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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 %z(nZ%,Z  
    XCGJ~  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of i5>]$j1/  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of AC$:.KLI  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @@,l0/  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]0VjVU-  
    a/Cd;T2  
    %fid=fopen('e21.dat','w'); lJfn3  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) /GK1}h  
    M1 =3000;              % Total number of space steps 5 ,0fL  
    J =100;                % Steps between output of space Z>)(yi9+  
    T =10;                  % length of time windows:T*T0 Hvn{aLa.  
    T0=0.1;                 % input pulse width b`@aiXN)+  
    MN1=0;                 % initial value for the space output location >&|C E2'  
    dt = T/N;                      % time step O;u&>BMk  
    n = [-N/2:1:N/2-1]';           % Index q&h&GZ  
    t = n.*dt;   rI\G&OqpP  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 o2FQ/EIE  
    u20=u10.*0.0;                  % input to waveguide 2 s/,wyxKd  
    u1=u10; u2=u20;                 R).?lnS  
    U1 = u1;   liW0v!jBo  
    U2 = u2;                       % Compute initial condition; save it in U p?mQ\O8F  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. a)+;<GZ~  
    w=2*pi*n./T; /e^q>>z  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ltKUpRE\?  
    L=4;                           % length of evoluation to compare with S. Trillo's paper X  8V^  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 N{}XHA  
    for m1 = 1:1:M1                                    % Start space evolution `g2DN#q[0  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS #PzRhanX  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; eB`7C"Z  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform ohFUy}y  
       ca2 = fftshift(fft(u2)); A8?uCkG  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation CH6^;.  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   pq 4/>WzE  
       u2 = ifft(fftshift(c2));                        % Return to physical space  Pa .D+  
       u1 = ifft(fftshift(c1)); vjy59m  
    if rem(m1,J) == 0                                 % Save output every J steps. +ht -Bl  
        U1 = [U1 u1];                                  % put solutions in U array wzr3 y}fCe  
        U2=[U2 u2]; jt?937{  
        MN1=[MN1 m1]; s3+^q  
        z1=dz*MN1';                                    % output location ,4bqjkX5q  
      end qRXb 9c  
    end 6]=$c<.&  
    hg=abs(U1').*abs(U1');                             % for data write to excel  a=<l}`*  
    ha=[z1 hg];                                        % for data write to excel SjT8 eH #  
    t1=[0 t']; &{): x  
    hh=[t1' ha'];                                      % for data write to excel file -lKk.Y.}r  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format WUQlAsme  
    figure(1) 9sQ4 $  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn - J9K  
    figure(2) PVGvjc  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn sx;7  
    UN7>c0B  
    非线性超快脉冲耦合的数值方法的Matlab程序 vJ__jO"Sq  
    R<}n?f\#JZ  
    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。   <P)vx  
    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 0B0Uay'd_  
    ]] R*sd*  
    50 :gk*hy  
    p`@7hf|hm  
    %  This Matlab script file solves the nonlinear Schrodinger equations yF &"'L  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of A.a UWh  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear K5O8G  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 $"z|^ze  
    :wn9bCom?M  
    C=1;                           :Ogt{t  
    M1=120,                       % integer for amplitude VKW9Rn9Qg  
    M3=5000;                      % integer for length of coupler ={[s)G  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) eyq8wQT  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ou;E@`h;x  
    T =40;                        % length of time:T*T0. UADD 7d  
    dt = T/N;                     % time step %F'*0<  
    n = [-N/2:1:N/2-1]';          % Index D$W&6'  
    t = n.*dt;   =-XI)JV#  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. #7!P3j  
    w=2*pi*n./T; }@ Nurs)%_  
    g1=-i*ww./2; Tw|cgB  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; T %   
    g3=-i*ww./2; {H FF|Dx  
    P1=0; 8lAs~c  
    P2=0; KkVFY+/)  
    P3=1; g4(vgWOW`  
    P=0; \ W3\P=  
    for m1=1:M1                 >syQDB  
    p=0.032*m1;                %input amplitude 4l0ON>W(  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ^oNk}:>  
    s1=s10; [42vO  
    s20=0.*s10;                %input in waveguide 2 @D<q=:k  
    s30=0.*s10;                %input in waveguide 3 R5iv]8X4W  
    s2=s20; 's.%rre%  
    s3=s30; iNn]~L1  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   1&S34wJF  
    %energy in waveguide 1 <ob+Ano$  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   os|Y=a  
    %energy in waveguide 2 6#egy|("nF  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   )<w`E{q  
    %energy in waveguide 3 Nqih LUv  
    for m3 = 1:1:M3                                    % Start space evolution RP}.Ei  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS $is|B9B  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 739J] M  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ig Mm.1>  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 8Vcg30_+  
       sca2 = fftshift(fft(s2)); rQ0V3x1"Qx  
       sca3 = fftshift(fft(s3)); ;J"b%~Gn  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   *82f {t]  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); "c[ D 0{\{  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); i *W9 4  
       s3 = ifft(fftshift(sc3)); m'|{AjH z6  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 9mdp \A  
       s1 = ifft(fftshift(sc1)); kHj|:,'sV  
    end Z)RoFD1]C  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); $ b Q4[  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); .8[Db1W  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); {VWX?Mm  
       P1=[P1 p1/p10]; qPJU}(9#B  
       P2=[P2 p2/p10]; P<AN`un  
       P3=[P3 p3/p10]; gwvy$H   
       P=[P p*p]; JGS4r+   
    end J|k~e,C  
    figure(1) *], ]E;  
    plot(P,P1, P,P2, P,P3); Dps0$f c  
    &|t*9 D  
    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~!~