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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 2e-bt@0t  
    )s, t BU+N  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of )S`[ gK  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of K\8zhY  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear yqL"YD  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 PUZcb+%]h  
    %eIaH!x:  
    %fid=fopen('e21.dat','w'); tCGx]\  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) =_ N[mR^  
    M1 =3000;              % Total number of space steps BKb#\(95*  
    J =100;                % Steps between output of space y06**f)  
    T =10;                  % length of time windows:T*T0 qz3 Z'  
    T0=0.1;                 % input pulse width TecMQ0 KD  
    MN1=0;                 % initial value for the space output location IvY3iRq6  
    dt = T/N;                      % time step { gs$pBu  
    n = [-N/2:1:N/2-1]';           % Index qq<T~^  
    t = n.*dt;   Ml{ ]{n  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 oaPWeM+  
    u20=u10.*0.0;                  % input to waveguide 2 4KR`  
    u1=u10; u2=u20;                 ISK 8t  
    U1 = u1;   l:JVt`A4?  
    U2 = u2;                       % Compute initial condition; save it in U v7KBYN  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. + WMXd.iN,  
    w=2*pi*n./T; \f(zMP  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T -LUZ7,!/>o  
    L=4;                           % length of evoluation to compare with S. Trillo's paper vyJ8" #]qY  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 w%iw xo   
    for m1 = 1:1:M1                                    % Start space evolution ){'<67dK  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS _#&oQFdYR  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; S$$SLy:P  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform B&B:P  
       ca2 = fftshift(fft(u2)); YVgH[-`,  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 2PRiiL@  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   .Tq8Qdl  
       u2 = ifft(fftshift(c2));                        % Return to physical space /^k%sG@?  
       u1 = ifft(fftshift(c1)); 6_u!{  
    if rem(m1,J) == 0                                 % Save output every J steps. _6r[msH"  
        U1 = [U1 u1];                                  % put solutions in U array %g@\SR.  
        U2=[U2 u2]; "JLE  
        MN1=[MN1 m1]; n^l*oEl  
        z1=dz*MN1';                                    % output location 8OV =;aM?{  
      end jIrfJ*z  
    end bfZt<-  
    hg=abs(U1').*abs(U1');                             % for data write to excel uYg Q?*Z  
    ha=[z1 hg];                                        % for data write to excel Z4As'al  
    t1=[0 t']; (hZNWQ0  
    hh=[t1' ha'];                                      % for data write to excel file qpCaW0]7  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 4;AQ12<[1  
    figure(1) m;{HlDez  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn rXMc0SPk  
    figure(2) se2Y:v  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn hE`d@  
    KU oAxA  
    非线性超快脉冲耦合的数值方法的Matlab程序 PI`Y%!P  
    '/6f2[%Y"  
    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。   G"-V6CA[  
    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 )uo".n|n~B  
    ^9LoxU-  
    cNmAr8^}  
    wEX<[#a-  
    %  This Matlab script file solves the nonlinear Schrodinger equations hHVAN3e  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of wL3RcXW``e  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear G7+{O7  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @sZ7Ka  
    k \T]*A  
    C=1;                           0)b1'xt',  
    M1=120,                       % integer for amplitude hFr+K1  
    M3=5000;                      % integer for length of coupler iV?8'^  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) H!X*29nX  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. /.!&d^  
    T =40;                        % length of time:T*T0. Y%eW6Y#  
    dt = T/N;                     % time step >yn]h4M  
    n = [-N/2:1:N/2-1]';          % Index Yu_ eCq5/  
    t = n.*dt;   cQThpgha  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. u?MhK# Mr  
    w=2*pi*n./T; RfD#/G3|  
    g1=-i*ww./2; OAW_c.)5D  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; |zP~/  
    g3=-i*ww./2; CL7 /J[TS  
    P1=0; {fl[BX]kZ  
    P2=0; ,P`GIGvkA  
    P3=1; ts@$*  
    P=0; 2W_[|.;'  
    for m1=1:M1                 .-& =\}^2l  
    p=0.032*m1;                %input amplitude DA>nYj-s  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 R[v<mo[s  
    s1=s10; t B`"gC~  
    s20=0.*s10;                %input in waveguide 2 i>CR{q  
    s30=0.*s10;                %input in waveguide 3 #4LTUVH  
    s2=s20; F-ofR]|) >  
    s3=s30; tK{#kApHGG  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   K3tW Y 4-  
    %energy in waveguide 1 iWr #H  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   noa+h<vGb  
    %energy in waveguide 2 V?x&\<;,  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   <[}zw!z  
    %energy in waveguide 3 4h--x~ @  
    for m3 = 1:1:M3                                    % Start space evolution 'sa)_?Hy  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS F^!O\8PFd  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; AT3HH QD  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ^z, B}Nz  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform LCA+y1LP-_  
       sca2 = fftshift(fft(s2)); Y`-q[F?\y  
       sca3 = fftshift(fft(s3)); AU%Yr 6  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ( )ldn?v  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); <^{(?*  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); = B;qy7?  
       s3 = ifft(fftshift(sc3)); :KG=3un]  
       s2 = ifft(fftshift(sc2));                       % Return to physical space $J)`Ru6.  
       s1 = ifft(fftshift(sc1)); udr|6EjD.  
    end *,O3@,+>H  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); <GQ=PrT|/  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); iS.gN&\z^  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 4K`b?{){+a  
       P1=[P1 p1/p10]; KOXG=P0  
       P2=[P2 p2/p10]; f8r7 SFwUv  
       P3=[P3 p3/p10]; `<<9A\Y-f  
       P=[P p*p]; &X` lh P  
    end G}NqVbZ9]  
    figure(1) &c&TQkx  
    plot(P,P1, P,P2, P,P3); c>/7E-T  
    saQ ~v@  
    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~!~