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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 2YaTT& J  
    O~nBz):2  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of Z"4VH rA  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of xu`d`!Tx  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear K90D1sD  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8xc8L1;  
    an pJAB:1  
    %fid=fopen('e21.dat','w'); neK*jdaP  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) x_]",2 W'  
    M1 =3000;              % Total number of space steps .QNjeMu.  
    J =100;                % Steps between output of space SIj6.RK  
    T =10;                  % length of time windows:T*T0 {_": / A  
    T0=0.1;                 % input pulse width t*eleNYeS~  
    MN1=0;                 % initial value for the space output location ^u=PdBY  
    dt = T/N;                      % time step W<Bxm|  
    n = [-N/2:1:N/2-1]';           % Index :v|r=#OI  
    t = n.*dt;   *;>V2!N=U  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 3we.*\2$  
    u20=u10.*0.0;                  % input to waveguide 2 uPM8GIvZX.  
    u1=u10; u2=u20;                 Ym3 "  
    U1 = u1;   e?_c[`sg  
    U2 = u2;                       % Compute initial condition; save it in U .LWOM8)  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. F+lm[4n  
    w=2*pi*n./T; V]+o)A$  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T tU8g(ep,o  
    L=4;                           % length of evoluation to compare with S. Trillo's paper Z $ p^v*y  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 de*,MkZN  
    for m1 = 1:1:M1                                    % Start space evolution ;a#}fX  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Xi1q]ps  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ';i"?D?NAk  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 6RR4L^(m  
       ca2 = fftshift(fft(u2)); rTN"SQt  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation <\qY " .`  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Y*]l|)a6_]  
       u2 = ifft(fftshift(c2));                        % Return to physical space cq+nWHqF{J  
       u1 = ifft(fftshift(c1)); NN31?wt  
    if rem(m1,J) == 0                                 % Save output every J steps. dqIZ#;:g  
        U1 = [U1 u1];                                  % put solutions in U array FKDamHL<  
        U2=[U2 u2]; ~}hba3&b;#  
        MN1=[MN1 m1]; :Vu7,o  
        z1=dz*MN1';                                    % output location *[XN.sb8E  
      end +&&MUT{ 3  
    end 2@"0} po#  
    hg=abs(U1').*abs(U1');                             % for data write to excel @5<]W+jk4  
    ha=[z1 hg];                                        % for data write to excel Ek gZxT_&  
    t1=[0 t']; l}U~I 3}).  
    hh=[t1' ha'];                                      % for data write to excel file 1]a*Oer}  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format :)^# xE(  
    figure(1) ~v{C6)  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn S,d ngb{  
    figure(2) EF*oPn0|  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn B^Rw?: hN  
    GU;TK'Yy?  
    非线性超快脉冲耦合的数值方法的Matlab程序 muqfSF  
    Wl9I`Itg  
    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。   %XDip]+rb  
    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 mGM inzf  
    b#/V;  
    ,6cbD  
    F3H:I"4  
    %  This Matlab script file solves the nonlinear Schrodinger equations rFt,36#  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ;T"m [D  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear b3CspBgC  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 '6d D^0dZ  
    `-9*@_ -=M  
    C=1;                           #J<`p  
    M1=120,                       % integer for amplitude s)`1Rf  
    M3=5000;                      % integer for length of coupler _{Fdw  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) iuH8g  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 7~%  
    T =40;                        % length of time:T*T0. >%jEo'0;_  
    dt = T/N;                     % time step >M8^ Jgh  
    n = [-N/2:1:N/2-1]';          % Index h[[/p {z  
    t = n.*dt;   `o^;fcnG  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. +r#=n7 t  
    w=2*pi*n./T; "p6:ekw  
    g1=-i*ww./2; mPw56>  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ba:mO$  
    g3=-i*ww./2; 7-G'8t  
    P1=0; |GVGny<  
    P2=0; {W:)oh>  
    P3=1; yv#c =v|  
    P=0; hq&  
    for m1=1:M1                 -G^t-I  
    p=0.032*m1;                %input amplitude ;nAg4ll8Q  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 .9[8H:Fe  
    s1=s10; X T)hPwg.  
    s20=0.*s10;                %input in waveguide 2 X{9JSq  
    s30=0.*s10;                %input in waveguide 3 'nj&}A'  
    s2=s20; kVG6\<c]  
    s3=s30; f@xfb ie !  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ^S;RX*  
    %energy in waveguide 1 _sf0{/< )  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ^%'tD  
    %energy in waveguide 2 !=q:> }g  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   R1b )  
    %energy in waveguide 3 ,N@Icl  
    for m3 = 1:1:M3                                    % Start space evolution #G4~]Qml  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS < 4EB|@E  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Ymk4Cu.s  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; uYFcq  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform CrwcYzrRWl  
       sca2 = fftshift(fft(s2)); J9$]]\52s.  
       sca3 = fftshift(fft(s3)); ;o)`9<es!2  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   @qr3v>3X<  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); [&O:qaD^  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); %]:vT&M  
       s3 = ifft(fftshift(sc3)); [:hy  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ? /|@ #&  
       s1 = ifft(fftshift(sc1)); dnWt\>6& 2  
    end lWyP[>*  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); #3:'lGBIK  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); s2' :&5(  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); >-@{vyoOy  
       P1=[P1 p1/p10]; HV.|Eh_7  
       P2=[P2 p2/p10]; N mjBJ_G  
       P3=[P3 p3/p10]; _ry En  
       P=[P p*p]; vdFQf ^l  
    end B+q+)O+  
    figure(1) p ra-8z-  
    plot(P,P1, P,P2, P,P3); j C1^>D  
    !=Kay^J~.  
    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~!~