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    [分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

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    离线tianmen
     
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    只看楼主 倒序阅读 楼主  发表于: 2011-06-12
    计算脉冲在非线性耦合器中演化的Matlab 程序 OhEL9"\<  
    _AYF'o-Cm  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 3IFU{0a`  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of q|J]  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear _y UFe&  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 P7-3Vf_L  
    >`'9V| 1  
    %fid=fopen('e21.dat','w'); Kx0dOkE  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) .vMi <U;  
    M1 =3000;              % Total number of space steps kM`#U *j  
    J =100;                % Steps between output of space !&[4T#c  
    T =10;                  % length of time windows:T*T0 q3`t0eLZ  
    T0=0.1;                 % input pulse width >k|[U[@  
    MN1=0;                 % initial value for the space output location e.V){}{V  
    dt = T/N;                      % time step 2wQ CQ"  
    n = [-N/2:1:N/2-1]';           % Index PK" C+o;:  
    t = n.*dt;   hgGcUpJy?  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 %>TdTt  
    u20=u10.*0.0;                  % input to waveguide 2 @jKB!z9{  
    u1=u10; u2=u20;                 2l?J9c}Wo  
    U1 = u1;   @4$E.q<0  
    U2 = u2;                       % Compute initial condition; save it in U %R"Fx$tQ  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ez{&Y>n  
    w=2*pi*n./T; Lt_]3g o  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T y e'5 A   
    L=4;                           % length of evoluation to compare with S. Trillo's paper }R$%MU5::  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 4NV1v&"  
    for m1 = 1:1:M1                                    % Start space evolution -; }Wm[  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Gj3/&'k6  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; x]Ef}g  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform t ,$)PV  
       ca2 = fftshift(fft(u2)); 1CbC|q  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation k W,|>  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   k1J}9HNYR  
       u2 = ifft(fftshift(c2));                        % Return to physical space 2uIAnbW]M  
       u1 = ifft(fftshift(c1)); 4<|u~n*JF  
    if rem(m1,J) == 0                                 % Save output every J steps. 7|rT*-Ia  
        U1 = [U1 u1];                                  % put solutions in U array 5S LF1u;  
        U2=[U2 u2]; d yd_dK/  
        MN1=[MN1 m1]; qb&*,zN  
        z1=dz*MN1';                                    % output location Ry C7  
      end YSbN=Rj  
    end xX ZN<<f59  
    hg=abs(U1').*abs(U1');                             % for data write to excel -|mABHjx*  
    ha=[z1 hg];                                        % for data write to excel x% 1Rp[  
    t1=[0 t']; ]7;;uhn`  
    hh=[t1' ha'];                                      % for data write to excel file s/V[tEC*z  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Cb.Aw!  
    figure(1) B_> Fd&  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn YC~+r8ME$j  
    figure(2) J3=jC5=J4  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn w]_a0{Uh  
    ?=/l@d  
    非线性超快脉冲耦合的数值方法的Matlab程序 i+}M#Y-O  
    *"@P2F&  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   r_G`#Z_5F  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 D$ \ EZ   
    `|R{^Sk1o  
    k.%F!sK  
    M5]w U   
    %  This Matlab script file solves the nonlinear Schrodinger equations -UO$$)Q  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ]P.S5s'  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear y03l_E,  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Ne%X:h  
    RaAq>B WPr  
    C=1;                           #]rw@c  
    M1=120,                       % integer for amplitude VuGSP]$q  
    M3=5000;                      % integer for length of coupler @ o]F~x  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) l<5!R;?$  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. XZhhr1-<a  
    T =40;                        % length of time:T*T0. BtspnVB ez  
    dt = T/N;                     % time step xfb%bkr  
    n = [-N/2:1:N/2-1]';          % Index lG2){){j  
    t = n.*dt;   Ks4TBi&J   
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. [30e>bSf`  
    w=2*pi*n./T; p~t$ll0s  
    g1=-i*ww./2; @ B+];lr/-  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; - 0zo>[c/p  
    g3=-i*ww./2; .fgoEB,(  
    P1=0; Js'|N%pi  
    P2=0; :H~r _>E  
    P3=1; 6`'^$wKs  
    P=0; 4R6X"T9-  
    for m1=1:M1                 bbz86]AhY  
    p=0.032*m1;                %input amplitude m|!sY[!  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 I)clGMS,  
    s1=s10; 1!~9%=%  
    s20=0.*s10;                %input in waveguide 2 grZN.zTO  
    s30=0.*s10;                %input in waveguide 3 xaPTTa  
    s2=s20; BP`UB  
    s3=s30; d%WFgf}  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   mWZV O,t$  
    %energy in waveguide 1 K~uoZ~_gA  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   bp }~{]:b  
    %energy in waveguide 2 fSj^/>  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   #]9yzyb_y  
    %energy in waveguide 3 6uDNqq  
    for m3 = 1:1:M3                                    % Start space evolution g%K3ah v  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS IlH*s/  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Q~jUZ-qN  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; iKu5K0x{>I  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform ,$*$w<  
       sca2 = fftshift(fft(s2)); 8$1<N  
       sca3 = fftshift(fft(s3)); x k#/J]j  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   &Oe,$%{hBh  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); T3\Q<  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); $N~8 ^6  
       s3 = ifft(fftshift(sc3)); +ft?aB@  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ;#AV~Y- s  
       s1 = ifft(fftshift(sc1)); dD=dPi#  
    end |',Gy\Sj  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); J5429Soo  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); i),W1<A1  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); *edB3!!  
       P1=[P1 p1/p10]; ^hU7QxW  
       P2=[P2 p2/p10]; v=!]t=P)t  
       P3=[P3 p3/p10]; k5((@[  
       P=[P p*p]; b?y3m +V`  
    end  E;k'bz  
    figure(1) Iu=iC.50}  
    plot(P,P1, P,P2, P,P3); 8!1vsEqv  
    fxjs"rD5  
    转自:http://blog.163.com/opto_wang/
     
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    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~