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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 ~\.w^*$#Y  
    )Xak JU^o  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of rI>aAW'  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Rhz_t@e  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear zj`v?#ET  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 c^u"I'#Q  
    #H{<gjs]  
    %fid=fopen('e21.dat','w'); 'wI"Bo6e  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) "@d[h,TM  
    M1 =3000;              % Total number of space steps qT"Q1xU[  
    J =100;                % Steps between output of space 8p9bCE>\  
    T =10;                  % length of time windows:T*T0 fX.>9H[w@~  
    T0=0.1;                 % input pulse width _$f9]bab  
    MN1=0;                 % initial value for the space output location MHai%E  
    dt = T/N;                      % time step [}8|R0KF  
    n = [-N/2:1:N/2-1]';           % Index YZ7|K<   
    t = n.*dt;   < hO /jB  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 #hf ak  
    u20=u10.*0.0;                  % input to waveguide 2 AvSM ^  
    u1=u10; u2=u20;                 !+4cqO  
    U1 = u1;   PSVc+s[Q+V  
    U2 = u2;                       % Compute initial condition; save it in U Ucm :S-  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. a{J,~2>  
    w=2*pi*n./T; ^Au _U  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T J-) XQDD  
    L=4;                           % length of evoluation to compare with S. Trillo's paper A~ +S1  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 2 fS[J'-o  
    for m1 = 1:1:M1                                    % Start space evolution 9}uW}yJ  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS >teO m?@U  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; IlE_@gS8  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform @@rEs40  
       ca2 = fftshift(fft(u2)); pT1[<X!<s  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation IWveW8qJ  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   2@~M4YJf  
       u2 = ifft(fftshift(c2));                        % Return to physical space 6{+{lBm=y  
       u1 = ifft(fftshift(c1)); f=!VsR2o  
    if rem(m1,J) == 0                                 % Save output every J steps. o{EC&-  
        U1 = [U1 u1];                                  % put solutions in U array $:j G-r  
        U2=[U2 u2]; \, &co  
        MN1=[MN1 m1]; C2xL1`  
        z1=dz*MN1';                                    % output location WN5`;{\  
      end nJ"YIT1K]p  
    end HJ[/|NZU$  
    hg=abs(U1').*abs(U1');                             % for data write to excel r"a5(Q;n  
    ha=[z1 hg];                                        % for data write to excel .OqSch|  
    t1=[0 t']; ""h)LUrl  
    hh=[t1' ha'];                                      % for data write to excel file Vc%R$E%  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 'vq:D$A  
    figure(1) RJH,  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn <b?!jV7  
    figure(2) d]i(h~?_  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn RZ7( J  
    ;?~$h-9)  
    非线性超快脉冲耦合的数值方法的Matlab程序 >'xGp7}y  
    ND,Kldji  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   5"]~oPK  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8kOKwEX  
    EVUq--)~  
    { "xln/  
    #D9e$E(J^  
    %  This Matlab script file solves the nonlinear Schrodinger equations KdUnD4d  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ^o@,3__7Q  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear j.ldaLdG  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 7`H 1f]d  
    3bd5FsI^pU  
    C=1;                           (N K9vW4F  
    M1=120,                       % integer for amplitude K+)%KP  
    M3=5000;                      % integer for length of coupler ZBG}3Z   
    N = 512;                      % Number of Fourier modes (Time domain sampling points) s/e"'Hz  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. xc:!cA{V  
    T =40;                        % length of time:T*T0. 9F- )r'  
    dt = T/N;                     % time step 1w0OKaF5  
    n = [-N/2:1:N/2-1]';          % Index f0SAP0M3  
    t = n.*dt;   m8JR@!t7  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. u=NS sTP&  
    w=2*pi*n./T; /.eeO k  
    g1=-i*ww./2; q )lnS )  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Dbaf0  
    g3=-i*ww./2; tYqs~B3  
    P1=0; BH@)QVs-  
    P2=0; X$b={]b  
    P3=1; o}'bv  
    P=0; omf  Rs  
    for m1=1:M1                 H{c?lT  
    p=0.032*m1;                %input amplitude )Vk6;__  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 >x@P|\  
    s1=s10; \mN[gT}LHm  
    s20=0.*s10;                %input in waveguide 2 "SoHt]%#  
    s30=0.*s10;                %input in waveguide 3 o1OBwPj  
    s2=s20; .LRxP#B  
    s3=s30; -g/hAxb5  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   cj|*_}  
    %energy in waveguide 1 T\# *S0^  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ` C+HE$B  
    %energy in waveguide 2 R,!Q Zxmg  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   o:dR5v  
    %energy in waveguide 3 l0Ti Z  
    for m3 = 1:1:M3                                    % Start space evolution x2#qg>`l  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS a>B[5I5  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; qy!Ou3^  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; >(tn"2  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform ~Z lC '  
       sca2 = fftshift(fft(s2)); zMK](o1Vj  
       sca3 = fftshift(fft(s3)); W:VP1 :  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   8g7,2f/ }  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); @TA9V@?)  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 7C?.L70ZY  
       s3 = ifft(fftshift(sc3)); l??;3kh1  
       s2 = ifft(fftshift(sc2));                       % Return to physical space kao}(?x%  
       s1 = ifft(fftshift(sc1)); Y/8K;U|  
    end td-3h,\\  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); &yz&LNn'  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); q1hMmMi  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); pY^9l3y^  
       P1=[P1 p1/p10]; i(wgB\9i4  
       P2=[P2 p2/p10]; AzpV4(:an.  
       P3=[P3 p3/p10]; f.pkQe(  
       P=[P p*p]; qq0?e0H  
    end 4*UP. r@  
    figure(1) :Px\qh}K  
    plot(P,P1, P,P2, P,P3); -#A:`/22  
    ;<G<1+  
    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~!~