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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 Vc?=cQ'c  
    UwVc!Lys  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of * $v`5rP  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 48"=,IrM  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear -/gAb<=  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @V71%D8{  
    >Z!H9]f(  
    %fid=fopen('e21.dat','w'); l_0/g^(  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) uH=^ILN.  
    M1 =3000;              % Total number of space steps jR@J1IR<  
    J =100;                % Steps between output of space y5$AAas  
    T =10;                  % length of time windows:T*T0 sq1v._^s  
    T0=0.1;                 % input pulse width VY_<c98v  
    MN1=0;                 % initial value for the space output location w5R?9"d@  
    dt = T/N;                      % time step ~pve;(e=  
    n = [-N/2:1:N/2-1]';           % Index ;.#l[  
    t = n.*dt;   X}R Q&k  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 J>%uak<  
    u20=u10.*0.0;                  % input to waveguide 2 ODE^;:z !  
    u1=u10; u2=u20;                 oC >l|?h,  
    U1 = u1;   Q|i`s=|  
    U2 = u2;                       % Compute initial condition; save it in U 3iv;4e ;  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. bbAJ5EqL  
    w=2*pi*n./T; jp viX#\S_  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T }S}9Pm,:  
    L=4;                           % length of evoluation to compare with S. Trillo's paper e'L$g-;>4b  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 k(%h{0'  
    for m1 = 1:1:M1                                    % Start space evolution o}VW%G"  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 3,$G?auW  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 4Up \_  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform XR.Sm<A[  
       ca2 = fftshift(fft(u2)); z2DjYTm[~  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation g*[DyIm  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   NkL>ru!b9  
       u2 = ifft(fftshift(c2));                        % Return to physical space rIo)'L$uU  
       u1 = ifft(fftshift(c1)); 3*;S%1C^  
    if rem(m1,J) == 0                                 % Save output every J steps. ]] Jg%}o  
        U1 = [U1 u1];                                  % put solutions in U array GK\`8xWE  
        U2=[U2 u2]; wTK>U`o  
        MN1=[MN1 m1]; 3tAX4DnYrq  
        z1=dz*MN1';                                    % output location sH `(y)`_  
      end }`*DMI;-  
    end U5pg<xI  
    hg=abs(U1').*abs(U1');                             % for data write to excel kNDN<L  
    ha=[z1 hg];                                        % for data write to excel J sc`^a%`'  
    t1=[0 t']; H;=++Dh  
    hh=[t1' ha'];                                      % for data write to excel file aH+n]J] =)  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format `6BjNV  
    figure(1) ``9`Xq  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn b0ablVk  
    figure(2) |6y(7Ha  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn +tSfx  
    "Z70 jkW[  
    非线性超快脉冲耦合的数值方法的Matlab程序 \V/;i.ng  
    y`Km96 Ui  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   Hb|y`Ok  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 q>H f2R  
    TOvpv@?-  
    .GH#`j  
    +ZU@MOni  
    %  This Matlab script file solves the nonlinear Schrodinger equations f )K(la^'  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of OZed+t=  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >UDb:N[  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ,a1 1&"xl  
    (TQhO$,  
    C=1;                           )mvD2]fK  
    M1=120,                       % integer for amplitude Weu%&u-  
    M3=5000;                      % integer for length of coupler >+8Kl`2sw;  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) Q\k|pg?  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. !w #x@6yq  
    T =40;                        % length of time:T*T0. iZbY@-3fc  
    dt = T/N;                     % time step >;M?f!  
    n = [-N/2:1:N/2-1]';          % Index BiI}JEp4o  
    t = n.*dt;   ^ua8Ya  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. jUg.Y98  
    w=2*pi*n./T;  #:st>V_h  
    g1=-i*ww./2; Q@HW`@i  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ;&8  
    g3=-i*ww./2; x;L.j7lzA;  
    P1=0; -D-]tL6w  
    P2=0; bQelU  
    P3=1; u iEAi  
    P=0; Z;4pI@ u  
    for m1=1:M1                 bL9EX$P  
    p=0.032*m1;                %input amplitude ;S_\- ]m&g  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 lX*IEAc  
    s1=s10; :*0l*j  
    s20=0.*s10;                %input in waveguide 2 0X'2d  
    s30=0.*s10;                %input in waveguide 3 M);@XcS  
    s2=s20; f~{@(g&Gl  
    s3=s30; z0Bw+&^]}  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   <~}# Q,9  
    %energy in waveguide 1 JZM:R  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   G<f"_NT  
    %energy in waveguide 2 ?.%'[n>P  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   V(A p|I:G  
    %energy in waveguide 3 13v#  
    for m3 = 1:1:M3                                    % Start space evolution B[Gl}(E  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS dD{{G :V  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; S+7:fu2?+  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; "spAYk\  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform \Rff3$  
       sca2 = fftshift(fft(s2)); aO'lk  
       sca3 = fftshift(fft(s3)); +_h1JE_}D  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   K9 tuiD+j  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); \vR&-+8dk  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); }q~M$  
       s3 = ifft(fftshift(sc3)); ` e~nn  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ">V.nao  
       s1 = ifft(fftshift(sc1)); RO10$1IW.2  
    end .tny"a&  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); )n&@`>vm  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); @C34^\aH+  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); lm 1Mz  
       P1=[P1 p1/p10]; dLq)Z*r  
       P2=[P2 p2/p10]; Hve'Z,X  
       P3=[P3 p3/p10]; ; Fi(zl  
       P=[P p*p]; O%KP,q&}Y  
    end .2V`sg.!  
    figure(1) :UrS@W^B  
    plot(P,P1, P,P2, P,P3); ">LX>uYmX-  
    wh~g{(Xvq  
    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~!~