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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 */:uV B,b2  
    aJ Z"D8C  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of V!v:]E  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ':{>a28=  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /!h;c$  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N IdZ  
    WOzf]3Xcj  
    %fid=fopen('e21.dat','w'); 6AG`&'"  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) wX  >*H  
    M1 =3000;              % Total number of space steps Hso|e?Z  
    J =100;                % Steps between output of space jTO), v:w  
    T =10;                  % length of time windows:T*T0 Od f[*  
    T0=0.1;                 % input pulse width (T`E!A0I\?  
    MN1=0;                 % initial value for the space output location MZ+^-@X  
    dt = T/N;                      % time step Xtt ? ]  
    n = [-N/2:1:N/2-1]';           % Index Bn@(zHG+5&  
    t = n.*dt;   }\J2?Et{  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 fU=B4V4@  
    u20=u10.*0.0;                  % input to waveguide 2 8J$|NYv_b  
    u1=u10; u2=u20;                 x }Ad_#q  
    U1 = u1;   PB;eHy  
    U2 = u2;                       % Compute initial condition; save it in U 1-lu\"H`  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. %_!bRo  
    w=2*pi*n./T; VD_$$Gn*q  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 2hzsKkrA {  
    L=4;                           % length of evoluation to compare with S. Trillo's paper _ODbY;M  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 _S>JKz  
    for m1 = 1:1:M1                                    % Start space evolution (L^]Lk x)  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS lpz2 m\  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 'Ut7{rZ5  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 0lhVqy}:}o  
       ca2 = fftshift(fft(u2)); !1e6Ss  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation /p8dZ+X  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   %CK^Si%+  
       u2 = ifft(fftshift(c2));                        % Return to physical space |*}4 m'c  
       u1 = ifft(fftshift(c1)); bv&;R  
    if rem(m1,J) == 0                                 % Save output every J steps.  }Y;K~J  
        U1 = [U1 u1];                                  % put solutions in U array /!c${W!sY  
        U2=[U2 u2]; d_IAs  
        MN1=[MN1 m1]; |JQQU! x  
        z1=dz*MN1';                                    % output location IiG6<|d8H  
      end "'D=,*  
    end )c `7( nY  
    hg=abs(U1').*abs(U1');                             % for data write to excel @`gk|W3  
    ha=[z1 hg];                                        % for data write to excel V4_=<W  
    t1=[0 t']; dq]0X?[6  
    hh=[t1' ha'];                                      % for data write to excel file N;\'N ne  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format nDHTV !]<  
    figure(1) Z]B~{!W1  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn !QvZ<5(  
    figure(2) Uu`9 "  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 3\XU_Xs(]  
    Y'8?.a]'  
    非线性超快脉冲耦合的数值方法的Matlab程序  5~>z h  
    DAXX;4  
    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。   Ft&]7dT{W  
    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 "'t0h{W r8  
    u fw]=h)  
    1,% R;7J=g  
    Y\No4w ^|d  
    %  This Matlab script file solves the nonlinear Schrodinger equations b45-:mi!&#  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ~^1{B\I  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ,%M$0poKM  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4rLL[??  
    PK`D8)=u  
    C=1;                           2+e}*&iQpp  
    M1=120,                       % integer for amplitude ee^{hQi  
    M3=5000;                      % integer for length of coupler `Tv[DIVW  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) njputEGX  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. eS~LF.^Jw  
    T =40;                        % length of time:T*T0. ?`PvL!'  
    dt = T/N;                     % time step ui/a|Q  
    n = [-N/2:1:N/2-1]';          % Index %-1O.Q|f  
    t = n.*dt;   'F9jq  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Pu"P9  
    w=2*pi*n./T; zd >t-?g  
    g1=-i*ww./2;  &7K?w~  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; KV0]m^@x  
    g3=-i*ww./2; %`1q-,>v  
    P1=0; ZzJ?L4J5v  
    P2=0; U_I5fK =  
    P3=1; |xdsl,  
    P=0; 6\q]rfQ  
    for m1=1:M1                 K3#@SY j  
    p=0.032*m1;                %input amplitude dtRwTUMe?  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 b?tB(if!I  
    s1=s10; %D\[*  
    s20=0.*s10;                %input in waveguide 2 x"~8*V'0  
    s30=0.*s10;                %input in waveguide 3 #."-#"0  
    s2=s20; Q7jb'y$ozO  
    s3=s30; z`f($t[  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   #_^Lb]jkM  
    %energy in waveguide 1  Ac2n  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   2y;Skp  
    %energy in waveguide 2 VJ]JjB j  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   '!!CeDy  
    %energy in waveguide 3 .$+#1-  
    for m3 = 1:1:M3                                    % Start space evolution F%@aB<Nu  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS /<|%yE&KhJ  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; *zb Nd:i9  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Whm,F^  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform .6+Z^,3  
       sca2 = fftshift(fft(s2)); dMv=gdY  
       sca3 = fftshift(fft(s3)); $5aV:Z3P  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   4.[^\N  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); l5!|I:/*;  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Nfrw0b  
       s3 = ifft(fftshift(sc3)); ^/I 7|u]  
       s2 = ifft(fftshift(sc2));                       % Return to physical space OEA&~4&{7  
       s1 = ifft(fftshift(sc1)); SB H(y)  
    end P}n_IV*@  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); {?}E^5Z*g  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); R3gdLa.  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); r*2+xDoEi  
       P1=[P1 p1/p10]; L*xhGoC=  
       P2=[P2 p2/p10]; 5Ha9lM2gh  
       P3=[P3 p3/p10]; RzE_K'M  
       P=[P p*p]; ls\WXCH  
    end S&Zm0Ku  
    figure(1) . qO@Q=  
    plot(P,P1, P,P2, P,P3); C~,a!qY  
    5F)C  jQ  
    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~!~