CN1527119A - Genetic algorithm design of Er-doping fiber and Er-doping fiber amplifier - Google Patents

Abstract

The present invention discloses new design method of Er-doping fiber and Er-doping fiber amplifier. Globally optimized genetic algorithm is adopted, and with signal gain and bandwidth as target function and under different pumping power, Er ion density rate equation of Er-doping fiber amplifier and light propagation equation under single-mode condition are calculated numerically. By means of inversion method, seven optimal parameter values, including Er-doping density, fiber core radius, Er-doping radius, refractive index difference, fiber length, pumping wavelength and signal power, of Er-doping fiber and Er-doping fiber amplifier are determined simultaneously via signal gain and bandwidth values. The present invention relates to the overall configuration of Er-doping fiber and Er-doping fiber amplifier parameters, is suitable for open-looped and stable state operation conditions, and has the features of high single mode and single fiber gain, wide bandwidth, low noise, high efficiency, etc.

Description

With genetic Algorithm Design Er-doped fiber and Erbium-Doped Fiber Amplifier (EDFA)

Foreword

Erbium-Doped Fiber Amplifier (EDFA) (EDFAs) has the very big concern that outstanding advantages such as high-gain, wide bandwidth, low noise, high-level efficiency are subjected to people owing to it.At present, the gain of single fiber EDFA has reached 25～30dB, and-three dB bandwidth has reached～20nm, and noise figure can reach 3～4dB.EDFAs is the critical component of dense wave division multipurpose light communication system, at aspects such as laser, photoswitch, nonlinear optical devices important use is arranged also.

In the design of EDFAs, general by setting up erbium ion population rate equation and the luminous power propagation equation among the EDFAs, at facular model is that Gaussian distribution is approximate or the Bezier distribution is down approximate, numerical solution rate equation and luminous power propagation equation, thereby under given optical fiber, given pumping wavelength and given pump power situation, determine optimum fiber length among the EDFAs etc.Sometimes,, also adopt some approximation methods as a kind of estimation, for example: the light propagation power when equaling pumping threshold power by analytical Calculation output pump power, in conjunction with " optical time domain reflectometry " etc., can roughly determine optimum fiber length etc.The optimum fiber length of Que Dinging etc. is a local like this, and it only is applicable to given optical fiber or a regional area, Er-doped fiber itself and amplifier is not come together to design, and might have the problem of local maximum (little).

In recent years, some global optimization methods have been applied to many fields.Different with traditional gradient algorithm optimization, the global optimization method does not have local maximum (little) problem, and wherein a kind of global optimization method is a genetic algorithm ^[1,2]Genetic algorithm comes from the principle of the natural assortment of genes and natural selection.Because genetic algorithm has advantages such as thought novelty, global search, algorithm are simple, therefore, has obtained in recent years developing than faster and using, and for example is applied to the design of design, photonic crystal and the laser instrument of electromagnetic antenna, or the like.

Given optical fiber is designed Erbium-Doped Fiber Amplifier (EDFA), closely for some years, many theories and experiment report have been arranged.Giles et al. ^[3]A typical EDFA theoretical model has been proposed.In this model, provided in detail in the open cycle system along two energy level erbium ion density rate equations in the power equation of spread fiber and the uniform dielectric, under steady state conditions, numerical solution has been discussed.Roudas et al. ^[4]An EDF model that is applied to dense wave division multipurpose has been discussed.Pan et al. ^[5]Summarized in recent years to low-cost, miniature, intelligent EDFAs progress of research of future generation.Some optimal design and new pump technology also have report (as document [6]).Yet up to now, no matter also do not have report is with genetic algorithm or with the method for other global optimization, designs Er-doped fiber and Erbium-Doped Fiber Amplifier (EDFA) (EDFAs) simultaneously, and most work all only limits to utilize existing optical fiber to design image intensifer.

In patent of the present invention, we disclose a kind of new method that Er-doped fiber and Erbium-Doped Fiber Amplifier (EDFA) (EDFAs) are designed together.This method is used the genetic algorithm of global optimization, with signal gain and bandwidth is objective function, the light propagation equation under erbium ion density rate equation and the single mode condition among the numerical evaluation EDFAs under different pump powers, use the method for inversion, signal gain and bandwidth value by output are oppositely determined Er-doped fiber and 7 required optimum parameter values of amplifier thereof, comprising: concentration of Er, fiber core radius, er-doped radius, refringence, fiber lengths, pumping wavelength and signal power.

The parameter configuration of Er-doped fiber that the present invention relates to and the Erbium-Doped Fiber Amplifier (EDFA) that is made of this kind optical fiber is applicable to open loop, steady-state operation condition, has the advantages that single-mode optics is propagated.Feature is that Er-doped fiber and Erbium-Doped Fiber Amplifier (EDFA) (EDFAs) are designed together, and have single fiber gain high (more than the 35dB), wide bandwidth (greater than 25nm), noise low (～3dB is almost near quantum noise limit), efficient is high.Can be directly used in wavelength-division multiplex or dense wavelength division multiplexing system, other optoelectronic device or the system that also can be applicable to constitute by EDFAs.

● method for designing

Adopt the EDFAs of two-level energy system, it is constant that erbium ion concentration keeps, i.e. n _t≡ n ₁+ n ₂(wherein 1,2 represent the upper and lower energy state of laser respectively), and radial distribution is even.The luminous power P that in EDFAs, propagates during stable state along the z direction _kCan describe by following equation ^[3]:

$\frac{d{P}_k}{\mathrm{dz}}=\frac{a_k+g_k}{{\mathrm{\Γ}}_k}{P}_k\underset{0}{\overset{b}{\∫}}\frac{n_2(r,z)}{n_t}{i}_k\left(r\right)2\mathrm{\πrdr}-(a_k+l_k)P_k+\frac{g_k}{{\mathrm{\Γ}}_k}\mathrm{mh}{v}_k\mathrm{\Δ}{v}_k\underset{0}{\overset{b}{\∫}}\frac{n_2(r,z)}{n_t}{i}_k\left(r\right)2\mathrm{\πrdr},\left(1\right)$

K is a frequency in the formula.If erbium ion radially is evenly distributed among the radius b, then P _kSatisfy

$P_k\left(z\right)=\underset{0}{\overset{b}{\∫}}{I}_k(r,z)2\mathrm{\πrdr},---\left(2\right)$

I wherein _kIt is the light intensity of k frequency.The normalization light intensity can be written as

i _k(r)＝I _k(r，z)/P _k(z). (3)

In equation (1), a _kAnd g _kBe optical fiber absorption coefficient and gain coefficient, they are defined as follows:

${\mathrm{\α}}_k={\mathrm{\σ}}_{\mathrm{ak}}\underset{0}{\overset{b}{\∫}}{i}_k\left(r\right)n_t(r,z)2\mathrm{\πrdr},$

(4)

$g_k={\mathrm{\σ}}_{\mathrm{ek}}\underset{0}{\overset{b}{\∫}}{i}_k\left(r\right)n_t(r,z)2\mathrm{\πrdr},$ σ wherein _Ak, σ _EkBe absorption cross section and radiation cross-section.Overlap integral between er-doped ion and the optical mode is defined as

${\mathrm{\Γ}}_k=\underset{0}{\overset{b}{\∫}}{i}_k\left(r\right)2\mathrm{\πrdr},---\left(5\right)$

Equation (4) can be written as again

a _k＝σ _akΓ _kn _t，

(6)

g _k＝σ _ekΓ _kn _t，

N in the formula _tIt is the erbium ion gross density.For fiber core refractive index n _Core, cladding index n _Clad, fiber core radius is the optical fiber of the step change type of a, basic mode LP ₀₁The normalization light intensity be

$i_k\left(r\right)=\frac{1}{\mathrm{\&pi;}}[\frac{{\mathrm{\&upsi;}}_k}{a{V}_k}\frac{J_0(u_{k}r/a)}{J_1\left(u_k\right)}{]}^2,r<a---\left(7\right)$

J in the formula _0,1Be 0,1 rank Bessel's function, variable υ _k=1.1428V _k-0.9960, $u_k=\sqrt{V_k^2-{\mathrm{\&upsi;}}_k^2}.$ Optical fiber constant V _k=2 π aNA/ λ _k(1≤V _k≤ 3), numerical aperture $\mathrm{NA}=\sqrt{n_{\mathrm{core}}^2-n_{\mathrm{clad}}^2}.$

By separating stable state E _r ³⁺The density equation, the erbium ion density that can obtain in the equation (1) is [3]

$n_2(r,z)=n_t\frac{\underset{k}{\mathrm{\&Sigma;}}\frac{{\mathrm{\&tau;\&sigma;}}_{\mathrm{ak}}}{h{v}_k}{P}_k\left(z\right)i_k\left(r\right)}{1+\underset{k}{\mathrm{\&Sigma;}}\frac{({\mathrm{\&sigma;}}_{\mathrm{ak}}+{\mathrm{\&sigma;}}_{\mathrm{ek}})}{h{v}_k}{P}_{k\left(z\right)}{i}_k\left(r\right)},---\left(8\right)$

τ is the erbium ion metastable state life-span in the formula.In the equation (1), l _kBe other loss in the optical fiber, comprise scattering loss, diffraction loss and other loss of high index of refraction fibre core.Mhv _kΔ v _kBe population, n ₂(wherein modulus m=2 has two polarization states, Δ v corresponding to the lowest-order optical mode for r, the z) contribution of the spontaneous emission noise that is produced _kBe effective noise bandwidth, be defined as ${\mathrm{\&Delta;v}}_k=\mathrm{\&Delta;v}=\underset{0}{\overset{\&infin;}{\&Integral;}}({\mathrm{\&sigma;}}_e\left(v\right)/{\mathrm{\&sigma;}}_{e,\mathrm{peak}})\mathrm{dv}.$ Notice and include 3 independently equations in the equation (1): be respectively about signal and pumping, this moment m=0; About noise, this moment m=2.

Radiation and absorption cross section can adopt the data of Al/P-Si optical fiber ^[7]In addition, also can adopt some other cross sections, for example Ge:Si, Al/Ge-Si ^[3]GeO ₂-SiO ₂ ^[8]By equation (1) as seen, the luminous power of in EDFAs, propagating and 4 optical fiber parameter (concentration of Er n _t, fiber core radius a, er-doped radius b and refractive indices n) and operational factor (fiber lengths L, the pump wavelength of 4 amplifiers _p, initial input signal power P _sWith pump power P _p) relevant.But because signal gain or bandwidth are with pump power P _pDull increase or reduce, thus pump power can be not at the row of optimization.Respectively to P _p=25,50, the pumping situation of 75...200mW is optimized.Objective function in the genetic algorithm is defined as

$f_{\mathrm{obJ}1}=G_c(n_t,a,b,\mathrm{\&Delta;n},L,{\mathrm{\&lambda;}}_p,P_s)10\log \frac{P_s^{\mathrm{out}}}{P_s^{\mathrm{in}}},-----\left(9\right)$

f _ObJ2=Δ λ (n _t, a, b, Δ n, L, λ _p, P _s)+γ G _c(n _t, a, b, Δ n, L, λ _p, P _s). (G _c＞20dB) G in the formula _cBe center signal gain (λ=1550nm), f _ObJ2Be effective bandwidth, it has two: first Δ λ is usually definition-three dB bandwidth, introduces second γ G _cIt is situation appearance for fear of the low gain wide bandwidth.Use different γ values can satisfy different demand to high-gain or wide bandwidth.Here, we select γ=0.02nm/dB.

The hunting zone of 7 EDFA parameters to be optimized of table 1

Erbium ion concentration fiber core radius er-doped radius refringence fiber lengths pumping wavelength signal power

n _t(m ^-3) a(μm) b(μm) Δn L(m) λ _p(nm) P _s(mW)

(1～12.5)×10 ²⁴ 0.2～2.4 0.01～(a-Δ) 0.01～0.46 1～100 1450～1540 0.001～0.1

Annotate: Δ is a number relevant with the random value of fiber core radius.

In program design, with genetic algorithm as master routine, with the dependent equation of EDFA as subroutine.7 parameter (n _t, a, b, Δ n, L, λ _p, P _s) produce by the computer random function, its size (sees Table 1) in scope given in advance.By equation (9) as seen, 7 parameter (n _t, a, b, Δ n, L, λ _p, P _s) after the generation, can determine the target function value of a correspondence.In master routine, according to the rule of genetic algorithm, respectively the chromosome of the different parameters combination size by its target function value is sorted, abandon poor half, half that retain carried out crisscrossing again, forms new chromosome.New chromosome carries out the next round circulation with the good chromosome that remains.Experience chromosome mutation etc. again,, converge to chromosome at last with optimal parameter combination through the circulation in about 30～40 generations.The involved related data of genetic algorithm sees Table 2.

Related data in table 2 genetic algorithm

The chromosome number single cross points is the every gene byte religion of point of crossing sudden change probability cyclic algebra gene number relatively

1,200 0.9 2% 30-40 7 10 at random

In calculating, roughly determine the scope of parameters optimization change earlier according to table 1, then, dwindle the hunting zone, so that make converges faster, and obtain more accurate result.In order to keep single mode propagation,, satisfy single-mode fiber constant condition V (λ all the time to any chromosome and any signal wavelength _s)＜2.4048.Signal wavelength adopts the mode of scanning, from 1450nm to 1650nm, and step-length 2.5nm.Respectively to pump power P _p=25,50,75 ..., the situation of 200mW is calculated.In the initial end of optical fiber z=0, input noise power is 0.05P _s, P wherein _sIt is the signal power of input z=0 end to be optimized, as to have at random size.The refractive index perseverance of fibre core is made as 1.46, and the refractive indices n of covering changes (table 1) between 0.01～0.46.If Δ n=0.46, then being equivalent to covering is air (air optical fiber).Separate the related data of propagation equation (1) and see Table 3.Only considered the situation of forward pumping when solving an equation (1).For backward pumping, only need to add a negative sign at the right-hand member of pumping equation, omit here.

Table 3 is separated the required data of propagation equation (1)

Input noise power scan wavelength coverage scanning wavelength step-length center signal wavelength E _r ³⁺The metastable level fiber loss

P _ASEΔ λ λ _cLife-span τ l _k

0.05P _s 1450～1650nm 2.5nm 1550nm 10ms 0.03dB/m

● the result

According to said method, obtained at pump power P _p=25,50,75,100,125,150,175, the new parameter of totally 7 EDFAs under eight kinds of situations of 200mW comprises: concentration of Er, fiber core radius, er-doped radius, refringence, fiber lengths, pumping wavelength and signal power.Determined best optical fiber parameter and best amplifier parameter thus simultaneously, concrete outcome slightly.

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Claims (1)

1. According to said method, be P at pump power _p=25,50,75,100,125,150,175, under eight kinds of situations of 200mW, determined best Er-doped fiber parameter and best amplifier parameter totally 7 parameters simultaneously.In these 7 parameters, wherein there are 4 to be constant, be characterised in that: best fiber core radius a ≡ 0.548 μ m, best er-doped radius b ≡ 0.548 μ m, best refringence $\mathrm{\&Delta;n}\&equiv;0.460$ (being air cladding layer optical fiber) and best input signal power P _s≡ 0.001mW.Other 3 parameter (concentration of Er n _t, fiber lengths L, pump wavelength _p) eigenwert and corresponding center signal gain ,-three dB bandwidth and center signal noise figure are as shown in the table:

   Right wants pumping the best to mix the best pump of optimal light center letter-3dB center signal

   Ask the fine length pumping wavelength of sequence number power erbium concentration gain bandwidth (GB) noise figure

   P _p(mW) n _t(×10 ²⁵m ^-3) L(m) λ _p(nm) G _c(dB)

   

   NF(dB)

   1 25 1.19 6.75 1462.0 28.56 22.5 3.923

   2 50 1.21 7.24 1458.5 31.85 25.0 3.798

   3 75 1.22 7.40 1458.2 33.74 22.5 3.772

   4 100 1.25 7.50 1457.8 35.08 25.0 3.757

   5 125 1.25 7.71 1457.6 36.11 25.0 3.749

   6 150 1.17 8.46 1457.4 36.93 25.0 3.743

   7 175 1.11 9.00 1457.2 37.63 25.0 3.739

   8 200 1.09 9.26 1457.1 38.23 22.5 3.736

   Annotate: each provisional capital has the best features parameter in addition in the table: fiber core radius a ≡ 0.548 μ m, er-doped radius b ≡ 0.548 μ m, refringence $\mathrm{\&Delta;n}\&equiv;0.460$ (being air cladding layer optical fiber) and input signal power P _s≡ 0.001mW.

   The error of above-mentioned parameter is ± 1%, and parameter is applicable to EDFAs device or the system that open loop, steady-state operation, single-mode optics are propagated.