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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 [ByQ;s5tY  
    vf<UBa;Xm  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of fD{II+T  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ltoqtB\s  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 9x? B5Ap[  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [![ G7H%f  
    H-(q#?:  
    %fid=fopen('e21.dat','w'); 77*qkKr  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) rnO0-h-;  
    M1 =3000;              % Total number of space steps x` 2| }AP(  
    J =100;                % Steps between output of space X D)  8?  
    T =10;                  % length of time windows:T*T0 |g<*Rk0  
    T0=0.1;                 % input pulse width yxwWj>c  
    MN1=0;                 % initial value for the space output location pj!:[d  
    dt = T/N;                      % time step z1vw'VT>  
    n = [-N/2:1:N/2-1]';           % Index (bv,02  
    t = n.*dt;   NG" yPn  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 \gItZ}+c4}  
    u20=u10.*0.0;                  % input to waveguide 2 R"3 M[^  
    u1=u10; u2=u20;                 W`rMtzL5  
    U1 = u1;   VYaSB?`/  
    U2 = u2;                       % Compute initial condition; save it in U b}@(m$W  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. WhFS2Jl0  
    w=2*pi*n./T; H-I{-Fm  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T |CIC$2u  
    L=4;                           % length of evoluation to compare with S. Trillo's paper s]H^wrg&  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 pjw aL^  
    for m1 = 1:1:M1                                    % Start space evolution Y%Ieg.o  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS \G>ZkgU  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; }"_j0ax  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform u[")*\CP  
       ca2 = fftshift(fft(u2)); =X-Tcj?3g  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation yfEb  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   nWJ:=JQ i"  
       u2 = ifft(fftshift(c2));                        % Return to physical space $*\L4<(  
       u1 = ifft(fftshift(c1)); f<<rTE6  
    if rem(m1,J) == 0                                 % Save output every J steps. gsPl _  
        U1 = [U1 u1];                                  % put solutions in U array brSi<  
        U2=[U2 u2]; =P`~t<ajB  
        MN1=[MN1 m1]; T5|c$doQ  
        z1=dz*MN1';                                    % output location 88lxHoPV  
      end S&(^<gwl  
    end k1='c7s  
    hg=abs(U1').*abs(U1');                             % for data write to excel }T.?c9l X  
    ha=[z1 hg];                                        % for data write to excel " xR[mJ@U  
    t1=[0 t']; J!TBREK  
    hh=[t1' ha'];                                      % for data write to excel file sbo^"&%w  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format j U[ O  
    figure(1) A6{b?aQ  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 909md|9K3  
    figure(2) QA;!caNp  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ~@4'HMQ  
    }]+xFj9[>  
    非线性超快脉冲耦合的数值方法的Matlab程序 o' 'wCr%  
    ;%!B[+ut"  
    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。   zhblLBpeE\  
    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 ;%Hf)F  
    > cN~U3  
    *7$P]  
    /i_ @  
    %  This Matlab script file solves the nonlinear Schrodinger equations bZ 443SG  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 6!q#x[A  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear iv&v8;B  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =f1B,%7G+5  
    \or G63T:  
    C=1;                           A],ooiq<  
    M1=120,                       % integer for amplitude LF*&(NC  
    M3=5000;                      % integer for length of coupler )ev<7g9*q  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) } JiSmi6o  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. JC#>Td  
    T =40;                        % length of time:T*T0. e]Fp=*#  
    dt = T/N;                     % time step Kw5Lhc1V  
    n = [-N/2:1:N/2-1]';          % Index &miexSNeF  
    t = n.*dt;   EME.h&A\G`  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Anm=*;*M`  
    w=2*pi*n./T; 0N:XIGFa  
    g1=-i*ww./2; Wu1{[a|  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; MJ{%4S{K,p  
    g3=-i*ww./2; a W%5~3  
    P1=0; 5n lMrK  
    P2=0; [I;^^#'P  
    P3=1; I+(/TP  
    P=0; ^W?Z  
    for m1=1:M1                 ++-{]wB3=.  
    p=0.032*m1;                %input amplitude q MYe{{r  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 HQP}w%8x  
    s1=s10; sTRJ:fR  
    s20=0.*s10;                %input in waveguide 2 {aYY85j  
    s30=0.*s10;                %input in waveguide 3 ]3iH[,KU3  
    s2=s20; zDTv\3rZ4X  
    s3=s30; @A<PkpNL  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   .L6Zm U  
    %energy in waveguide 1 % ps$qB'  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   J%H;%ROx  
    %energy in waveguide 2 [K/m  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   _~u2: yl (  
    %energy in waveguide 3 IiBD?}  
    for m3 = 1:1:M3                                    % Start space evolution }J:+{4Yn  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 4LH[4Yj?`  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; cD|Htt"  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; UBv@+\Y8m  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform ?:{sH#ua  
       sca2 = fftshift(fft(s2)); ^5GW$  
       sca3 = fftshift(fft(s3)); +HT1ct+dI  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   a|7a_s4(  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ikD1N  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); b75 $?_+  
       s3 = ifft(fftshift(sc3)); DV)3  
       s2 = ifft(fftshift(sc2));                       % Return to physical space !TM*o+;  
       s1 = ifft(fftshift(sc1)); q$(5Vd:  
    end #|GSQJ$F)`  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); <_Z:'~Zp  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); gD`>Twa&6  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); $d S@y+  
       P1=[P1 p1/p10]; B.r4$:+jb2  
       P2=[P2 p2/p10]; BVsD( @lX  
       P3=[P3 p3/p10]; l5xCz=dw  
       P=[P p*p]; $$APgj"|<  
    end tVrY3)c  
    figure(1) @yd4$Mv8%  
    plot(P,P1, P,P2, P,P3); S"Lx%  
    =@2FX&&E_  
    转自:http://blog.163.com/opto_wang/
     
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    离线ciomplj
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    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~