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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 u*S-Pji,x  
    n1Wo<$#  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of #iiXJnG  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of `x:O&2  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear &}rmDx  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1a]P+-@u[  
    &v/>P1Z G  
    %fid=fopen('e21.dat','w'); e~ZxDAd  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) )z_5I (?&  
    M1 =3000;              % Total number of space steps 3 ,f3^A  
    J =100;                % Steps between output of space 9*2Q'z}_  
    T =10;                  % length of time windows:T*T0 .WVIdVO7  
    T0=0.1;                 % input pulse width /8? u2 q  
    MN1=0;                 % initial value for the space output location UrmnHc>}c  
    dt = T/N;                      % time step edL sn>\*#  
    n = [-N/2:1:N/2-1]';           % Index 7PW7&]-WQ  
    t = n.*dt;   _u9bZ'  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 KIGMWS^^  
    u20=u10.*0.0;                  % input to waveguide 2 @s|G18@  
    u1=u10; u2=u20;                 U1)!X@F{  
    U1 = u1;   D=jtXQF  
    U2 = u2;                       % Compute initial condition; save it in U vNQ|tmn  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. RgD%pNhI  
    w=2*pi*n./T; )B9/P>c  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ;w<r/dK   
    L=4;                           % length of evoluation to compare with S. Trillo's paper FmhT^  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 v[\Z^pccgj  
    for m1 = 1:1:M1                                    % Start space evolution n65fT+;  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS :I^4ILQCD  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 9Dyw4'W.N  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform R%JEx3)0m  
       ca2 = fftshift(fft(u2)); mG%cE(j*D  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation nTsPX Tat  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   nZ`=Up p)  
       u2 = ifft(fftshift(c2));                        % Return to physical space .yb8<qs  
       u1 = ifft(fftshift(c1)); -./ Y  
    if rem(m1,J) == 0                                 % Save output every J steps. R!WeSgKCs  
        U1 = [U1 u1];                                  % put solutions in U array 7A  
        U2=[U2 u2]; VKi3z%kwK  
        MN1=[MN1 m1]; kEg~yN  
        z1=dz*MN1';                                    % output location Ds\f?\Em  
      end /sl#M  
    end ^fM=|.?  
    hg=abs(U1').*abs(U1');                             % for data write to excel )' 2vUt`_7  
    ha=[z1 hg];                                        % for data write to excel wDs#1`uTq  
    t1=[0 t']; }J=zO8OL  
    hh=[t1' ha'];                                      % for data write to excel file x_EU.924uY  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 5a* Awv}  
    figure(1) / `w'X/'VJ  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ND5E`Va5R  
    figure(2) ,aa %{  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 7p18;Z+6>X  
    ^N~Jm&I  
    非线性超快脉冲耦合的数值方法的Matlab程序 1xwq:vFC.  
    +Jc-9Ko\c;  
    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。   16I(S  
    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 qj?I*peK)  
    U3w*z6OG  
    ,qlFk|A|  
    1z[blNs&  
    %  This Matlab script file solves the nonlinear Schrodinger equations >2)!w  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of I3?:KVa  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ~0n9In%  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {XYf"ONi  
    Vs[!WJ 7  
    C=1;                           !Jo.Un7  
    M1=120,                       % integer for amplitude QLTE`t5w3'  
    M3=5000;                      % integer for length of coupler W&^2Fb  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) yDw^xGws  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. .{ ]=v  
    T =40;                        % length of time:T*T0. t,;b*ZR  
    dt = T/N;                     % time step H %PIE1_  
    n = [-N/2:1:N/2-1]';          % Index NPR{g!tK%  
    t = n.*dt;   *-9b!>5eD  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. :Ee5:S   
    w=2*pi*n./T; #D!3a%u0  
    g1=-i*ww./2; jNseD  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; VAR/"  
    g3=-i*ww./2; hO:X\:G  
    P1=0; Xq%!(YD|  
    P2=0; "i*Gi \U  
    P3=1; 8|,-P=%t  
    P=0; v6?<)M%  
    for m1=1:M1                 :Zd# }P  
    p=0.032*m1;                %input amplitude >Y/1%Hp9  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ]H<C Rw  
    s1=s10; R:JS)>B  
    s20=0.*s10;                %input in waveguide 2 H\!u5o&}`  
    s30=0.*s10;                %input in waveguide 3 -.WVuc`  
    s2=s20; -/&6}lD  
    s3=s30; j|WaWnl=  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Bj7\{x,?  
    %energy in waveguide 1 egi?Qg  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   2=NYBOE  
    %energy in waveguide 2 I@q>ES!1H  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Qi7^z;  
    %energy in waveguide 3 jW",'1h<n  
    for m3 = 1:1:M3                                    % Start space evolution 9Au+mIN  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 73(T+6`  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ?-'Q-\j  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; |qNrj~n@  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform U^0vLyqW^5  
       sca2 = fftshift(fft(s2)); A1f]HT  
       sca3 = fftshift(fft(s3)); 0+:.9*g=k  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   {UZli[W1  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); c\4n7m,y  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); C12 7he  
       s3 = ifft(fftshift(sc3)); k*c:%vC!  
       s2 = ifft(fftshift(sc2));                       % Return to physical space J0p,P.G  
       s1 = ifft(fftshift(sc1)); qc'tK6=jp  
    end +msHQk5#$m  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); |2 wff?  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Da-(D<[0  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 5\Y/so=  
       P1=[P1 p1/p10]; Pe wPl0  
       P2=[P2 p2/p10]; ]:E]5&VwV}  
       P3=[P3 p3/p10]; 16G v? I h  
       P=[P p*p]; 3Ob"r`  
    end j*:pW;)^  
    figure(1) kdYl>M  
    plot(P,P1, P,P2, P,P3); *E)Y?9u"  
    ^]R0d3?>\  
    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~!~