EP1461849A1

EP1461849A1 - Method for modelling optical fiber amplifiers

Info

Publication number: EP1461849A1
Application number: EP02799787A
Authority: EP
Inventors: Razvigor Ossikovski; Patrick Even; Nicolas Tallaron
Original assignee: Highwave Optical Technologies SA
Current assignee: Highwave Optical Technologies SA
Priority date: 2001-12-07
Filing date: 2002-12-06
Publication date: 2004-09-29
Also published as: US7151631B2; US20050068610A1; WO2003049240A8; AU2002364430A1; FR2833416B1; WO2003049240A1; JP2005512332A; FR2833416A1; CA2469591A1

Abstract

The invention concerns a method for modelling an optical fiber amplifier, characterized in that it comprises steps which consist in: establishing (100) speed equations and propagation equations of physical phenomena or effects intervening in an optical fiber amplifier; obtaining (112) accurate analytical solution of the equations of signal propagation in the fiber, discretizing them and interpolating them along the fiber; solving (120) the speed equations previously discretized by injecting therein, the solutions obtained from the propagation equations; delivering (130) the performance parameters of the fiber in terms of amplification.

Description

METHOD OF MODELING FIBER OPTIC AMPLIFIERS

The present invention relates to the optical telecommunications sector, and more particularly to the field of fiber optic amplifiers. More specifically, the present invention relates to a method for modeling optical fiber amplifiers.

The present invention applies in particular to the modeling of double sheath optical fiber amplifiers doped Erbium Ytterbium.

Fiber amplifiers allow fully optical signal amplification, hence their wide use in optical telecommunications. We will usefully refer to documents [1], [2], [3] and [4] on this point.

A possible diagram of a fiber optic amplifier is presented in Figure 1 attached.

In this FIG. 1, a fiber amplifier has been shown diagrammatically, in which there is successively in cascade, from upstream to downstream: at 12 an optical input signal for example of the DWDM type, 14 a coupler for example at 5%, 16 an isolator, 18 an optical pump source, for example at 980 nm, 20 a fiber section for example of the Erbium doped single mode type, 22 an isolator, 24 a GFF section, 26 a multimode optical pump source, for example in the form of a diode, 28 a fiber section, for example of the Ytterbium and Erbium doped type with double sheath, 30 an isolator, 32 a coupler for example at 5% and at 34 the output signal.

The amplifying fiber used 10 can be doped in Er or Yb or co-doped in Er / Yb in order to achieve a higher gain. In the latter case it is often double sheathed (as shown schematically in Figures 2 and 3) and is pumped by one or more multimode laser pumps 26.

Figure 2 corresponds to a first variant of doped double cladding fiber.

More precisely we see on the lower part of Figure 2, a cross section of such a fiber and on the upper part of Figure 2 the index profile of this fiber. It comprises a single-mode core 40 surrounded by a first multimode sheath 42, of index less than that of the heart 40. The first sheath 42 is itself even surrounded by a second sheath 44 having an index lower than the first sheath 42.

Figure 3 corresponds to a second variant of doped double cladding fiber. Again we see on the lower part of Figure 3, a cross section of such a fiber and on the upper part of Figure 3 the corresponding index profile. We find in Figure 3 a fiber which comprises a single-mode core 40 surrounded by a first sheath 42, multimode, of lower index. The first sheath 42 is surrounded by a second sheath 44 having an index lower than the first sheath 42. The fibers of FIGS. 2 and 3 can be doped with Er or Yb or Er and Yb.

Note that according to Figure 2, the first sheath 42 has a circular outline of revolution, while according to Figure 3, the first sheath 42 has a rectangular outline.

The parameters of the fiber amplifier, such as gain, noise figure, flatness of the amplified spectrum, have a direct impact on the performance and quality of the optical link of which the amplifier is a part. Hence the need to be able to design amplifiers with given characteristics and optimize their performance.

There are several known more or less advanced processes dealing with the design of fiber amplifiers.

To the knowledge of the inventor, the existing methods take into account only a limited number of physical effects specific to the co-doped fiber Er / Yb, which can lead to an inaccurate prediction of the performances of the amplifier. Furthermore, the known methods require a significant processing time. The object of the present invention is therefore to propose a new method making it possible to predict the performance, in terms of amplification (in particular gain and noise factor spectra, amplified spontaneous emission, residual pump), of an amplifier including a co fiber. -Er / Yb doping, from the parameters of the fiber used (cross-sections, dopant concentrations, life time, opto-geometric parameters), powers and wavelengths of the pumps and input signals, in steady state stationary. This object is achieved in the context of the present invention by a method which consists in:

. establish the equations for the speeds and the equations for the propagation of the physical phenomena or effects entering the issue in a fiber optic amplifier,. obtain, exact analytical solutions of the equations of propagation of the signals in the fiber, discretize them and carry out their interpolation along the fiber,. solve the equations at speeds previously discretized by injecting into them, solutions obtained from the propagation equations, and. deliver the performance parameters, in terms of amplification, of the fiber. According to another preferred characteristic of the present invention, the resolution of the equations at speeds is obtained by means of numerical and iterative methods of resolution of systems of non-linear equations.

The present invention makes it possible in particular to take into account all the physical effects specific to the amplifying medium, hitherto neglected in existing methods (for example, pairs of Er - Er ions, Er-Yb retro-transfer, conversion of Er ions, absorption by excited state).

Thus, the method according to the present invention makes it possible to design and optimize an optical amplifier with Er / Yb co-doped fiber, taking into account the characteristics of the fiber and of the other components of the amplifier (isolators, couplers, equalizing filters of gain). It also makes it possible to predict the behavior of an existing amplifier in operating modes different from that for which the amplifier was designed. It also makes it possible to optimize the manufacturing processes of Er / Yb co-doped fibers in order to improve their performance. The process according to the present invention is also directly applicable to fibers with single cladding Er / Yb co-doped, as well as fibers doped with Er only (double or single cladding). On the other hand, it supports mono- or multimode pumping in the case of double-clad fibers. Thus, the method according to the present invention constitutes a powerful tool for designing and optimizing fiber amplifiers and fibers alone. The process according to the present invention also allows, with great speed of execution, a faithful and detailed modeling of the medium. amplifier ensuring greater precision than existing processes.

Other characteristics, aims and advantages of the present invention will appear on reading the detailed description which follows, and with reference to the appended drawings, given by way of nonlimiting examples and in which:. FIG. 1 previously described represents the schematic structure of a known fiber optic amplifier,

. FIGS. 2 and 3 previously described represent the cross section and the index profile of two doped fibers usable in the context of the invention,

. FIG. 4 schematically represents the energy levels of the elements Er and Yb in a silica matrix,

. FIG. 5 represents a general flow diagram of the method according to the present invention and

. FIG. 6 represents different curves, respectively resulting from measurements on the one hand and from modeling in accordance with the present invention on the other hand, illustrating the gain of the amplifier as a function of the wavelength. The present invention is based on the following considerations. The particular description which follows relates to the case of an Er doped fiber and

Yb. However, the present invention is not limited to this particular case. It applies for example as well to the case of a fiber doped only with Er or only with Yb or any equivalent doping (single or double cladding with mono- or multimode pumping in the latter case).

The amplifying medium can be described by a given number of energy levels of the elements Er and Yb in the silica matrix (the latter being able to be further doped with P, Al, etc.); as illustrated in Figure 4. The populations of these levels, as well as their interactions, are governed by a system of equations at coupled speeds through the parameters of the fiber (cross sections, time of life, dopant concentrations, opto parameters -géométriques).

The speed equation system is completed by differential propagation equations for each of the signals present in the fiber (input signal, pump, amplified spontaneous emission). The general flow diagram of the modeling method according to the present invention is shown in FIG. 5.

The first step 100 consists in establishing the input parameters and the velocity and propagation equations. The speed equations are initialized on the basis of the parameters specific to the case analyzed, in step 110.

In parallel, in step 112, the formal analytical solutions of the differential propagation equations are uniformly discretized along the fiber and expressed as a function of the populations of the energy levels. The populations of the levels are also uniformly discretized and interpolated between the discretization points, for example by the cubic spline method.

Then the solutions thus obtained for the propagation equations are injected into the speed equations in step 120. Using numerical and iterative methods of solving systems of non-linear equations, the speed equations are solved simultaneously along the fiber compared to the populations of the levels.

The solutions thus obtained provide in step 130 the powers of the different signals. From these powers, we go directly to the desired parameters of the amplifier (gain, noise figure, etc.).

More precisely still, the process in accordance with the present invention is preferably based on the following series of steps and on the equations mentioned in Tables 1 to 8 which follow.

When constituting the velocity and propagation equations, in addition to the main effect of direct energy transfer Yb - Er, account is taken, in the context of the present invention, of a number of typical physical effects of the amplifying medium and likely to influence these performances under certain conditions: 1) absorption by excited state of the pump, 2) upconversion of Er ions, 3) presence of pairs of Er - Er ions, 4) retro-transfer of energy Er -Yb, 5) direct pumping of Er, 6) amplified spontaneous emission of Yb.

More specifically, in the context of the invention, each of these effects can be included or excluded from the model in order to estimate its importance in the amplification process. In addition, in the context of the present invention, an arbitrary combination of effects can be formed.

The input data of the process according to the present invention are: 1) the opto-geometrical parameters of the co-doped fiber (radius of the core, surface of the doped section and of the internal cladding, cut-off frequency), 2) the physical parameters of the fiber (cross sections, time of life of the levels, dopant concentrations, length, linear losses), 3) the effects specific to the amplifying medium (transfer time Yb - Er, retro-transfer time Er - Yb , ion pair rate Er - Er, upconversion coefficient Er, absorption cross sections by excited state), and 4) stationary input signals (powers, wavelengths and directions of pumps, powers and signal wavelengths, multi or single mode absorption of the pump).

The method according to the present invention preferably takes into account, in step 100, the input parameters of the model and the following corresponding physical phenomena. 1. Parameters of the amplifying fiber: a. Opto-geometric parameters Cutoff wavelength λ _c in nm Radius of the heart r in m: a (surface of the heart: m) Surface doped in m ² Multimode surface in m ² b. Physical parameters Length L in m Linear signal / pump losses l _s I l _p in dB / m

Er N _E concentration in m ^'3

Concentration in Yb Ny in m ^"

Lifetime Er T _E in s

Life time Yb τyen s Life time unstable level Er τ ₃₂ in 5

Absorption / emission spectral cross sections Er σ _a ^E I σ _e ^E in m ² Absorption / emission spectral cross sections Yb σ „I σ _e in m ESA cross section (absorption by excited state) pump σ _a ^ESA in m ² Transfer time Yb - Er τ _tr in s Retro-transfer time Er - Yb τ en s Rate of Er ion pairs

Up-conversion coefficient C _EE (OU) in m ³ / s

2. Amplifier parameters

Input signal: powers in mW I wavelengths in nm Co-propagating pump: powers in mW / wavelengths in nm Counter-propagating pump: powers in mW / wavelengths in nm Fiber input losses in dB Fiber output losses in dB Chromatic losses in dB (gain equalizer filter)

3. Control parameters (flags with value 0 or 1) a. Pumping

Co-propagative pumping

Counter propagative pumping

Mono / multimode pumping b. Physical phenomena Presence of Er ion pairs

Taking into account the ASE (amplified spontaneous emission) Yb

Consideration of direct pumping Er

Consideration of retro-transfer

Presence of up-conversion Presence of ESA (absorption by excited state) pump

The vast majority of the parameters cited enter directly ("as is") in the equations for speeds, propagation and expressions of gains (cf.

Tables 1, 2 and 3). The surface of the heart noted a in table 1 corresponds to the expression m- ² in the notations above. The recovery factor r encountered in the expressions of the gains (cf. table 3) is estimated as the simple Sdop / Smult ratio in the case of multimode propagation; in the single mode case it is calculated according to the “classic” formula from the cut-off frequency λ _c and the spectral range of interest. The signal flows F (pump, useful signal, amplified spontaneous emission Er and Yb) propagating in the fiber (cf. tables 1 and 2) are calculated by direct conversion of the corresponding powers into the number of photons per second.

Table 1 explains the system of equations at speeds taken into account in step 110, governing the populations of the quantum levels of the amplifying medium Er - Yb. These are therefore the main equations of the phenomenon, the unknowns being the populations along the fiber. There are as many equations as there are inversions of unknown populations: “ ₃ ', excited level Yb; ni, unstable level Er; 11 ₂ , metastable level Er; n ₂ ', excited level of Er ion pairs. Table 1: EQUATIONS AT SPEEDS 1. Ytterbium: excited level (population inversion n ' ₃ )

Sp ^YF _P ⁺ ASE ^F ASE ⁺ W ^{Y dv +} ^ ^N Y ^{a +}

I 1 1 1 end (1 - Tl - U) fi (1 - U.) (1 - ")" o

₊ _3 ^ 2 _{N + 2k} _ LN _a ~ 213_tf _y α = 0

{l + 2k) τ _tr Y (+ 2k) τ _tr Y (X + 2k) τ _bt ^Y 2. Erbium: unstable level (population inversion " ₃ ) ⁿ 3 ΛT" 3 G - "2 - ⁿ 3) _{N a +} (l - »3 * 3 ^r 32 (l + 2k) τ _tr (l + 2k) τ _bt

3. Erbium: metastable level (population inversion ni): g, F, + hg _ASE FÏs _E + 4β ^E ) dv + ^ N _E a - ^ N _E a + C _EE NÎnîa = 0

^JT E ^T 32 4. Erbium: ion pair level (population inversion n ₂ ):

The quantities F entering into the equations at the speeds represent the number of photons per second (the fluxes) of the signals propagating along the fiber: pump (co- and counter-propagative), “useful” signal, ASE (spontaneous emission amplified, co- and counter-propagative).

Their evolution is governed by the propagation equations, given in table 2. The variable z marks the position along the fiber, 0 <z ≤ L, L being its length. Table 2: PROPAGATION EQUATIONS

Pump propagation (co- and counter-propagative): dF ^± ± - ^~ - = (gp + _p ^Y - a _ES A ^{~ l} p ^F P

Signal propagation: dK s E dz = teï -W

ASE propagation (amplified spontaneous, co- and counter-propagative emission):

az The different gains g- participating in the velocity equations and the propagation equations are expressed in table 3 through the population inversions (ntfz) and the physical parameters of the fiber: absorption and emission cross sections σ _e and σ _a as a function of the wavelength (for Er and Yb), dopant concentrations Er and Yb, N _E and Ny, overlap factor F. For the pump signal, the latter depends on the mode of propagation in the fiber: mono- or multimode (the amplified signal always propagating in monomode).

Table 3: EXPRESSIONS OF EARNINGS

Gain: pump, signal, ASE (amplified spontaneous emission): g = [(σ _e + σ _a ) n -σ _a ] NT Gain: ion pairs Er: g ^pr = [(σ + 2σ K - 2σξ] N _E T

ESA absorption (absorption by excited state): ^a ESA = ^ a ^SΛn 2 ^N E ^T

Source term ASE (amplified spontaneous emission): β = σ _e nNT The propagation equations (mentioned in table 2) represent ordinary linear differential equations with respect to the fluxes F; they can therefore be resolved analytically, in step 112, with respect to the flows, as indicated in table 4.

Table 4: ANALYTICAL SOLUTIONS OF THE PROPAGATION EQUATIONS Pump propagation (co- and counter-propagative): z L

\ g _p dx \ g _p dx

F; {z) = F; ) e ^» F- {z) = F ^~ (L) e *

Signal propagation: z

\ g _s dx

F _s (z) = F _s (0) e °

ASE propagation (amplified spontaneous, co- and counter-propagative emission):

F ⁺ _SE (z)

Consequently, after injection of these formal solutions into the speed equations, in step 120 a system of non-linear functional equations is obtained for determining the inversions of unknown population nι (z).

To avoid the problems of analytical resolution of a system of functional equations, in the context of the present invention, the fiber is discretized along its length in M points, for example equidistant (the equi distance is not required in general) and we replace the unknown functions n _{ (z) by the vectors ni (z _{/ ς} ), k = 1, 2, ..., M, with M unknown components. In this way, we obtain a system of non-linear equations with 4 x M unknowns. This is the collocation method, summarized in Table 5.

Table 5: METHOD OF COLLOCATIONS

/, (*; ", (*)) = O / _/ (**; ** (**)) = k = 1,2, ..., M

The analytical solutions of the propagation equations are then discretized in M points along the fiber, as shown in the table. 6. Table 6: DISCRETISATION OF SOLUTIONS OF EQUATIONS OF

SPREAD

Pump propagation (co- and counter-propagative): ^Z A- + 1 * k + l

\ g _p dx \ g _p dx (z _{k +} ι = ^ _{/ c} ) * ^zk F ^~ (z _k ) = F _p - {z _{k + l} ) e *

Signal propagation:

^Z A + 1

\ g _s dx

F _s {^ ι) = F _s {z _k ) e - Propagation ASE (amplified spontaneous emission, co- and counter-propagative):

^z k

F2 _SE M = F _SE (z _{k + 1} ) e ^ + 2 J? E ^z * tfx

However, before substituting them in the equations for velocities, the integrals on z, taken between z * and appearing therein are determined explicitly, or at least approximately. For this purpose, and in order to improve the approximation of the integrals, we apply for example the cubic spline interpolation method.

This method consists in connecting the M points nfak) for an inversion given i by cubic polynomials having their first and second derivatives continuous in these points. The method is formally summarized in Table 7 where the functions Fi and ₂ make it possible to calculate the first and second derivatives of the spline, x ^ and X _k ", given the functional values X _k , k = 1, 2, ... , M. The application of this method on population inversions n _t (z) amounts to interpolating their form (by cubic polynomial, in this case) between the discretization points z *.

Table 7: CUBIC SPLINE METHOD

By applying spline interpolation, the integrals taken between two successive points z * and Z _{k +} j can be calculated with very good precision. In the case of the integrals of the gains g the calculation is exact (for a cubic polynomial) and the formula is given in table 8. The passage of the gains g in inversions n is immediate, the gains being linear functions of inversions (cf. table 3). Regarding the composite integrals appearing as second terms in the expressions of the ASE (cf. table 6), they are approximated by the Simpson formula (parabolic formula). Table 8: RESOLUTION OF THE ENTIRE GAIN

^z k

After substitution of the solutions of the propagation equations in the velocity equations, these are resolved iteratively in step 120 with respect to the four unknown vectors n, (z _k ), i ^~ 1, 2, 3, 4; k = 1, 2, ..., M; cf. table 9.

To do this, we express the inversions n contained in all the gains g appearing as a factor in expressions of type gF; in this way one obtains an iterative diagram compared to the inversions n explained in table 9, second equation.

Table 9: ITERATIVE DIAGRAM Vectors of the unknowns: i = 2, 2 3, 3 '(index of population inversions) "i = Yn _i z _x n _i {z ₁ ..., n _i {z _M \ Simple iterations: m = 0, 1, 2, ... (counter of iterations):

Iterations with relaxation parameter m: n = (l-ω) ^" ° + ωF _i {iii ^{n ) = * r + ω [F _i (n ^) -n ^") ] (0 <ω <\) The methods Numerical resolution of the system of non-linear equations are preferably based on iterative procedures including methods of acceleration of convergence (Aitken process) and of transformation of divergence into convergence (relaxation procedure). Thus in order to accelerate the convergence of this diagram, as well as to convert the divergence into convergence for certain sets of particular physical parameters, one can use a more general iterative diagram, defined by the relaxation parameter m; Fig. 9, third equation. The judicious choice of the parameter m, typically between 0.4 and 0.6, considerably improves the convergence of the iterative process. In parallel with the main iterations, in the context of the present invention, a second iterative process is launched representing a generalization to M dimensions of the Aitken process given in table 10. In practically all cases, this converges more quickly than the main iterative diagram 5, thus making it possible to reduce, sometimes considerably, the execution time.

Table 10: ACCELERATION OF CONVERGENCE Matrix of successive M approximations and its finite differences:

_o ΔN ^} = Ni ^m) - N _k ^{{m ~ l)} Δ ² N> = A (ANl ^m) )

Aitken formula generalized to M dimensions:

The output data preferably include at least: 1) the powers of the signal, of the pumps and of the spontaneous amplified co-and 5 counter-propagative emissions at the fiber end, and 2) the spectral gain and noise figure values in piece of fiber.

It should be noted that, in the context of the present invention, other parameters in addition to those described in 1) and in 2) above, can be calculated and displayed (for example spectral densities of the spontaneous amplified emissions co- and counter propagative).

Thus in the context of the present invention, the output parameters can include:

1. Evolution of the signal power along the fiber / output power

2. Evolution of the pump power (co- or counter-propagating) along the fiber / residual pump power (at the fiber input or output)

3. Accumulation of co-and counter-propagating ASE (amplified spontaneous emission) Er and Yb along the fiber / ASE Er and Yb at the input or output of the fiber

4. Gain spectrum: calculated as the output signal / input signal 0 ratio

5. Noise factor spectrum: calculated from gain and ASE (emission amplified spontaneous) Er at the fiber outlet and

6. Evolution of population inversions along the fiber. The process according to the present invention has been validated by comparison with experience on several types of co-doped fibers. Figure 6 illustrates the agreement of the model with the experiment for a typical Er / Yb co-doped fiber.

Of course the present invention is not limited to the particular embodiment which has just been described, but extends to any variant in accordance with its spirit. In particular, the process according to the present invention can be generalized in the case of a multi-stage amplifier, that is to say an amplifier comprising several stages each comprising a fiber, separated by passive inter-stage losses (chromatic - gain equalizer filter, e.g. - or not). BIBLIOGRAPHY

[1] T. Kasamatsu et al, Appl. Phys. B 69 (1999), 491; F. di Pascuale et al., Proc. OFC, vol. 2 (TEEE, Piscata ay, NJ, 1999), 4 [2] P. R. Morkel, in Opt. Amplifiers Appl. Tech. Dig., Vol. 17 (OSA, Washington, DC, 1992), 206; P. F. Wysocki, in OSA Trends Opt. Photon. Opt. Ampl. Appl. 16 (1997), 46

[3] E. Delevaque et al., IEEE Photonics Technol. Lett. 5 (1993), 73 [4] F. Sanchez et al., Phys. Rev. A 48 (1993), 2220; E. Delevaque, Ph.D. Thesis (University of Lilles, Villeneuve d'Ascq, 1993), 137.

Claims

1. A method of modeling an optical fiber amplifier, characterized in that it comprises the steps which consist in:

. establish (100) the speed equations and the propagation equations for the physical phenomena or effects involved in a fiber optic amplifier,

. obtain (112), exact analytical solutions of the equations of propagation of the signals in the fiber, discretize them and carry out their interpolation along the fiber,. solve (120) the equations at speeds previously discretized by injection into them, solutions obtained from the propagation equations, and. deliver (130) the performance parameters, in terms of amplification, of the fiber.

2. Method according to claim 1, characterized in that the resolution of the equations at speeds is obtained by means of numerical and iterative methods of resolution of systems of non-linear equations.

3. Method according to one of claims 1 or 2, characterized in that it takes into account parameters chosen from the group comprising: pairs of ions, such as Er - Er, direct transfers, such as Yb - Er, retro-transfers, such as Er - Yb, ion conversions, such as Er, absorptions by excited state, direct pumping, such as Er, amplified spontaneous emissions, such as l Yb.

4. Method according to one of claims 1 to 3, characterized in that it takes into account parameters chosen from the group comprising: 1) opto-geometric parameters of the doped fiber, in particular radius of the heart, surface of the doped section and the internal cladding, cut-off frequency, 2) physical parameters of the fiber, in particular cross-sections, time of life of the levels, dopant concentrations, length, linear losses, 3) effects specific to the amplifying medium, in particular transfer time Yb - Er, retro-transfer time Er - Yb, ion pair rate Er - Er, upconversion coefficient Er, cross sections of absorption by excited state, and 4) of the input signals stationary, especially pump powers, wavelengths and directions, signal powers and wavelengths, multi or single mode absorption of the pump.

5. Method according to one of claims 1 to 4, characterized in that the populations of the levels are uniformly discretized and interpolated between the discretization points, for example by a cubic spline method.

6. Method according to one of claims 1 to 5, characterized in that the resolution of the equations at speeds is based on an iterative procedure comprising a method of acceleration of convergence.

7. Method according to claim 6, characterized in that the resolution of the equations at speeds is based on an iterative procedure comprising a method of acceleration of convergence of the Aitken process type.

8. Method according to one of claims 1 to 7, characterized in that the resolution of the equations at the speeds is based on an iterative procedure comprising a method of transforming the divergence into convergence.

9. Method according to one of claims 1 to 8, characterized in that the parameters delivered comprise elements chosen from the group comprising: the powers of the signal, pumps and spontaneous amplified emissions co- and counter-propagative at the end fiber and the gain and noise spectral values at the end of the fiber.

10. Method according to one of claims 1 to 9, characterized in that the parameters delivered comprise elements chosen from the group comprising: the evolution of the signal power along the fiber / output power, the evolution of the pump power (co- or counter-propagative) along the fiber / residual pump power (in fiber input or output), the accumulation of ASE (amplified spontaneous emission) co- and counter propagating Er and Yb along the fiber / ASE Er and Yb at the input or output of the fiber, the gain pecters calculated as the output signal / input signal ratio, the spectrum of the noise factor calculated at from the gain and from the ASE (amplified spontaneous emission) Er at the fiber output and the evolution of population inversions along the fiber.

11. Method according to one of claims 1 to 10, characterized in that it applies to the modeling of an Er or Yb doped fiber amplifier, or Er and Yb.