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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 .oM;D~(=9  
    / hg)=p  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of JmC2buO  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Z.`0  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ;OC{B}.vH  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 E~c>j<'-"<  
    woa|h"T  
    %fid=fopen('e21.dat','w'); :w]NN\  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) =om<*\vsO  
    M1 =3000;              % Total number of space steps 9a#Y D;-p  
    J =100;                % Steps between output of space @=OX7zq\h-  
    T =10;                  % length of time windows:T*T0 :Wihb#TO)  
    T0=0.1;                 % input pulse width ~l('ly  
    MN1=0;                 % initial value for the space output location (coaGQ@d  
    dt = T/N;                      % time step Wcbm,O4u  
    n = [-N/2:1:N/2-1]';           % Index 'U,\5jj'Y  
    t = n.*dt;   kzVK%[/  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ^fV-m&F)K*  
    u20=u10.*0.0;                  % input to waveguide 2 qOAP_\@T  
    u1=u10; u2=u20;                 cqaq~  
    U1 = u1;   7pN&fAtj/  
    U2 = u2;                       % Compute initial condition; save it in U 3L-$+j~u  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. X/bu z  
    w=2*pi*n./T; V/xjI<,  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T )Fw#]~Z  
    L=4;                           % length of evoluation to compare with S. Trillo's paper +i[@+`  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 /8 y v8  
    for m1 = 1:1:M1                                    % Start space evolution ZFtJoGaR  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS '!`| H 3  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 7X8*7'.2  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform |tC=  j.  
       ca2 = fftshift(fft(u2)); _0y]U];ce  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Uu|2!}^T  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   )LsUO#%DO  
       u2 = ifft(fftshift(c2));                        % Return to physical space |n;5D,r0C  
       u1 = ifft(fftshift(c1)); `QZKW  
    if rem(m1,J) == 0                                 % Save output every J steps. K+d{R=s^  
        U1 = [U1 u1];                                  % put solutions in U array `4e| I.`^r  
        U2=[U2 u2]; Rp!"c  
        MN1=[MN1 m1];  4&%E?_M  
        z1=dz*MN1';                                    % output location zCv)%y  
      end KpIY>k  
    end |"[;0)dw^  
    hg=abs(U1').*abs(U1');                             % for data write to excel (w`_{%T  
    ha=[z1 hg];                                        % for data write to excel R2Lq??XA=  
    t1=[0 t']; 1d$wP$  
    hh=[t1' ha'];                                      % for data write to excel file S~W;Ld<>fB  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format %q.5; L  
    figure(1) *,)1Dcv(  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn P F);KQ  
    figure(2) IpM"k)HR  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn WR u/7$8  
     C~^T=IP  
    非线性超快脉冲耦合的数值方法的Matlab程序 )`S5>[6  
    (=j/"Mb  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   %L$ ?Mey  
    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 .J=QWfqt  
    Bc`L ]<  
    Urol)_3X  
    n<F3&2w  
    %  This Matlab script file solves the nonlinear Schrodinger equations HG)$ W  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of n'?]_z<  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear WEoD ?GLS8  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4sfq,shRq  
    >[~`rOU*|Y  
    C=1;                           #Zi6N  
    M1=120,                       % integer for amplitude Nfv` )n@  
    M3=5000;                      % integer for length of coupler t3*.Bm:^  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) p@h<u!rL8  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. bM }zGFt  
    T =40;                        % length of time:T*T0. Ft}nG&D  
    dt = T/N;                     % time step ?X\uzu  
    n = [-N/2:1:N/2-1]';          % Index U lCw{:#F  
    t = n.*dt;   F&Rr&m  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. y-S23B(  
    w=2*pi*n./T; r oBb o  
    g1=-i*ww./2; vP_mS 4X  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ~mZ[@ Z  
    g3=-i*ww./2; Ir(U7D  
    P1=0; _,? xc"  
    P2=0; b?<@  
    P3=1; sxdDI?W4  
    P=0; L>lxkq8!Q  
    for m1=1:M1                 >.H}(!  
    p=0.032*m1;                %input amplitude 4F<wa s/  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 J3/e;5w2Z  
    s1=s10; iG"1~/U  
    s20=0.*s10;                %input in waveguide 2 W}|k!_/  
    s30=0.*s10;                %input in waveguide 3 b?2 \j}  
    s2=s20; p9!jM\(  
    s3=s30; G7KOJZb+D  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   l\2"u M#7  
    %energy in waveguide 1 <e wcWr  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   dz/3=0  
    %energy in waveguide 2 jF(R;?,  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   P,#l~\  
    %energy in waveguide 3 u Tdz$Nh  
    for m3 = 1:1:M3                                    % Start space evolution -zZb]8\E  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS z~i>GN_  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; cV7a, *  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; tVNFulcz$  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform HcV,r,>e  
       sca2 = fftshift(fft(s2)); 0d89>UB-8q  
       sca3 = fftshift(fft(s3)); ,>nf/c0.  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ! GtF%V  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Moi>Dp  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); };'~@%U]/  
       s3 = ifft(fftshift(sc3)); ]4'V59\  
       s2 = ifft(fftshift(sc2));                       % Return to physical space y>cT{)E$  
       s1 = ifft(fftshift(sc1)); B->oTC`5  
    end ,,g: x  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); cnDF`7xrT  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); BFqM6_/J  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); @udc/J$  
       P1=[P1 p1/p10]; YllW2g:  
       P2=[P2 p2/p10]; ?\<Kb|Q  
       P3=[P3 p3/p10]; 9U@>&3[v  
       P=[P p*p]; j*~z.Q|  
    end O7J V{'?  
    figure(1) w;kiH+&  
    plot(P,P1, P,P2, P,P3); |-%dN }O  
    YWDd[\4  
    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~!~