information obtained by the wavelength allocation information obtaining unit so that gain deviation in a wavelength band due to spectral hole burning decreases. 
   The wavelength allocation information obtaining unit may be comprised of a spectrum analyzer monitoring wavelength allocation of a signal beam inputted to or outputted from the amplification medium. The wavelength allocation information obtaining unit may obtain the wavelength allocation information from a control signal beam transmitted together with the signal beam. 
   The pumping source controlling unit may comprise a second power monitor for obtaining powers of the input signal beam and the output signal beam in each of a plurality of bands divided on the basis of a result of the simulation obtained by the amplification medium performance simulation apparatus, and an automatic average gain control unit for outputting a signal for controlling the pumping source on the basis of the powers of the input signal beam and the output signal beam in each of the bands obtained by the second power monitor so that average gains in the bands are equalized. 
   As above, according to the apparatus and method for amplification medium performance simulation of this invention, the simulation executing unit introduces a simple approximate expression to be able to output gain deviation occurring due to a local fluctuation in ion population in a wavelength region at a metastable energy level in each minute unit of the length in the longitudinal direction of the amplification medium, involving gain deviation in a region other than the neighborhood of the signal wave, through a process within a short period of time, as a result of simulation. 
   In the optical amplifier according to this invention, it is possible to control the pumping source by the pumping source controlling unit or designed the gain equalizer on the basis of a result of highly accurate simulation obtained through a process within a short period of time from the simulation executing unit of the amplification medium performance simulation apparatus of this invention, whereby gain deviation due to a local fluctuation in ion population in a wavelength region at a metastable energy level in the amplification medium is compensated. It is thus possible to largely improve the stability of the automatic gain control. 
   Particularly, in an optical amplifier which is a constitutional element of a node in a photonic network in which the wavelength allocation of a signal beam can be dynamically changed, it is possible to improve the stability of the amplification characteristic according to a large change in wavelength allocation and the number of wavelengths. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
       FIG. 1  is a block diagram showing an amplification medium performance simulation apparatus according to a first embodiment of this invention; 
       FIGS. 2 and 3  are diagrams for illustrating an operating process in the apparatus according to this invention. 
       FIG. 4  is a flowchart for illustrating an operation of the amplification medium performance simulation apparatus according to the first embodiment of this invention; 
       FIGS. 5 through 7  are diagrams in each of which a results of simulation by the amplification medium performance simulation apparatus according to the first embodiment is compared with measured values obtained by experiment; 
       FIG. 8  is a block diagram showing an optical amplifier according to a second embodiment of this invention; 
       FIG. 9  is a diagram for illustrating a gain equalization characteristic of a gain equalizer disposed in the following stage of an EDFA shown in  FIG. 8 ; 
       FIG. 10  is a block diagram showing an optical amplifier according to a third embodiment of this invention; 
       FIG. 11  is a block diagram showing a modification of the third embodiment; 
       FIG. 12  is a flowchart for illustrating an operation of the optical amplifier according to the third embodiment; 
       FIGS. 13 through 18  are diagrams for illustrating a working effect given by superimposing correction of a fluctuation in gain due to SHB on an automatic gain control in the optical amplifier according to the third embodiment; 
       FIG. 19  is a block diagram showing an optical amplifier according to a fourth embodiment of this invention; 
       FIG. 20  is a block diagram showing an optical amplifier according to a fifth embodiment of this invention; 
       FIG. 21  is a flowchart for illustrating an operation of the optical amplifier according to the fifth embodiment of this invention; 
       FIGS. 22 and 23  are diagrams for illustrating a working effect given by the optical amplifier according to the fifth embodiment of this invention; 
       FIG. 24  is a diagram for illustrating an example where a wavelength characteristic (gain spectrum) is approximated and grasped according to a value of a population inversion rate with the whole amplification band of an EDFA being one unit; 
       FIG. 25  is a block diagram showing an example of the structure of an optical repeater used in a known optical network system in which wavelength allocation and the number of wavelengths are assumed not to be largely changed; 
       FIG. 26  is a diagram for illustrating an example where the output power of the optical repeater is made constant by adjusting a loss quantity in a variable optical attenuator shown in  FIG. 25 ; and 
       FIG. 27  is a diagram showing a gain deviation characteristic due to SHB of an EDFA. 
   

   BEST MODE FOR CARRYING OUT THE INVENTION 
   Hereinafter, description will be made of embodiments of the present invention with reference to the drawings. 
   (a) Description of First Embodiment 
     FIG. 1  is a block diagram showing an amplification medium performance simulation apparatus  1  according to a first embodiment of this invention. The amplification medium performance simulation apparatus  1  shown in  FIG. 1  simulates the performance of an amplification medium. Particularly, the amplification medium performance simulation apparatus  1  can carry out simulation of the output power characteristic and gain characteristic of an amplification medium in an optical amplifier applied to an apparatus configuring a photonic network. 
   When an optical amplifier assumed to be applied to an optical network in which wavelength allocation and the number of wavelengths are largely changed is designed, the gain wavelength characteristic of an amplification medium to be evaluated is accurately grasped, whereby the input/output power characteristic and the characteristics of a gain equalizer are so designed as to secure the gain flatness. 
   In the amplification medium performance simulation apparatus  1 , an EDFA, for example, can be used as the amplification medium to be simulated. Hereinafter, a case where an EDFA is used as the amplification medium, but another amplification medium other than the EDFA can be used. 
   The amplification medium performance simulation apparatus  1  according to the first embodiment can simulate the gain deviation characteristic of an EDFA occurring due to SHB as above by obtaining basic data of the EDFA and information on the input signal beam. Now, description will be made of a principle of calculation of the gain deviation characteristic of the EDFA due to SHB in the amplification medium performance simulation apparatus  1 . 
   As described above with reference to  FIG. 27 , it is found that the effect of inhomogeneous broadening at the wavelength level in the gain saturated state in an EDFA is significant particularly at the signal beam wavelength and in a 1530 nm band. Giving attention to the effect of the bands in which the inhomogeneous broadening is particularly large, the amplification medium performance simulation apparatus  1  according to this embodiment calculates the quantity of a change in the population inversion rate. Hereinafter, the gain fluctuation occurring at the signal beam wavelength will be referred to as “main hole,” whereas the gain fluctuation occurring in the vicinity of 1530 nm will be referred to as “second hole.” 
     FIGS. 2 and 3  are diagrams for illustrating an operating process in the apparatus  1  according to this embodiment. The gain fluctuation due to SHB at a certain wavelength is caused by that the number of ions of ER 3+  at the metastable energy level of transition corresponding to the length of the optical wavelength changes, that is, the population inversion rate changes from its average value. 
   Assuming that the quantity of a change in the population inversion rate causing gain fluctuation due to SHB is Δn SHB  when the signal beam propagates from a position with a coordinate z by a minute portion Δz (refer to  FIG. 2 ) in the longitudinal direction of an EDF  50 , the optical power P (z+Δz) at the minute portion Δz is expressed by an equation (1). In the equation (1), n represents the population inversion rate at a position with the coordinate z in the longitudinal direction of the EDF  50 , P(z) represents the signal beam power at a position with the coordinate z in the longitudinal direction of the EDF  50 , and G(n) represents the gain of the EDF  50  in the case of the population inversion rate n.
 
 P ( z+Δz )= P ( z )+ G ( n ( z )+Δ n   SHB (λ, z ))× P ( z )   (1)
 
   The propagation equation of the EDF  50  can be expressed as shown in an equation (2). In the equation (2), the population inversion rate n is represented as a function value n(z) according to the coordinate z in the longitudinal direction of the EDF  50 , the value of Δn SHB (λ,z) is represented as a function of the signal beam wavelength λ along with the coordinate z in the longitudinal direction of the EDF  50 .
 
 dP ( z )/ dz ={( g (λ)+α(λ))( n ( z )+Δ n   SHB (λ, z ))−(α(λ)+1(λ))}· P ( z )  (2)
 
   In the equation (2), g(λ) represents the gain coefficient in the EDF  50 , α(λ) represents the absorption coefficient, and l(λ) represents the loss, which are beforehand given as functions according to the wavelength λ of the signal beam. From the equation (2), the quantity of a minute change dP(z)/dz in the optical power at a position with the coordinate z in the longitudinal direction of the EDF  50  can be determined by obtaining the optical power P(z) at a position with the coordinate z and n(z)+Δn SHB (λ,z). Incidentally, n(z) can be obtained through a known calculation equation on the basis of the optical power P(z) at a position with the coordinate z in the longitudinal direction of the EDFA [refer to an equation (14) in the above Non-Patent Document 1]. 
   Giving attention to a change in the population inversion rate in the signal beam wavelength band causing the main hole and a change in the population inversion rate in the vicinity of 1530 nm causing the second hole, Δn SHB (λ,z) in the formula (2) can be expressed as an equation (3): 
   
     
       
         
           
             
               
                 
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   The above equation (3) has a structure in which Gaussian functions representing changes in the population inversion rates corresponding to the main hole and the second hole are added. 
   A term (the first function to be described later) of the population inversion rate change corresponding to the main hole is modeled with a total of changes in the population inversion rate each represented by one Gaussian function for each signal beam wavelength (channel) to be transmitted as a signal beam. A term (the second function to be described later) of the population inversion rate change corresponding to the second hole is modeled with a total of a plurality (j) of Gaussian functions not depending on the signal beam wavelength. 
   When the signal beam wavelength is one wavelength, for example, a change in the population inversion rate corresponding to the main hole can be expressed as a single Gaussian function G1 having the signal beam wavelength (or the saturation signal wavelength) as the center wavelength, whereas a change in the population inversion rate corresponding to the second hole can be expressed by a sum of two Gaussian functions G2 and G3 having a wavelength in the 1530 nm band as the center wavelength, as shown in  FIG. 3 . 
   In the equation (3), the first term represents the main hole, the second term represents the second hole, wherein λ i  represents the signal beam wavelength of a channel i, λ j  represents the center wavelength of the Gaussian function of the second hole, P i (z) represents the signal power in a channel i propagating at a position with the coordinate z, P total (z) is the total power of a signal beam propagating at a position with the coordinate z, and BW i  and BW j  are full width half maximums of the respective Gaussian functions. 
   C(λ i , P i (z), P total (z)) is a depth function determining the depth of the main hole formed by the signal beam in a channel i. D j (λ j , P total (Z), n(z)) is a depth function determining the second hole, for both of which a function whose depth increases as the total power of the signal beam propagating at a position with the coordinate z increases, and saturates when the power is above a predetermined value can be used. 
   The function C(λ i , P i (z), P total (z)) and the function D j (λ j , P total (z), n(z)) can be expressed by equations (4) and (5), respectively. 
   
     
       
         
           
             
               
                 
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   From a relationship between the above equations (2) and (3), a value of Δn SHB (λ,0) in the equation (3) is calculated along with n(z) on the basis of the power (P i (0)) at the time that the signal beam is inputted to the EDF  50 , and the calculated Δn SHB (λ,0) is used for the equation (2), whereby a minute change in the optical power propagating at the position of the minute portion Δz at a signal beam input end of the EDF  50 . 
   Further, the minute change in the optical power calculated as above is added to the input signal beam power P i (0) to obtain a signal beam power P i (Δz) propagating at a position Δz. Whereby, a change in the optical power in the case where the signal beam further propagates by the minute portion Δz from the coordinate z=Δz in the longitudinal direction of the EDF  50  can be calculated in a manner similar to the above. 
   By repeating the above calculation, it is possible to calculate a change in the optical power in the case where the signal beam further propagates by the minute portion Δz from the coordinate z in the longitudinal direction between the signal beam input end (z=0) and the output end (z=L) of the EDF  50 . An optical power at the time that the signal beam is outputted from the output end position of the EDF  50  can be finally calculated. 
   Namely, since an optical power after amplified by the EDF  50  at each signal beam wavelength can be obtained through the arithmetic process of the equations (2) and (3), the gain deviation gain characteristic of each signal wavelength of the EDF  50  can be calculated from the input signal beam power and the optical power at each signal beam wavelength calculated as above. 
   Next, description will be made of a structure for simulating the gain deviation characteristic of the EDFA caused by SHB according to the above principle on the basis of basic data of the EDFA and information on the input signal beam in the amplification medium performance simulation apparatus  1  according to this embodiment. 
   The amplification medium performance simulation apparatus  1  comprises, as shown in  FIG. 1 , an input interface (input IF)  10  such as a keyboard or the like, a storage unit  20  such as a hard disk or a memory, an arithmetic processing unit  30  such as a CPU (Central Processing Unit) or the like, and an output interface  40  such as a display, a printer or the like. 
   The amplification medium performance simulation apparatus  1  is inputted thereto the basic data of an EDFA to be evaluated and information on an input signal beam to be inputted to the EDFA through the input interface  10 , retains the basic data and the input signal beam information in the storage unit  20 , calculates a result of simulation of the performance of the EDFA through an arithmetic process in the arithmetic processing unit  30  using the data stored in the storage unit  20 , and outputs the result through the output interface  40 . 
   The storage unit  20  comprises a basic data retaining unit  21  for retaining the basic data of the EDFA whose characteristic is to be evaluated, and an input signal beam information retaining unit  22  for retaining wavelength values and optical power values of the input signal beam as information on the input signal beam to be inputted to the EDFA whose characteristic is to be evaluated. 
   As the basic data of the EDFA inputted through the above input interface  10  and held in the basic data retaining unit  21 , information or the like on coefficients, constants or known functions specified by the adopted EDFA and used in the arithmetic process by the above arithmetic processing unit  30  can be included, along with the fiber length L and the fiber diameter of the EDFA whose characteristic is to be evaluated. 
   Namely, the gain coefficient g(λ), the absorption coefficient α(λ), the loss l(λ), the population inversion rate n(z), the center wavelength λ in the Gaussian functional equation corresponding to the second hole, the full width half maximums BW i  and BW j  of the respective Gaussian functions, the coefficients c 1  to C 4 , d 1 , d 2,j  and d 3,j  of the depth functions of respective Gaussian functions used in the arithmetic process of the above equations (2) through (5) can be retained in the above basic data retaining unit  21  as the basic data of the EDF  50 . 
   The amplification medium performance simulation apparatus  1  can calculate a change in the gain characteristic caused by SHB in order to cope with a case where a wavelength multiplexed signal beam is inputted to the EDFA. In such case, the input signal beam information retaining unit  22  retains data of each wavelength of the wavelength-multiplexed signal beam, data of the power of the signal beam at each wavelength and the total power of the inputted wavelength-multiplexed signal beam as the input signal beam information. 
   The arithmetic processing unit  30  executes a program stored in the storage unit  20 , and outputs a result of the execution to the output interface  40 , having a function as a simulation executing unit  31 . The function as being the simulation executing unit  31  can be realized by loading the program in a storage medium and executing the program by the arithmetic processing unit  30 . 
   The simulation executing unit  31  approximates and calculates a signal beam power at each signal beam wavelength outputted from the EDFA including a fluctuation in the ion population at the metastable energy level of the EDFA to be evaluated due to input of the input signal beam, by using the contents retained in the basic data retaining unit  21  and the input signal beam information retaining unit  22 , and outputs a result of the calculation as a result of simulation of the performance of the EDFA. 
   The simulation executing unit  31  comprises a population inversion rate change quantity calculating unit  31 - 1 , a signal beam power change calculating unit  31 - 2 , a signal beam power calculating unit  31 - 3 , an uncorrected population inversion rate calculating unit  31 - 4  and an outputting process unit  31 - 5 . 
   The population inversion rate change quantity calculating unit  31 - 1  calculates a quantity of a change in the population inversion rate that can occur due to a fluctuation in the ion population at the metastable energy level of the EDF  50  caused by that the input signal beam is inputted, by using a population inversion rate calculated by the uncorrected population inversion rate calculating unit  31 - 4  to be described later and contents retained in the basic data retaining unit  21  and the input signal beam information retaining unit  22 . 
   In concrete, the population inversion rate change quantity calculating unit  31 - 1  calculates a quantity of a change in the population inversion rate as a function of a wavelength of the input signal beam and a coordinate in the longitudinal direction of the EDF  50  through an arithmetic operation using at least one or more wavelength functions having a mountain- or valley-like shape having a center wavelength and a width. 
   The signal power change calculating unit  31 - 2  calculates a change in the optical power of a signal beam propagating in the EDF  50  from the signal beam input end in the EDF  50  within each of minute propagation ranges started from the signal beam input end and terminated at the signal beam output end as a unit, by using a differential equation defined by a quantity of a change in the population inversion rate calculated by the population inversion rate change quantity calculating unit  31 - 1  and the contents retained in the basic data retaining unit  21  and the input signal beam information retaining unit  22 . 
   The signal beam power change calculating unit  31 - 2  obtains coefficient data or constant data in the above equation (2) by using the contents retained in the basic data retaining unit  21  and the input signal beam information retaining unit  22 , thereby calculating a change in the optical power of the signal beam propagating at a position with the coordinate z in the longitudinal direction of the EDF  50 . 
   The population inversion rate change quantity calculating unit  31 - 1  obtains coefficient data or constant data in the above equations (3) to (5) by using the contents retained in the basic data retaining unit  21  and the input signal beam information retaining unit  22 , thereby calculating a change quantity Δn SHB (λ,z) of the population inversion rate to be used in calculation by the above signal power change calculating unit  31 - 2 . 
   Namely, the population inversion rate change quantity calculating unit  31 - 1  for calculating a quantity of a change in the population inversion rate comprises a first function arithmetic unit  311  for operating the first term in the equation (3) as the first function having the first wavelength band (signal beam wavelength band) in the gain saturated state as the center, a second function arithmetic unit  312  for operating the second term in the equation (3) as the second function comprised of a function having the second wavelength band (1530 nm band) characteristic of the EDFA, and an adding unit  313  for adding results of calculation by the first function arithmetic unit  311  and the second function arithmetic unit  312 . 
   The first function operated by the first function arithmetic unit  311  is composed of a total of Gaussian functions given according to respective wavelengths λ i  of the input signal beam, whereas the second function operated by the second function arithmetic unit  312  is composed of a total of a plurality [j in the equation (3)] of Gaussian functions. 
   The Gaussian function given according to a wavelength of the input signal beam in the first function is determined as a value in terms of a wavelength λ i  of the input signal beam as the center wavelength and a full width half maximum BW i  according to the EDFA. Each of the Gaussian functions configuring the second function is determined as a value in terms of the second wavelength band (1530 nm band) characteristic of the amplification medium as the center wavelength and a full width half maximum BW j  according to the EDFA. The full width half maximums BW i  and BW j  in the first function and the second function are retained in the basic data retaining unit  21 . 
   The depth of each of the Gaussian functions in the first function is defined by a depth function C [refer to the equation (4)] which increases as the total power of the input signal increases, and saturates above a fixed value. Similarly, the depth of each of the Gaussian functions in the second function is defined by a depth function D [refer to equation (5)] which increases as the total power of the input signal beam increases, and saturates above a fixed value. 
   Namely, the depth function in each Gaussian function given according to a wavelength of the input signal beam in the first function is defined by a function having a wavelength λ i  of the input signal beam, an optical power P i (z) at a position with a coordinate z in the longitudinal direction of the EDFA at the wavelength λ i  of the input signal beam, and a total power P total (z) of the signal beam propagating at a position with the coordinate z in the longitudinal direction of the EDFA as variables, as shown in the above equation (4). 
   The depth function in each Gaussian function in the second function is defined by a function having a wavelength λ j  in the second wavelength band, a total power P total (z) of the signal beam propagating at a position with the coordinate z in the longitudinal direction of the EDFA, and a population inversion rate n(z) of the EDFA as variables, as shown in the above equation (5). 
   The signal beam power calculating unit  31 - 3  adds, in order, changes in the optical power within respective minute ranges calculated by the signal power change calculating unit  31 - 2  to a power value of the input signal beam retained in the input signal beam information retaining unit  22 , from the input end of the signal beam as the starting point and to the output end of the signal beam as the terminating point in the EDFA, thereby calculating a signal beam power according to a position with the coordinate z in the longitudinal direction of the signal beam propagating in the EDFA, which involves a fluctuation in the ion population at the metastable energy level in the EDFA due to input of the input signal beam. 
   The uncorrected population inversion rate calculating unit  31 - 4  calculates, as an uncorrected population inversion rate, a population inversion rate n (z) not added thereto a fluctuation in the ion population at the metastable energy level in the EDFA to be used when a change in the optical power is calculated. In concrete, the uncorrected population inversion rate calculating unit  31 - 4  calculates a population inversion rate n(z) by using an equation of n(z) retained in the basic data retaining unit  21 , on the basis of a signal beam power according to a position with a coordinate in the longitudinal direction of the signal beam propagating in the EDFA calculated by the above signal beam power calculating unit  31 - 3 . 
   The signal beam power change calculating unit  31 - 2  calculates a minute change dP(z)/dz of the optical power in each minute unit of the length with respect to the longitudinal direction of the EDFA by using the above equation (2), on the basis of a population inversion rate n(z) calculated by the uncorrected inversion rate calculating unit  31 - 4 , a quantity of a change Δn SHB (λ,z) in the population inversion rate calculated by the population inversion rate change quantity calculating unit  31 - 1  and the above basic data retained in the basic data retaining unit  21 . 
   The outputting process unit  31 - 5  outputs a result of calculation of the signal beam power outputted from the signal beam output end in the EDFA calculated by the signal beam power calculating unit  31 - 3  as a result of simulation of the performance of the EDFA. 
   Next, description will be made of an operation of the amplification medium performance simulation apparatus  1  with the above structure according to the first embodiment of this invention with reference to a flowchart shown in  FIG. 4 . 
   First, the above basic data of the EDFA and data (wavelength data and an input signal beam powers) relating to the input signal beam are obtained as input parameters through the input interface  10  (step S 1 ). The basic data of the EDFA is retained in the basic data retaining unit  21 , whereas the input signal beam data is retained in the input signal beam information retaining unit  22 . 
   Next, at a population inversion rate change quantity calculating step, a quantity of a change Δn SHB (λ,z) in the population inversion rate caused by a fluctuation in the ion population at the metastable energy level of the EDFA due to input of the signal beam is calculated. 
   The uncorrected population inversion rate calculating unit  31 - 4  calculates n(z=0) as the uncorrected population inversion rate at the signal beam input end in the EDF  50  on the basis of the input signal beam information retained in the input signal beam information retaining unit  22 . 
   The population inversion rate change quantity calculating unit  31 - 1  calculates a value of Δn SHB  (λ, 0) by using the above equation (3) on the basis of the data together with the above n(n=0) retained in the basic data retaining unit  21  and the input signal beam information retaining unit  22 . 
   At an optical power change calculating step, a change in optical power of the signal beam propagating in the amplification medium from the signal beam input end of the EDFA in each minute propagation range is calculated, from the signal beam input end as the starting point to the signal beam output end as the terminating point, by using a propagation equation of the EDFA on the basis of the corrected population inversion rate corrected with a change quantity of the population inversion rate calculated at the population inversion rate quantity calculating step. 
   In concrete, at an optical power change calculating step, the signal beam power change calculating unit  31 - 2  calculates a minute change in the optical power at the time that the signal beam propagates through a position of a minute portion Δz at the signal beam input end of the EDF  50  by using the equation (2) on the basis of Δn SHB (λ, 0) calculated by the population inversion rate change quantity calculating unit  31 - 1  along with a value of n(z=0) calculated by the uncorrected population inversion rate calculating unit  31 - 4  (steps S 2  and S 3 ). 
   At an output signal beam power calculating step, changes in the optical power within respective minute propagation ranges calculated at the optical power change calculating step are added to the power value of the input signal beam in order from the signal beam input end as the starting point to the signal beam output end as the terminating point, whereby an output signal beam power outputted from the EDFA which involves a fluctuation in the ion population at the metastable energy level in the amplification medium due to input of the input signal beam is calculated. 
   Namely, the signal optical power calculating unit  31 - 3  adds a minute change in the optical power calculated as above to the input signal optical power P i (0) to obtain a signal beam power P i (Δz) propagating at a position of the position Δz (step S 4 ). 
   A change in the optical power in the case where the signal beam further propagates from a position with the coordinate z=Δz in the longitudinal direction of the EDF  50  by a minute portion Δz can be calculated after A n SHB (λ, Δz) is calculated in a similar manner to the above. By repeating the above calculation, it is possible to calculate a change in the optical power in each minute propagation range Δz from the signal beam input end (z=0) to the output end (z=L) of the EDF  50  (from NO route at step S 5  to step S 3 ). 
   At an outputting process step, a result of calculation calculated at the output signal beam power calculating step is outputted as a result of simulation of the performance of the EDFA. Namely, when the signal beam power calculating unit  31 - 3  obtains an optical power at the time that the signal beam is outputted from the output end position of the EDF  50 , the output processing unit  31 - 5  outputs the optical power at the time that the signal beam is outputted from the output end as a result of simulation of the output characteristic of the EDFA (step S 6 ). 
   The simulation executing unit  31  can output a result of the simulation as dependency of the gain deviation on a wavelength spectrum according to the input signal beam power from a relationship between a signal beam power at the time that the signal beam is inputted to the EDFA and a signal beam power at the time that the signal beam is outputted from the EDFA at each optical wavelength, or output it as dependency of the gain deviation on a wavelength spectrum according to a saturation signal wavelength, or output it as dependency of the gain deviation on a wavelength spectrum according to a gain value which is a target (target value) of the automatic gain control. 
     FIGS. 5 through 7  are diagrams in which results (calculated values) of simulation obtained by carrying out simulation by the simulation executing unit  31  is compared with measured values (experimental values) obtained in experiments. 
     FIG. 5  shows dependency of gain deviation on a wavelength spectrum according to an input signal beam power. In  FIG. 5 , “♦” represents experimental values obtained when the input signal beam power is 2.3 dBm, “□” represents experimental values obtained when the input signal beam power is 0 dBm, “▪” represents experimental values obtained when the input signal beam power is −5 dBm, “X” represents experimental values obtained when the input signal beam power is −10 dBm, and “⋄” represents experimental values obtained when the input signal beam power is −15 dBm. Solid lines represent results of simulation with input signal beam powers corresponding to the respective experimental values. 
     FIG. 6  shows dependency of gain deviation on a wavelength spectrum according to a saturation signal wavelength. In  FIG. 6 , “♦” represents experimental values obtained when the saturation signal wavelength is 1529.7 nm, “⋄” represents experimental values obtained when the saturation signal wavelength is 1534.7 nm, “X” represents experimental values obtained when the saturation signal wavelength is 1536.7 nm, “▪” represents experimental values obtained when the saturation signal wavelength is 1540.7 nm, “□” represents experimental values obtained when the saturation signal wavelength is 1544.7 nm, and “●” represents experimental values obtained when the saturation signal wavelength is 1549.7 nm. Solid lines show results of simulation with input signal optical powers corresponding to the respective experimental values. 
     FIG. 7  shows dependency of gain deviation on a wavelength spectrum according to a gain value to be targeted in the automatic gain control. In  FIG. 7 , “♦” represents experimental values obtained when the target in the automatic gain control is 20 dB, “□” represents experimental values obtained when the target in the automatic gain control is 25 dB, and ““▾” represents experimental values obtained when the target in the automatic gain control is 29.5 dB. Solid lines show results of simulation with input signal beam powers corresponding to the respective experimental values. 
   From the results of simulation shown in  FIGS. 5 through 7 , it can be confirmed that the amplification medium performance simulation apparatus  1  according to this embodiment can accurately calculate a gain fluctuation due to SHB. Accordingly, it becomes possible to largely improve the accuracy of gain flatness of an optical repeater by designing the input/output power of the EDFA or the gain equalization characteristic of the gain equalizer on the basis of the results of simulation. 
   In the amplification medium simulation apparatus according to the first embodiment of this invention, the simulation executing unit  31  can output gain deviation occurring due to a fluctuation in ion population at the metastable energy level in each minute unit of the length in the longitudinal direction of the amplification medium, which involves gain deviation in an area other than the vicinity of the signal wave, in a process within a short period of time by introducing a simple approximation equation. 
   (b) Description of Second Embodiment 
     FIG. 8  is a block diagram showing an optical amplifier  60  according to a second embodiment of this invention. In  FIG. 8 , reference numeral  61  denotes a pumping source outputting a pumping beam,  62  denotes an EDFA as being a signal beam amplification medium excited by a pump beam from the pumping source  61  to amplify an input signal beam, and  63  denotes a gain equalizer equalizing the gain of an output signal beam outputted from the EDFA  62 . 
   The gain equalizer  63  is so designed as to compensate the gain deviation due to a fluctuation in the ion population at the metastable energy level in the EDFA  62  caused by input of the input signal beam, on the basis of a result of simulation fed from the simulation executing unit  31  of an amplification medium performance simulation apparatus  1  similar to that according to the above first embodiment. 
     FIG. 9  is a diagram for illustrating the gain equalization characteristic of the gain equalizer  63  disposed in the following stage of the EDFA  62  shown in  FIG. 8 . In  FIG. 9 , broken line denotes the gain equalization characteristic of a gain equalizer designed on the basis of the gain deviation characteristic obtained in the amplification medium performance simulation apparatus  1  according to the above first embodiment, solid line denotes the gain equalization characteristic of a gain equalizer when the gain characteristic of the EDFA is approximated to be of a single band. 
   From  FIG. 9 , a gain equalizer designed on the basis of the gain deviation characteristic obtained by the amplification medium performance simulation apparatus  1  is expected to be able to compensate gain deviation particularly in the vicinity of 1530 nm. 
   In the optical amplifier  60  according to the second embodiment of this invention, the gain equalization characteristic of the gain equalizer  63  can be designed on the basis of a result of highly accurate simulation obtained by the simulation executing unit  31  of the amplification medium performance apparatus  1  through a process within a short period of time, whereby a fluctuation in ion population at the metastable energy level in the EDFA  62  due to input of the input signal beam can be compensated. 
   Particularly, in an optical amplifier which is a constitutional element of a node in a photonic network in which allocation of wavelengths of the signal beam may be dynamically changed, it is possible to stabilize the amplification characteristic, coping with a large change in the wavelength allocation and the number of the wavelengths. 
   (c) Description of Third Embodiment 
     FIG. 10  is a block diagram showing an optical amplifier  70 A according to a third embodiment of this invention. In the optical amplifier  70 A shown in  FIG. 10 , reference numeral  71  denotes a pumping source outputting a pump beam,  72  denotes an EDFA as being a signal beam amplification medium excited by a pump beam from the pumping source  71  to amplify the input signal beam,  73  denotes a pumping source controlling unit controlling the pumping source  71 ,  74  denotes a branching coupler branching a part of the signal beam inputted to the EDFA  72 ,  75  denotes a branching coupler branching a part of an output signal beam outputted from the EDFA  72 , and  76  denotes a variable optical attenuator (VOA) variably attenuating the power of the output signal beam from the branching coupler  75 . 
   The pumping source controlling unit  73  controls the pumping source  71  to compensate the gain deviation due to a fluctuation in ion population at the metastable energy level in the EDFA  72  caused by input of the input signal beam. The pumping source controlling unit  73  comprises a photodiode (PD)  73   a , a spectrum analyzer (SAU)  73   b , an automatic gain control unit  73   c  and a correcting unit  73   d.    
   The photodiode  73   a  monitors the power of a signal beam branched by the branching coupler  74 . The spectrum analyzer  73   b  monitors the power of the output signal beam branched by the branching coupler  75  and information about allocation of the signal wavelengths. 
   The photodiode  73   a  and the spectrum analyzer  73   b  together function as a first power monitor for monitoring the powers of the input signal beam and the output signal beam. The spectrum analyzer  73   b  also has a function as a wavelength allocation information obtaining unit for obtaining wavelength allocation information on the signal beam propagating in the EDFA  72  as the amplification medium. 
   The automatic gain control unit  73   c  outputs a signal for controlling the pumping source  71  on the basis of the powers of the input and output signal beams monitored by the photodiode  73   a  and the spectrum analyzer  73   b  as the first power monitoring unit so that the gain is constant. 
   The correcting unit  73   d  corrects a control quantity for the pumping source  71  in the automatic gain control unit  73   c  on the basis of the wavelength allocation information obtained by the spectrum analyzer  73   b  so that gain deviation in the wavelength band due to spectral hole burning decreases. 
   For example, the correcting unit  73   d  has a table  73   d - 1  for retaining pump beam control information for decreasing the gain deviation obtained on the basis of a result of execution of simulation in the amplification medium performance simulation apparatus  1  according to the above first embodiment, and a retrieving unit  73   d - 2  for retrieving in the table  73   d - 1  with the signal beam wavelength allocation information, information on the power ratio (gain) of the input signal beam power to the output signal beam power and the output power as keys, and taking out the pump beam control information for decreasing the gain deviation according to the signal beam wavelength allocation. 
   Namely, the correcting unit  73   d  gives the pump beam control information retrieved by the retrieving unit  73   d - 2  to the automatic gain control unit  73   c  to correct the control quantity for the pumping source  71  in the automatic gain control unit  73   c.    
   With the above structure, the optical amplifier  70 A according to the third embodiment controls the pump beam from the pumping source  71  to compensate the gain deviation due to SHB, as shown in  FIG. 12 . 
   The automatic gain control unit  73   c  in the pumping source controlling unit  73  obtains wavelength allocation information on a signal beam along with an input signal beam power and an output signal beam power from the photodiode  73   a  and the spectrum analyzer  73   b  (step A 1 ), calculates the gain state of the EDFA  72  from the obtained data, and determines a target value for the output power so as to obtain a predetermined gain under the automatic gain control. 
   At this time, the correcting unit  73   d  receives the signal allocation information, gain information and a monitor value of the output power from the automatic gain control unit  73   c , and retrieves in the above table to determine on the basis of these values whether or not it is necessary to correct a fluctuation in gain due to SHB. When correction of SHB is necessary, the correcting unit  73   d  determines a correction quantity to be added to the target value of the output power on the basis of the signal allocation information, the gain and the output power (step A 2 ). 
   The automatic gain control unit  73   c  receives the correction value for the pump beam control determined by the correcting unit  73   d  to determine an output power to be targeted in the pump beam control. The automatic gain control unit  73   c  outputs a signal for controlling the intensity or the like of the pump beam supplied from the pumping source  71  so that the output signal beam power monitored by the spectrum analyzer  75  reaches the target value. 
   Since the output power of the EDFA  72  increases or decreases from an initially desired value when the correcting unit  73   d  corrects the pump beam control quantity to compensate the fluctuation in gain due to SHB, the VOA  76  controls the loss value so as to obtain the desired output power (step A 3 ). 
     FIGS. 13 through 18  are diagrams for illustrating a working effect given by superimposing correction of a fluctuation in gain due to SHB on the optical amplifier automatic gain control as above in the optical amplifier  70 A according to the third embodiment. 
   In an optical communication system having such high freedom that the wavelength allocation is dynamically changed, a local fluctuation in gain due to SHB occurs, which leads to an error between the gain wavelength characteristic of the EDFA and the characteristic of the gain equalizer. At this time, when the optical amplifier is operated under the automatic gain control with a pump power P AGC , a gain deviation of ΔG occurs due to SHB. The optical amplifier  70 A according to the third embodiment adds a change quantity ΔP SHB  of the pump power corresponding to the correction quantity in the correcting unit  73   d  to the pump power P AGC  to vary the population inversion rate in the optical amplifier  73   d , thereby controlling the gain deviation ΔG′ so that ΔG&gt;ΔG′. 
   For example, assuming here that a gain equalizer (GEQ) having such a characteristic that the gain wavelength characteristic for a wavelength-multiplexed signal beam of 40 channels becomes flat is inserted into the following stage of the EDFA  72 , as shown in  FIG. 13 . At this time, the gain equalizer has a loss characteristic as shown in  FIG. 14 . In  FIG. 13 , the gain characteristic obtained when the gain equalizer is inserted is denoted by A (with GEQ), whereas the gain characteristic obtained when the gain equalizer is not inserted is denoted by B (without GEQ). 
   As an example where the wavelengths are concentrated in longer wavelengths in the allocation, assuming that a wavelength-multiplexed signal beam having a wavelength allocation in which one channel (wavelength of 1533.5 nm) is arranged at a shorter wavelength and eight channels (1555–1560.6 nm) are arranged at longer wavelengths is inputted to the EDFA  72 , and the pump beam is so controlled that the average gain becomes constant under the automatic gain control by the automatic gain control unit  73   c.    
   When the automatic gain control unit  73   c  performs only the automatic gain control, the pumping source  71  supplies a pump beam having, for example, a co-propagating pump beam of 53 mW and a counter-propagating pump beam of 32 mW to the EDFA  72 .  FIG. 15  is a diagram showing the gain wavelength characteristic of the signal beam in each of the wavelength allocations in the case where the above automatic gain control unit  73   c  performs only the automatic gain control on the EDFA in which the signal beam having the above wavelength allocation propagates. 
   As the gain wavelength characteristic (refer to “♦” in  FIG. 15 ) denoted by C in  FIG. 15  at the time that 40 channels were amplified, the gain deviation was 0.03 dB between the channels. As the gain wavelength characteristic (refer to “▪” in  FIG. 15 ) at the time of amplification denoted by D (one channel at the shorter wavelength and eight channels at the longer wavelengths) in  FIG. 15 , the gain deviation was 0.51 dB. As this, it is found that it is difficult to sufficiently decrease the gain deviation by the automatic gain control. 
   For this, the correcting unit  73   d  controls the pumping source  71  with a control quantity corrected by using a correction quantity according to the wavelength allocation of the signal beam wavelengths and the optical output power, thereby decreasing the counter-propagating pump power from the pumping source  71  from 32 mW to 21 mW. By doing so, it is possible to largely compensate the gain deviation to about 0.09 dB although the average gain of the signal beam decreases, as denoted by D′ (refer to “▪” in  FIG. 16 ) in  FIG. 16 , for example. Incidentally, the decreased average gain of the EDFA  72  is interpolated by decreasing the loss quantity in the variable optical attenuator  76  (refer to “▾” of D″ in  FIG. 16 ). 
   Likewise, as an example where the wavelengths are concentrated in shorter wavelengths in the allocation, assuming that a wavelength-multiplexed signal beam having a wavelength allocation in which four channels (1529.6–1531.9 nm) are arranged at shorter wavelengths and one channel (1556.6 nm) is arranged at a longer wavelength is inputted, and the pump beam is so controlled that the average gain is constant under the automatic gain control by the automatic gain control unit  73   c.    
   When the automatic gain control unit  73   c  performs only the automatic gain control, the pumping source  71  supplies a pump beam having a co-propagating pump beam having a pump power of 81.3 mW and a counter-propagating pump beam having a pump power of 0 mW to the EDFA  72 , for example.  FIG. 17  is a diagram showing the gain wavelength characteristic of the signal beam in the above wavelength allocation in the case where the above automatic gain control unit  73   c  performs only the automatic gain control on the EDFA  72  in which the signal beam in the above wavelength allocation propagates. 
   As the gain wavelength characteristic (refer to “♦” in  FIG. 17 ) denoted by C in  FIG. 17  obtained when 40 channels were amplified, the gain deviation was 0.03 dB among the channels. As the gain wavelength characteristic (refer to “▪” in  FIG. 17 ) at the time of amplification denoted by E (four channels at the shorter wavelengths and one channel at the longer wavelength) in  FIG. 17 , the gain deviation was 0.5 dB. As this, it is found that it is difficult to sufficiently decrease the gain deviation by the automatic gain control. 
   For this, the correcting unit  73   d  controls the pumping source  71  with a control quantity corrected by using a correction quantity according to the wavelength allocation of the signal beam wavelengths and the optical output power, thereby increasing the counter-propagating pump power from the pumping source  71  from 0 mW to 15 mW. By doing so, it is possible to largely compensate the gain deviation to about 0.11 dB although the average gain of the signal beam increases, as denoted by E′ (refer to “▪” in  FIG. 18 ) in  FIG. 18 , for example. Incidentally, the increased average gain of the EDFA  72  is interpolated by increasing the loss quantity in the variable optical attenuator  76  (refer to “▾” on E” in  FIG. 18 ). 
   In the above description, the counter-propagating pump power is corrected to decrease the gain deviation. However, the pump power to be adjusted may be the co-propagating pump power, or both the copropating pump power and the counter-propagating pump power. 
   As above, in the optical amplifier  70 A according to the third embodiment of this invention, the pumping source controlling unit  73  can control the pumping source  71  on the basis of a result of highly accurate simulation obtained by the simulation executing unit  31  in the amplification medium performance simulation apparatus  1  through a process within a short period of time so that the gain deviation due to a fluctuation in ion population at the metastable energy level in the EDFA  72  is compensated. Accordingly it is possible to greatly improve the stability of the automatic gain control. 
   Particularly, in an optical amplifier which is a constitutional element in a node in a photonic network in which the wavelength allocation of a signal beam are dynamically changed, it is possible to stabilize the amplification characteristic, coping with a large change in the wavelength allocation and the number of wavelengths. 
   As a modification of the third embodiment, as in the optical amplifier  70 B shown in  FIG. 11 , the SAU  73   b  may be disposed on the input&#39;s side of the EDFA  72  to obtain the signal allocation information, and the photodiode  73   a  may monitor the power of the output signal beam outputted from the EDFA  72 . 
   (d) Description of Fourth Embodiment 
     FIG. 19  is a block diagram showing an optical amplifier  80  according to a fourth embodiment of this invention. The optical amplifier  80  shown in  FIG. 19  comprises a pumping source  71 , an EDFA  72 , branching couplers  74  and  75 , and a VOA  76 , like the optical amplifier according to the above third embodiment. Unlike the optical amplifier according to the third embodiment, the optical amplifier  80  further comprises a WDM (Wavelength Division Multiplexing) coupler  81  and a pumping source controlling unit  82 . 
   The WDM coupler  81  separates a wavelength of a control signal beam having the wavelength assigned as a control signal from a signal beam of a wavelength-multiplexed beam inputted to the optical amplifier  80 . The control signal is outputted to the pumping source controlling unit  82 , whereas the signal beam is outputted to the branching coupler  74 . 
   The pumping source controlling unit  82  controls the pumping source  71 . The pumping source controlling unit  82  comprises photodiodes (PDs)  82   a  and  82   b , a control signal analyzing unit  82   c , an automatic gain control unit  73   c  and a correcting unit  73   d.    
   The photodiode  82   a  monitors the power of the signal beam branched by the branching coupler  74 . The photodiode  82   b  monitors the power of an output signal beam branched by the branching coupler  75 . Accordingly, the above photodiodes  82   a  and  82   b  together function as a first power monitor for monitoring the powers of the input signal beam and the output signal beam. 
   The control signal analyzing unit  82   c  receives a control signal beam transmitted together with the signal beam by means of a photodiode through the WDM coupler  81 , and analyzes the received signal to take out wavelength allocation information as control information. The control signal analyzing unit  82   c  functions as a wavelength allocation information obtaining unit for obtaining the wavelength allocation information on the signal beam propagating in the EDFA  72  which is an amplification medium. Namely, the control signal analyzing unit  82   c  obtains the wavelength allocation information from the control signal beam transmitted together with the signal beam. 
   The automatic gain control unit  73   c  has a similar function as that according to the above third embodiment. The automatic gain control unit  73   c  outputs a signal for controlling the pumping source  71  on the basis of the powers of the input and output signal beams monitored by the photodiodes  82   a  and  82   b  as being the first power monitor so that the gain is constant. 
   Like the correcting unit  73   d  according to the third embodiment, the correcting unit  73   d  corrects the control quantity for the pumping source  71  in the automatic gain control unit  73   c  on the basis of the wavelength allocation information obtained by the control signal analyzing unit  82   c  so that the gain deviation in the wavelength band due to spectrum hole burning decreases. The correcting unit  73   d  comprises a table  73   d - 1  and a retrieving unit  73   d - 2 . 
   Next, description will be made of an operation of the optical amplifier  80  according to the fourth embodiment with reference to a flowchart in  FIG. 12 . 
   The control signal analyzing unit  82   c  of the pumping source controlling unit  82  obtains the wavelength allocation information on the signal beam from the control signal beam transmitted together with the signal beam, and monitor information on the input/output beam powers from the photodiodes  82   a  and  82   b  (refer to step A 1  in  FIG. 12 ). 
   The automatic gain control unit  73   c  performs the automatic gain control on the basis of results of input/output beam power monitoring by the photodiodes  82   a  and  82   b  (step A 2 ). The correcting unit  73   d  corrects the control quantity from the automatic gain control unit  73   c  for the pumping source  71  on the basis of the wavelength allocation information from the control signal analyzing unit  82   c  and the results of input/output beam power monitoring from the photodiodes  82   a  and  82   b  to compensate the gain deviation due to SHB. Incidentally, the increased or decreased average gain of the EDFA  72  is interpolated by adjusting the loss quantity in the variable optical attenuator  76  (step A 3 ). 
   In the optical amplifier  80  according to the fourth embodiment of this invention, the pumping source controlling unit  82  can control the pumping source  71  on the basis of a result of highly accurate simulation obtained by the simulation executing unit  31  of the amplification medium performance simulation apparatus  1  according to the above first embodiment through a process within a short period of time so that the gain deviation due to a fluctuation in ion population at the metastable energy level in the EDFA  72  is compensated. Thus, it becomes possible to greatly improve the stability of the automatic gain control. 
   Particularly, in an optical amplifier which is a constitutional element in a node in a photonic network in which the wavelength allocation of the signal beam may be dynamically changed, it is possible to stabilize the amplification characteristic, coping with a large change in the wavelength allocation and the number of the wavelength. 
   Further, since the wavelength allocation information obtaining unit can be configured without a spectrum analyzer, it is possible to reduce the apparatus fabrication cost as compared with the optical amplifier  80  according to the third embodiment. 
   (e) Description of Fifth Embodiment 
     FIG. 20  is a block diagram showing an optical amplifier  90  according to a fifth embodiment of this invention. Like the optical amplifier according to the third embodiment, the optical amplifier  90  shown in  FIG. 20  comprises a pumping source  71 , an EDFA  72 , branching couplers  74  and  75 , and a VOA  76 . However, the optical amplifier  90  further comprises a pumping source controlling unit  91  which differs from that according to the third embodiment. 
   The pumping source controlling unit  91  is designed on the basis of a result of simulation obtained by the amplification medium performance simulation apparatus  1  according to the first embodiment to control the EDFA so that the gain deviation due to a fluctuation in ion population at the metastable energy level in the EDFA  72  caused by input of an input signal beam is compensated. Unlike the optical amplifier according to the third and fourth embodiments, the optical amplifier  90  does not have a function as the wavelength allocation information obtaining unit. 
   Namely, the pumping source controlling unit  91  comprises band dividing filters  91   a  and  91   b , photodiodes  91   a - 1 ,  92   a - 2 ,  91   b - 1  and  91   b - 2  and an automatic average gain control unit  91   c.    
   Each of the band dividing filers  91   a  and  91   b  divides a power-branched beam of the signal beam on the input side of the EDFA  72  from the branching coupler  74  or on the output&#39;s side of the EDFA  75  into a plurality (two in the fifth embodiment) of signal beams, whereby the band of the power-branched beam is divided. 
   On the basis of assumption that the gain deviation occurs due to SHB, each of the band dividing filers  91   a  and  91   b  divides the signal beam according to a result of simulation by the amplification medium performance simulation apparatus  1  according to the above first embodiment so that the average gains of the bands are almost equivalent and stable. 
   For example, each of the wavelength dividing filers  91   a  and  91   b  can divide the wavelength band into two as shown in  FIGS. 22 and 23  to be described later. With respect to the gain fluctuation characteristic due to SHB of the EDFA  72  used as the amplification medium, results of simulation of it were obtained by the amplification medium simulation apparatus  1  as shown in above  FIGS. 5 through 7 . From these simulation results, it is found that the effect of SHB on the EDFA  72  is particularly large in the vicinity of 1530 nm. 
   The EDFA  72  is divided into two bands, which are a first band at shorter wavelengths (about 1529–1536 nm) and a second band at longer wavelengths (about 1536–1561 nm), according to the strength of SHB. 
   The photodiodes  91   a - 1  and  91   a - 2  monitor the signal beam powers of the signal beams in two bands divided by the band dividing filter  91   a . Similarly, the photodiodes  91   b - 1  and  91   b - 2  monitor the signal beam powers of the signal beams in two bands divided by the band dividing filter  91   b.    
   For example, the photodiodes  91   a - 1  and  91   b - 1  receive divided signal beams in the above first band, whereas the photodiodes  91   a - 2  and  91   b - 2  receive divided signal beams in the above second band. 
   The above band dividing filters  91   a  and  91   b , and the photodiodes  91   a - 1 ,  91   a - 2 ,  91   b - 1  and  91   b - 2  function together as a second power monitor for obtaining powers of the input signal beam and the output signal beam in the plural bands divided on the basis of a result of simulation obtained by the amplification medium performance simulation apparatus  1 . 
   The automatic average gain control unit  91   c  outputs a signal for controlling the pumping source  71  on the basis of the powers of the input signal beam and the output signal beam in the bands obtained by the photodiodes  91   a - 1 ,  91   a - 2 ,  91   b - 1  and  91   b - 2  so that the average gains in the bands are equivalent. 
   Since the magnitude of a fluctuation in gain caused by SHB differs according to the wavelength in the amplification band, the gain deviation occurs. Accordingly, each of the wavelength dividing filters  91   a  and  91   b  beforehand divides the amplification band of the EDFA  72  into a plurality of bands, and the automatic average gain control unit  91   c  adjusts the pump power so that the average gains of the bands become equal, thereby keeping the flatness of the gain. 
   Next, description will be made of an operation of the optical amplifier  90  according to the fifth embodiment of this invention with reference to a flowchart in  FIG. 21 . 
   The signal beam inputted to the EDFA  72  is branched by the branching coupler  74 , divided into the first band and the second band by the band dividing filter  91   a , and received by the photodiodes  91   a - 1  and the  91   a - 2 . Similarly, the output signal beam outputted from the EDFA  72  is branched by the branching coupler  75 , divided into the first band and the second band by the band dividing filter  91   b , and received by the photodiodes  91   b - 1  and  91   b - 2 . 
   When the automatic average gain controlling unit  91   c  receives signals according to input signal beam powers from the photodiodes  91   a - 1  and  91   a - 2 , and signals according to output signal beam powers from the photodiodes  91   b - 1  and  91   b - 2  (step B 1 ), the automatic average gain control unit  91   c  performs the known automatic gain control on the whole band (step B 2 ). 
   Namely, the automatic average gain control unit  91   c  outputs a control signal for controlling the pumping source  71  on the basis of the input/output signal beams in the first band from the photodiodes  91   a - 1  and  91   b - 1  and the input/output signal beams in the second band from the photodiodes  91   a - 2  and  91   b - 2  so that the gain of the whole band, which is addition of the first band and the second band, is constant. 
   After that, the automatic average gain control unit  91   c  calculates an average gain of each of the first band and the second band divided. When a gain deviation occurs due to the effect of SHB, deviation occurs between the average gains in the first band and the second band. Since the bands are divided according to the strength of SHB, each of the gain deviation in the first band and the gain deviation in the second band is smaller than a calculated gain deviation between the average gains in the divided bands. 
   Thus, the automatic average gain calculating unit  91   c  compares a calculated average gain G 1  in the first band with a calculated average gain G 2  in the second band, and outputs a control signal for increasing or decreasing the pump power in the pumping source  71  according to a result of the comparison. 
   Namely, when the average gain G 1  in the first band is larger than the average gain G 2  in the second band (G 1 &gt;G 2 ), the automatic average gain control unit  91   c  decreases the pump power so that the population inversion rate is small. When G 1  is smaller than G 2  (G 1 &lt;G 2 ), the automatic average gain control unit  91   c  outputs a control signal for increasing the pump power to the pumping source  71  so that the population inversion rate is large (step B 3 ). 
   Accordingly, the population inversion rate becomes smaller or larger under the control for increasing/decreasing the pump beam power from the pumping source  71 , whereby the average gains G 1  and G 2  can be approximately uniform. Incidentally, a fluctuation in gain of the output signal beam due to the pump beam power increasing/decreasing control is compensated by varying the loss quantity in the VOA  76  (step B 4 ). 
     FIGS. 22 and 23  show an example where the gain deviation due to SHB is compensated by controlling the pumping source  71  by the automatic average gain controlling unit  91   c  in the optical amplifier  90  according to the fifth embodiment of this invention. 
     FIG. 22  shows average gains in the both bands calculated by the automatic average gain control unit  91   c  when gain deviation due to SHB occurs because a signal having one channel in the first band BND# 1  at the shorter wavelength and eight channels in the second band BND# 2  at the longer wavelengths is inputted. As shown in  FIG. 22 , the average gain G 1  in the first band BND# 1  is 23.5 dB, the average gain G 2  in the second band BND# 2  is 23 dB, thus a gain deviation of 0.5 dB between the bands generates. 
   Since the average gain in the first band BND# 1  is larger than the average gain in the second band BND# 2  (G 1 &gt;G 2 ), the automatic average gain control unit  91   c  controls the co-propagating pump beam or the counter-propagating pump beam or the both to decrease the same. Whereby, the average gains in both the first band BND# 1  and the second band BND# 2  are almost equivalent as shown in  FIG. 23 , thus the gain deviation due to SHB is corrected. 
   Since the gain obtained after the SHB is corrected is smaller than the desired gain in this case, the loss quantity in the VOA  76  is decreased to compensate the decreased gain. 
   Like the above third and fourth embodiments, in the optical amplifier  90  according to the fifth embodiment, the pumping source controlling unit  91  can control the pumping source  71  on the basis of a result of highly accurate simulation obtained by the simulation executing unit  31  in the amplification medium performance simulation apparatus  1  according to the above first embodiment through a process within a short period of time so that the gain deviation due to a fluctuation in ion population at the metastable energy level in the EDFA  72  is compensated. Accordingly, it is possible to greatly improve the stability of the automatic gain control. 
   Particularly, in an optical amplifier which is a constitutional element of a node in a photonic network in which wavelength allocation of the signal beam may be largely changed, it is possible to stabilize the amplification characteristic, coping with a large change in the wavelength allocation and the number of wavelengths. 
   Unlike the above fourth embodiment, even in a system in which the control signal does not contain the signal allocation information, it is possible to correct the gain deviation due to SHB without an analyzer while decreasing the apparatus fabrication cost. 
   (f) Others 
   Note that the present invention is not limited to the above examples, but may be modified in various ways without departing from the scope of the invention. 
   For example, the amplification medium performance simulation apparatus  1  according to the first embodiment adopts a Gaussian function as shown in the equation (3) in order to calculate the quantity of a change in the population inversion rate due to SHB in the EDFA. However, this invention is not limited to this example. For example, it is alternatively possible to adopt a function having a mountain-like shape having a center wavelength and a width such as a Lorentzian function, Voigt function or the like to form the first function and the second function. 
   In concrete, the Gaussian function [refer to the equation (6)] forming the first function or the Gaussian function [refer to the equation (7)] forming the second function in the equation (3) can be appropriately replaced by a Lorentizian function shown in equation (8) or a Voigt function shown in equation (9). 
                   f   ⁡     (   λ   )       =     exp   ⁡     (       -     ln   ⁡     (   2   )         ⁢         (     λ   -     λ   i       )     2         (       BW   i     /   2     )     2         )               (   6   )                 f   ⁡     (   λ   )       =     exp   ⁡     (       -     ln   ⁡     (   2   )         ⁢     (         (     λ   -     λ   j       )     2         (       BW   j     /   2     )     2       )       )               (   7   )                 f   ⁡     (   λ   )       =       1   π     ⁢     BW         (     λ   -     λ   0       )     2     +     BW   0   2                   (   8   )                   f   ⁡     (   λ   )       =       1     BW   g       ⁢         ln   ⁡     (   2   )       π       ⁢     K   ⁡     (     x   ,   y     )           ⁢     
     ⁢   where   ⁢     
     ⁢             K   ⁡     (     x   ,   y     )       ≡       ⁢       y   π     ⁢       ∫     -   ∞     ∞     ⁢         ⅇ     -     I   2             y   2     +       (     x   -   t     )     2         ⁢           ⁢     ⅆ   t                       y   ≡       ⁢         BW   I       BW   g       ⁢       ln   ⁡     (   2   )                       x   ≡       ⁢         λ   -     λ   0         BW   g       ⁢       ln   ⁡     (   2   )                           (   9   )               
and BW g  is the full width half minimum of the Gaussian function, BW 1  is the full width half minimum of the Lorentzian function and λ 0  is the center wavelength.
 
   In the above embodiments, the gain deviation characteristic of the EDFA is simulated. However, this invention is not limited to this example. The gain deviation due to SHB of an amplification medium other than EDFA may be simulated by executing an operation using at least one or more functions (for example, Gaussian functions) by the simulation executing unit  31  in accordance with the embodiments. 
   Persons skilled in the art can manufacture the invention so long as the embodiments of the present invention are disclosed. 
   INDUSTRIAL APPLICABILITY 
   As described above, the amplification medium performance simulation apparatus according to this invention is useful when the performance of an amplification medium applied when a photonic network is configured, and is particularly suited to perform simulation of the gain deviation characteristic due to SHB of EDFA.