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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 |~#A?mK-  
    zhbSiw  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of #;5Q d'  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of $|@pY| f  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ?:&2iW7z  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 _s<s14+od  
    V(:wYk?ZR  
    %fid=fopen('e21.dat','w'); u'k+t`V&  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) vz|(KN[  
    M1 =3000;              % Total number of space steps A6J:!sY4A  
    J =100;                % Steps between output of space ^vTx%F  
    T =10;                  % length of time windows:T*T0 1GIBqs~-  
    T0=0.1;                 % input pulse width 2h#.:!/SMw  
    MN1=0;                 % initial value for the space output location G B,O  
    dt = T/N;                      % time step ,CN (;z)  
    n = [-N/2:1:N/2-1]';           % Index @!j6y (@  
    t = n.*dt;   H:OpS-b  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 C<(qk_  
    u20=u10.*0.0;                  % input to waveguide 2 W /*?y &  
    u1=u10; u2=u20;                 fmJK+  
    U1 = u1;   w{u,YM(Q  
    U2 = u2;                       % Compute initial condition; save it in U :R3iLy  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. kr@!j@j$  
    w=2*pi*n./T; +v'2s@e` #  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T FFcIOn  
    L=4;                           % length of evoluation to compare with S. Trillo's paper h_\( $"  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 5 UOqS#"0  
    for m1 = 1:1:M1                                    % Start space evolution )v*k\:Hw  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS s diWQv  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 'U*#7 1S  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform _ker,;{9C  
       ca2 = fftshift(fft(u2)); ` AD}6O+x  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 'rS\9T   
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   7+}WU4  
       u2 = ifft(fftshift(c2));                        % Return to physical space GmE`YW  
       u1 = ifft(fftshift(c1)); Ihr[44#  
    if rem(m1,J) == 0                                 % Save output every J steps. wnK6jMjkSf  
        U1 = [U1 u1];                                  % put solutions in U array ZHUW1:qs  
        U2=[U2 u2]; J#F HR/zV  
        MN1=[MN1 m1]; %#PWD7a\  
        z1=dz*MN1';                                    % output location /hmDeP o}  
      end bfEH>pQ>#  
    end tN_=&|{WE4  
    hg=abs(U1').*abs(U1');                             % for data write to excel AAW] Y#UwW  
    ha=[z1 hg];                                        % for data write to excel ==gL!e{  
    t1=[0 t']; T31F8K3x  
    hh=[t1' ha'];                                      % for data write to excel file @GGQ13Cj(  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format S8+l!$7   
    figure(1) Hz[1c4)'F  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 9<iM2(IW{  
    figure(2) Q[aF"5h%  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn %'=2Jy6h  
    ssS"X@VZ \  
    非线性超快脉冲耦合的数值方法的Matlab程序 mPqK k  
    UZmUYSu;  
    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 0wY  
    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 jUl_ToX  
    6J#R1.h  
    jJNl{nyq  
    O!hp=`B,jf  
    %  This Matlab script file solves the nonlinear Schrodinger equations n/ :#:  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of {Rb;1 eYj  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear FGie*t  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |Kjfh};-C  
    4}t&yu<P>  
    C=1;                           FV7'3fIa  
    M1=120,                       % integer for amplitude $T:;Kc W)  
    M3=5000;                      % integer for length of coupler H3vnc\d~  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) NS""][#  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. iOCs% J  
    T =40;                        % length of time:T*T0. +-SO}P  
    dt = T/N;                     % time step ;($xAAR  
    n = [-N/2:1:N/2-1]';          % Index PhV/WjCZ  
    t = n.*dt;   S.`hl/  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ;&f(7 Q+T_  
    w=2*pi*n./T; e6H}L:;  
    g1=-i*ww./2; ~% t'}JDZ  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; M;'GnGFf  
    g3=-i*ww./2; |,S]EHIy  
    P1=0; @%*@Rar  
    P2=0; EAm31v C  
    P3=1; X2;72  
    P=0; i `p1e5$  
    for m1=1:M1                 @Q{:m)\  
    p=0.032*m1;                %input amplitude m8x?`Gw~jw  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Nu3IYS5&  
    s1=s10; [{#T N  
    s20=0.*s10;                %input in waveguide 2 f%1\1_^g  
    s30=0.*s10;                %input in waveguide 3 Anpp`>}N  
    s2=s20; trjeGSt&  
    s3=s30; :w Y%=  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Z%LS{o~LK.  
    %energy in waveguide 1 5D?{dA:Rq  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ]Ol w6W?%  
    %energy in waveguide 2 +t1+1 Zv  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ,' t&L]  
    %energy in waveguide 3 bG*l_  
    for m3 = 1:1:M3                                    % Start space evolution "X._:||8  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS d2US~.;>l  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; J#4pA{01w  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; \fSruhD  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform $!!y v'K  
       sca2 = fftshift(fft(s2)); ]\>MDH  
       sca3 = fftshift(fft(s3)); !>!jLZ0  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ;14Q@yrZ0  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); -:Fr($^  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); i$}G[v<4  
       s3 = ifft(fftshift(sc3)); 7<(U`9W/q  
       s2 = ifft(fftshift(sc2));                       % Return to physical space #K$0%0=M  
       s1 = ifft(fftshift(sc1)); q o-|.I  
    end TNeL%s?B3  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 4T"L#o1  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); $Jn.rX0}$  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Y#-c<o}f  
       P1=[P1 p1/p10]; vl}}h%BC  
       P2=[P2 p2/p10]; `WxGU  
       P3=[P3 p3/p10];  tj8o6N#  
       P=[P p*p]; F.(e}EMyNh  
    end 1cMdoQ  
    figure(1) ygm6(+  
    plot(P,P1, P,P2, P,P3); PR(KDwsT&l  
    }TuMMO4+  
    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~!~