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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 M !6Fnj  
    PzPNvV/o  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of %<kfW&_>w  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Kyh6QA^  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear w9Yx2  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 . Z&5TK4I  
    QjLU@?&  
    %fid=fopen('e21.dat','w'); IGTO|sT"  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 1t e^dh:Vp  
    M1 =3000;              % Total number of space steps JM;bNW8  
    J =100;                % Steps between output of space !IOmJpl'  
    T =10;                  % length of time windows:T*T0 }#1.$a  
    T0=0.1;                 % input pulse width wwl,F=| Y  
    MN1=0;                 % initial value for the space output location )FwOg;=3M"  
    dt = T/N;                      % time step ftY&Q#[  
    n = [-N/2:1:N/2-1]';           % Index D:9^^uVp  
    t = n.*dt;   4&NB xe  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 a >fA-@  
    u20=u10.*0.0;                  % input to waveguide 2 KJFQ)#SW!  
    u1=u10; u2=u20;                 gp9O%g3'  
    U1 = u1;   MNs<yQ9I'  
    U2 = u2;                       % Compute initial condition; save it in U |Kd6.Mx  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. @zS/J,:v}  
    w=2*pi*n./T; G5qsnTxUJ  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T '\{ OQ H  
    L=4;                           % length of evoluation to compare with S. Trillo's paper Sp[9vlo8  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 N,w6  
    for m1 = 1:1:M1                                    % Start space evolution Fe[6Y<x+:  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS rX$-K\4W  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;  5V<6_o  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform !$HuH6_[  
       ca2 = fftshift(fft(u2)); s-*N_Dv  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation X:Y1g)|K  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   %;4#?.W8  
       u2 = ifft(fftshift(c2));                        % Return to physical space n^QDMyC;I  
       u1 = ifft(fftshift(c1)); q"Bd-?9  
    if rem(m1,J) == 0                                 % Save output every J steps. S*}GW-)oA  
        U1 = [U1 u1];                                  % put solutions in U array gS(JgN  
        U2=[U2 u2]; cMi9 Z]  
        MN1=[MN1 m1]; K/(LF}  
        z1=dz*MN1';                                    % output location ?Ho$fGz  
      end <;i&-,  
    end ~oOv/1v},  
    hg=abs(U1').*abs(U1');                             % for data write to excel NTJ,U2  
    ha=[z1 hg];                                        % for data write to excel {;bec%pq0  
    t1=[0 t']; j 1'H|4  
    hh=[t1' ha'];                                      % for data write to excel file 'NWvQR<X  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Jur$O,u40l  
    figure(1) 6AD&%v  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ' Sd&I:?  
    figure(2) RGV{KL  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn gu3)HCZ  
    CWs;1`aP  
    非线性超快脉冲耦合的数值方法的Matlab程序 e7G>'K  
    &\?{%xj  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   w}}+8mk[  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N0fE*xo  
    j5Yli6r?3-  
    p"\-iY]  
    Y\!:/h]E&  
    %  This Matlab script file solves the nonlinear Schrodinger equations nb5%a   
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of F`Vp   
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear \mN?5QCcE  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 (`n*d3  
    -GgV&%'a  
    C=1;                           gKU*@`6G  
    M1=120,                       % integer for amplitude =L$RY2S"  
    M3=5000;                      % integer for length of coupler ]H:K$nmX  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) AO$aWyI  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. [\HAJA,  
    T =40;                        % length of time:T*T0. C~iFFh6:  
    dt = T/N;                     % time step bv[*jr;45  
    n = [-N/2:1:N/2-1]';          % Index /9y'UKl7[  
    t = n.*dt;   a(o[ bH.|;  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. /7*qa G  
    w=2*pi*n./T; 1?+)T%"  
    g1=-i*ww./2; RmN\;G?}  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Q6Zh%\+h(  
    g3=-i*ww./2; '\m\$ {  
    P1=0; `0ju=FP'u5  
    P2=0; =7P; /EV  
    P3=1; N_!Zn"J  
    P=0; ;+qPV7Z  
    for m1=1:M1                 q33!X!br  
    p=0.032*m1;                %input amplitude CQY/q@7  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 8&f"")m  
    s1=s10; !as<UH"\  
    s20=0.*s10;                %input in waveguide 2 }\ui} \  
    s30=0.*s10;                %input in waveguide 3 Df/f&;`  
    s2=s20; 1/q iE{NW  
    s3=s30; J2#=`|t"  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ZsPBs4<p  
    %energy in waveguide 1 Ah2XwFg?  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Ip0@Q}^  
    %energy in waveguide 2 .J\U|r  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   [76mgj!K  
    %energy in waveguide 3 cfe[6N  
    for m3 = 1:1:M3                                    % Start space evolution qXW2a'~  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS /[#{#:lo2  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Y=rW.yK8  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; j'0*|f^z  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform vrW9<{  
       sca2 = fftshift(fft(s2)); 7#|NQ=yd  
       sca3 = fftshift(fft(s3)); 7erao-  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   GrQAho  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Y.*lO  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); qaGIU`}:$A  
       s3 = ifft(fftshift(sc3)); C1rCKKh  
       s2 = ifft(fftshift(sc2));                       % Return to physical space iii$)4V  
       s1 = ifft(fftshift(sc1)); (U dDp"/  
    end w)8@Tu:Q  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); $BBfsaJPT  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); |)JoxqR  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); .y2<2eW  
       P1=[P1 p1/p10]; >qUO_>  
       P2=[P2 p2/p10]; s* YFN#Wuc  
       P3=[P3 p3/p10]; >a-+7{};  
       P=[P p*p]; a@r K%Iff  
    end sBu"$ "]  
    figure(1) ".i{WyTt  
    plot(P,P1, P,P2, P,P3); h+^T);h};|  
    /eMZTh*1P  
    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~!~