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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 N"Mw1R4  
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    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of nr>Os@\BU  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 9W+RUh^W  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear [Z$E^QAP  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 l0GsY.~,  
    AttS?TZr  
    %fid=fopen('e21.dat','w'); "GY/2;  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) WO<a^g {  
    M1 =3000;              % Total number of space steps B>Xfs ZS  
    J =100;                % Steps between output of space q{E44 eQ7F  
    T =10;                  % length of time windows:T*T0 GiGXV @dq  
    T0=0.1;                 % input pulse width RI</T3%~  
    MN1=0;                 % initial value for the space output location (//f"c]/  
    dt = T/N;                      % time step \;F_QV  
    n = [-N/2:1:N/2-1]';           % Index /lqVMlz\77  
    t = n.*dt;   O[RivHCY  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 @M_p3[c\  
    u20=u10.*0.0;                  % input to waveguide 2 DSX.84  
    u1=u10; u2=u20;                 OD~B2MpM>  
    U1 = u1;   e_Un:r@)  
    U2 = u2;                       % Compute initial condition; save it in U m2h@*  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 6tKCY(#oO+  
    w=2*pi*n./T; <yw(7  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T MeMSF8zSQ  
    L=4;                           % length of evoluation to compare with S. Trillo's paper io^ L[  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 { M&Vh]  
    for m1 = 1:1:M1                                    % Start space evolution 0<'Q;'2* L  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS fq,LXQ#G  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; .{ +Ob i  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform ;I@@PUnR  
       ca2 = fftshift(fft(u2)); ~+OAAkJ9  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ?Q#yf8  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   [ :*Jn}  
       u2 = ifft(fftshift(c2));                        % Return to physical space eemw I  
       u1 = ifft(fftshift(c1)); f9FEH7S68  
    if rem(m1,J) == 0                                 % Save output every J steps. bxR6@  
        U1 = [U1 u1];                                  % put solutions in U array JT(6Uf  
        U2=[U2 u2]; Z36C7 kw  
        MN1=[MN1 m1]; .m/$ku{/J  
        z1=dz*MN1';                                    % output location |'ML )`c[  
      end 5N.-m;s  
    end SNl% ?j| f  
    hg=abs(U1').*abs(U1');                             % for data write to excel HJ^SqSm  
    ha=[z1 hg];                                        % for data write to excel TP R$oO2  
    t1=[0 t']; P|' eM%  
    hh=[t1' ha'];                                      % for data write to excel file eF=cMC  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format uzgQ_  
    figure(1) OJ!=xTU%h  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn +$y%H  
    figure(2) BWG*UjP M  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn qGVf! R  
    %!X9>i>  
    非线性超快脉冲耦合的数值方法的Matlab程序 X" m0||  
    97 eEqI$#  
    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。   0tb%h[%,M  
    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 QMAineO  
    LfsqtQ=J`  
    B3C%**~:e  
    RM|2PG1m  
    %  This Matlab script file solves the nonlinear Schrodinger equations P#o"T4 >  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ewrs D'?  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ta+MH,  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 F :p9y_W  
    %pG^8Q()   
    C=1;                           0s'h2={iI  
    M1=120,                       % integer for amplitude `G0GWh)`x  
    M3=5000;                      % integer for length of coupler 68 \73L=  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 8Z[YcLy"({  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. [@;q#.}Z  
    T =40;                        % length of time:T*T0. l.nd Wv  
    dt = T/N;                     % time step {i#z <ttu  
    n = [-N/2:1:N/2-1]';          % Index hteAuz4H  
    t = n.*dt;   !!:mjq<0  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. J1UG},-h  
    w=2*pi*n./T; 3LW_qX  
    g1=-i*ww./2; +, |aIF  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; >h3m/aeNC  
    g3=-i*ww./2; )sZJH9[K  
    P1=0; w Sd|-e  
    P2=0; A2 9R5  
    P3=1; SPN5H;{[]K  
    P=0; [L ?^+p>  
    for m1=1:M1                 ;lP/hG;`  
    p=0.032*m1;                %input amplitude A~)#  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 h"3Mj*s  
    s1=s10; sD ,=_q@  
    s20=0.*s10;                %input in waveguide 2 RIdh],-  
    s30=0.*s10;                %input in waveguide 3 s~'"&0Gz  
    s2=s20; 4^(aG7  
    s3=s30; FKBI.}A?!'  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   VS jt|F)t  
    %energy in waveguide 1 f"RS,]  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   H ]z83:Z  
    %energy in waveguide 2 O;lGh1.  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   [jEZ5]%  
    %energy in waveguide 3 cNl NJ  
    for m3 = 1:1:M3                                    % Start space evolution Us2IeR  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS K;Fs5|gFU  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 4&kC8 [r  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; c:I %jm  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 38#Zlc f  
       sca2 = fftshift(fft(s2)); u*=8s5Q[  
       sca3 = fftshift(fft(s3)); H!P$p-*.  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   _)kTlX:,  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); !9t,#?!  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ^_gH}~l+U  
       s3 = ifft(fftshift(sc3)); XY^]nm-{I  
       s2 = ifft(fftshift(sc2));                       % Return to physical space .]w=+~h  
       s1 = ifft(fftshift(sc1)); .+(R,SvN%<  
    end ^D8~s;?  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); '\M]$`Et  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));  alH6~  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ?[<#>,W  
       P1=[P1 p1/p10]; cDIZkni=  
       P2=[P2 p2/p10]; FD al;T  
       P3=[P3 p3/p10]; +Ly@5y"  
       P=[P p*p]; Ge7Uety  
    end WZM  
    figure(1) tj4/x7!  
    plot(P,P1, P,P2, P,P3); HtV8=.^  
    |*$0~mA  
    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~!~