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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 QE=Cum  
    Q^b_+M  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 'g|%Ro/  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of f&7SivS#  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear S%kE<M?  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 05=O5<l  
    J55K+  
    %fid=fopen('e21.dat','w'); f?2Y np=@  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) WFjNS'WI_  
    M1 =3000;              % Total number of space steps L!3{ASIN0  
    J =100;                % Steps between output of space "z=A=~~<{  
    T =10;                  % length of time windows:T*T0 +}I[l,,xy  
    T0=0.1;                 % input pulse width o3]B/  
    MN1=0;                 % initial value for the space output location /-8v]nRB  
    dt = T/N;                      % time step ;]i&AAbj  
    n = [-N/2:1:N/2-1]';           % Index s lDxsb  
    t = n.*dt;   gt';_  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 V%<<Udu<  
    u20=u10.*0.0;                  % input to waveguide 2 (|bMtT?"x  
    u1=u10; u2=u20;                 slOki|p;  
    U1 = u1;   yodJGGAzk  
    U2 = u2;                       % Compute initial condition; save it in U w4:n(.;HK  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. {5#P1jlT  
    w=2*pi*n./T; \-#~)LB]M  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T n&r-  
    L=4;                           % length of evoluation to compare with S. Trillo's paper TEh]-x`  
    dz=L/M1;                       % space step, make sure nonlinear<0.05  !|9$  
    for m1 = 1:1:M1                                    % Start space evolution 5w@  ;B  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS c^6v7wT5  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; gK-:t  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform _B 8e 1an  
       ca2 = fftshift(fft(u2)); Q2Yv8q_}Uq  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation "SNsOf  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   PC.$&x4w1  
       u2 = ifft(fftshift(c2));                        % Return to physical space ed'}ReLK  
       u1 = ifft(fftshift(c1)); -,TBUWg  
    if rem(m1,J) == 0                                 % Save output every J steps. X']>b   
        U1 = [U1 u1];                                  % put solutions in U array Mpk^e_9`<  
        U2=[U2 u2]; SV<*qz  
        MN1=[MN1 m1]; l0U6eOx  
        z1=dz*MN1';                                    % output location 5y(irbk7  
      end ;}A#ws_CD_  
    end Av.(i2  
    hg=abs(U1').*abs(U1');                             % for data write to excel b v\V>s  
    ha=[z1 hg];                                        % for data write to excel tmRD$O%:  
    t1=[0 t']; e&OMW ,7  
    hh=[t1' ha'];                                      % for data write to excel file U`W^w%  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format <^~Xnstl  
    figure(1) yD#w @yG  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn $a15 8  
    figure(2) a_waLH/  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Eh!%Ne O  
    _xl#1>G^J  
    非线性超快脉冲耦合的数值方法的Matlab程序 SjtGU47$!  
    {;n?c$r  
    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。   9`4h"9dO  
    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 c5;YKON  
    J}._v\Q7P  
    :`:<JA3,  
    / v5Pk.!o  
    %  This Matlab script file solves the nonlinear Schrodinger equations **_VNDK+  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of %f6l"~y  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear D'fP2?3FK  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 'x+0 yd  
    u\t[rC=yd  
    C=1;                           ^nbze  
    M1=120,                       % integer for amplitude Jgtv ia  
    M3=5000;                      % integer for length of coupler z9w@-])  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) $rFv(Qc^=  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 0a8nBo7A-X  
    T =40;                        % length of time:T*T0. 4TwU0N+>  
    dt = T/N;                     % time step )tFFa*Z'  
    n = [-N/2:1:N/2-1]';          % Index Se0/ysVB  
    t = n.*dt;   oq8~PTw  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. }K<;ygcWE@  
    w=2*pi*n./T; `3pe\s  
    g1=-i*ww./2; aCGPtA'  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 1Y}gki^F  
    g3=-i*ww./2; =!#D UfQf  
    P1=0;  o<Y|N   
    P2=0; 3C_g)5 _:  
    P3=1; }^`{YD  
    P=0; t$l[ 4 R-  
    for m1=1:M1                 M#<x2ojW  
    p=0.032*m1;                %input amplitude \M>AN Z}  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 U?$v 1||  
    s1=s10; )z/j5tnvm  
    s20=0.*s10;                %input in waveguide 2 Ql&P1|&  
    s30=0.*s10;                %input in waveguide 3 !cSD9q*  
    s2=s20; a.%]5%O;t  
    s3=s30; X){F^1CT{  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   \?3];+c9  
    %energy in waveguide 1 Tw!x*  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   2mU}"gf[  
    %energy in waveguide 2 u52; )"&=)  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Qbv)(&i# ~  
    %energy in waveguide 3 (]7@0d88  
    for m3 = 1:1:M3                                    % Start space evolution p-*BB_J"  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS M\`6H8aLn  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; |I OTW=>  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 3g-}k  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform D"^ogY#LK  
       sca2 = fftshift(fft(s2)); V{d"cs>9  
       sca3 = fftshift(fft(s3)); 1d\K{ 7i#  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   SCGQo.~,  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ; H:qDBH  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); )s6tj lf8  
       s3 = ifft(fftshift(sc3)); zR{TWk]  
       s2 = ifft(fftshift(sc2));                       % Return to physical space L"}@>&6  
       s1 = ifft(fftshift(sc1)); b]|7{yMV  
    end TS UN(_XGW  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); \2NiI]t]  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); YmF`7W  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); E+~~d6nB  
       P1=[P1 p1/p10]; E>4 \9  
       P2=[P2 p2/p10]; >`oO(d}n[0  
       P3=[P3 p3/p10]; Pyyx/u+?@  
       P=[P p*p]; 57[O)5u.+  
    end JBoo7a1  
    figure(1) X(WG:FP27  
    plot(P,P1, P,P2, P,P3); \H" (*["&  
    V KR6i  
    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~!~