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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 正序阅读 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 nVkx Q?2  
    T<(1)N1H`  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ITJ{]7N  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of F: %-x=q  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear c'cK+32  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 _DsA<SJ]  
    EdFCaW}""  
    %fid=fopen('e21.dat','w'); CXt9 5O?  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) hhd%j6  
    M1 =3000;              % Total number of space steps +GCN63 nX  
    J =100;                % Steps between output of space O b'B?  
    T =10;                  % length of time windows:T*T0 !/] F.0  
    T0=0.1;                 % input pulse width :T^!<W4  
    MN1=0;                 % initial value for the space output location U-Ia$b-5!  
    dt = T/N;                      % time step -^sW{s0Rc  
    n = [-N/2:1:N/2-1]';           % Index X[/>{rK  
    t = n.*dt;   d: D`rpcC  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10  gGF]Dq  
    u20=u10.*0.0;                  % input to waveguide 2 "fK`F/  
    u1=u10; u2=u20;                 {gh41G;n  
    U1 = u1;   Z9 X<W`  
    U2 = u2;                       % Compute initial condition; save it in U Fp'qn'){:#  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. I5]=\k($  
    w=2*pi*n./T; ldp x,  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T \kSoDY`l&  
    L=4;                           % length of evoluation to compare with S. Trillo's paper $pW6a %7  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ^b|Z<oF  
    for m1 = 1:1:M1                                    % Start space evolution yg({g "  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS )9/.K'o,dy  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; +B(x:hzY9  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform  x{K^u"  
       ca2 = fftshift(fft(u2)); 9/A$ 3#wF  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation aAM!;3j]B`  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   l-s%3E3  
       u2 = ifft(fftshift(c2));                        % Return to physical space 8vQGpIa,  
       u1 = ifft(fftshift(c1)); +;z^qn  
    if rem(m1,J) == 0                                 % Save output every J steps. kc*zP=  
        U1 = [U1 u1];                                  % put solutions in U array ^n8ioL\*i  
        U2=[U2 u2]; |OW/-&)  
        MN1=[MN1 m1]; !ieMhJ5r  
        z1=dz*MN1';                                    % output location N>h/!# ZC  
      end =5:L#` .  
    end `=m[(CLb  
    hg=abs(U1').*abs(U1');                             % for data write to excel V~#e%&73FH  
    ha=[z1 hg];                                        % for data write to excel kk|7{83O  
    t1=[0 t']; aq~>$CHa  
    hh=[t1' ha'];                                      % for data write to excel file w2*.3I,~)B  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Oi#4|*b{W  
    figure(1) U'(Exr[  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn n(X{|?  
    figure(2) /V'^$enK!}  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn =BD}+(3  
     R&oC9<  
    非线性超快脉冲耦合的数值方法的Matlab程序 tW<i;2 l  
    ]5(T{  
    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。   5x$/.U  
    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 +_^Rxx!XA  
    )m8ve)l  
    RLnsy,  
    Q` ?+w+y7  
    %  This Matlab script file solves the nonlinear Schrodinger equations $db]b  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of j /d? c5  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear .<xzf4C  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 V+\L@mz;  
    +65OR'd  
    C=1;                           3=[#(p:  
    M1=120,                       % integer for amplitude JFOto,6L:  
    M3=5000;                      % integer for length of coupler ,m4M39MWJ  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 2!-?  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. )-qWcf?   
    T =40;                        % length of time:T*T0. }iGpuoXT`  
    dt = T/N;                     % time step N5W;Zx]  
    n = [-N/2:1:N/2-1]';          % Index _(J;!,  
    t = n.*dt;   IE;Fu67wi  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 4Vv~  
    w=2*pi*n./T; By3y.}'Ub9  
    g1=-i*ww./2; [^N8v;O  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; NxOiT#YH  
    g3=-i*ww./2; 8]SJ=c"}Xf  
    P1=0; GUX! kj  
    P2=0; ]V*ku%L0  
    P3=1; i 4sd29v  
    P=0; |\HYq`!g%7  
    for m1=1:M1                 0P MF)';R  
    p=0.032*m1;                %input amplitude fj 14'T  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 A/bxxB7w  
    s1=s10; P<. TiF?@  
    s20=0.*s10;                %input in waveguide 2 l ~bjNhk  
    s30=0.*s10;                %input in waveguide 3 Drn{ucIs  
    s2=s20; J A=9EnTU  
    s3=s30; N 3M:|D  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Cx N]fo  
    %energy in waveguide 1 |)%]MK$;  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   /5x~3~  
    %energy in waveguide 2 o0yyP,?yh  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   q,e{t#t  
    %energy in waveguide 3 1/ZvcdYB  
    for m3 = 1:1:M3                                    % Start space evolution Z.Otci>J  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS <5 Ye')+  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Yg @&@S]  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; .,-,@ZK  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform g Kp5*  
       sca2 = fftshift(fft(s2)); Z`FEB0$  
       sca3 = fftshift(fft(s3)); "ITC P<+  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   y15 MWZ  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); *8QESF9  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); V XE85  
       s3 = ifft(fftshift(sc3)); L&gC  
       s2 = ifft(fftshift(sc2));                       % Return to physical space mbf'xGO  
       s1 = ifft(fftshift(sc1)); i146@<\G{P  
    end 3CKd[=-Z  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Ffv v8x  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ?MW *`U  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); "7]YvZYu0  
       P1=[P1 p1/p10];  <>|&%gmz  
       P2=[P2 p2/p10]; {2A| F{7>  
       P3=[P3 p3/p10]; 'ycr/E&m{  
       P=[P p*p]; ">8]Oi;g  
    end 2 }9of[  
    figure(1) kiah,7V/  
    plot(P,P1, P,P2, P,P3); 3 s@6pI  
    U@ ;W^Mt  
    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~!~