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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 |8^53*f ?  
    & -L$B  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of dC+WII`V  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of r Q)?Bhf  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ramYSX@  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 QS(aA*D  
    *|WS,  
    %fid=fopen('e21.dat','w'); DmzK* O{  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) lz1RAp0R "  
    M1 =3000;              % Total number of space steps v$~1{}iI5  
    J =100;                % Steps between output of space ! R rk  
    T =10;                  % length of time windows:T*T0 } )D E  
    T0=0.1;                 % input pulse width I)7STzlMj.  
    MN1=0;                 % initial value for the space output location {jdtNtw  
    dt = T/N;                      % time step rywui10x*  
    n = [-N/2:1:N/2-1]';           % Index Q8-;w{%  
    t = n.*dt;   %-9?rOr  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 RE)!b  
    u20=u10.*0.0;                  % input to waveguide 2 E%Tpby}^'  
    u1=u10; u2=u20;                 Z[9) hGh  
    U1 = u1;   (j<FS>##  
    U2 = u2;                       % Compute initial condition; save it in U xib?XzxGo  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Aw?i6d  
    w=2*pi*n./T; Yf1&"WW4  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T U-^qVlw  
    L=4;                           % length of evoluation to compare with S. Trillo's paper |w; hu]  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 X=C*PWa7  
    for m1 = 1:1:M1                                    % Start space evolution l$[7 pM[  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS  ;IV  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; /Z3 Mlm{  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform QjT$.pU d  
       ca2 = fftshift(fft(u2)); c_V^~hq  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation P"-*'q,9  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Ygeg[S!7  
       u2 = ifft(fftshift(c2));                        % Return to physical space |h^[/  
       u1 = ifft(fftshift(c1)); #3VOC#.  
    if rem(m1,J) == 0                                 % Save output every J steps. '%Fg+cZN\  
        U1 = [U1 u1];                                  % put solutions in U array \NZ(Xk  
        U2=[U2 u2]; # <?igtUO  
        MN1=[MN1 m1]; Fw{:fFZC[  
        z1=dz*MN1';                                    % output location &,DZ0xA  
      end ;*{"|l qe  
    end nm#ISueh  
    hg=abs(U1').*abs(U1');                             % for data write to excel ) wZ;}O  
    ha=[z1 hg];                                        % for data write to excel ]u5B]ZQnA  
    t1=[0 t']; D;1?IeS  
    hh=[t1' ha'];                                      % for data write to excel file SI)QX\is8  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format pseN!7+or  
    figure(1) I8x,8}o>V  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn T6ihEb$C  
    figure(2) g49G7sk  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn MiK -W  
    '@0Z#A  
    非线性超快脉冲耦合的数值方法的Matlab程序 %3%bRP  
    }yzCq+  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ]3D>ai?  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N4HIQ\p  
    Wg5<@=x!G  
    ']bw37_U,  
    0#G@F5; <  
    %  This Matlab script file solves the nonlinear Schrodinger equations ayGcc`  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of '^|u\$&U  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !eu\ShI  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 &xWej2a!  
    vZiuElxKi  
    C=1;                           2RbK##`vC  
    M1=120,                       % integer for amplitude C ^IPddw>  
    M3=5000;                      % integer for length of coupler }/bxe0px  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) =?3b3PZn  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. T)Y{>wT  
    T =40;                        % length of time:T*T0. oBS m>V  
    dt = T/N;                     % time step ]qd$rX   
    n = [-N/2:1:N/2-1]';          % Index A+=K<e  
    t = n.*dt;   ?S<`*O +  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. h}y]Pt?  
    w=2*pi*n./T; Q]{ `m  
    g1=-i*ww./2; wi/qI(O!  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 3<x1s2U  
    g3=-i*ww./2; ;7>k[?'e  
    P1=0; Yycfb  
    P2=0; <*Gd0 v%  
    P3=1; v]GQb  
    P=0; \1He9~6  
    for m1=1:M1                 V8hmfV~=]P  
    p=0.032*m1;                %input amplitude 9u;/l#?@T  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [.Rdq]w6  
    s1=s10; ^ 'ws/(  
    s20=0.*s10;                %input in waveguide 2 rT|wZz9$@  
    s30=0.*s10;                %input in waveguide 3 \ z3>kvk  
    s2=s20; 8w$q4fg0  
    s3=s30; J#DN2y <  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   &J\<"3  
    %energy in waveguide 1 4KX\'K  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   (zX75QSKV  
    %energy in waveguide 2 %M*2j%6  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   b%QcB[k[WB  
    %energy in waveguide 3 Ya &\b 6  
    for m3 = 1:1:M3                                    % Start space evolution Z8ds`KZM  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS *.6m,QqJ(  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; +-!2nk`"a  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; `F$lO2#k  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform ]]NTvr  
       sca2 = fftshift(fft(s2)); !%'"l{R  
       sca3 = fftshift(fft(s3)); P~*'/!@  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   e-Z ul.m  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); [X 9zrGHt  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 5uX-onP\[  
       s3 = ifft(fftshift(sc3)); af'gk&%  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 7NRm\%^q  
       s1 = ifft(fftshift(sc1)); mndKUI}d  
    end $H`{wJ?2(  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); N;v]ypak  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); {kghZur  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |=:<[FU  
       P1=[P1 p1/p10]; u}.mJDL  
       P2=[P2 p2/p10]; ?IG[W+M8  
       P3=[P3 p3/p10]; ,u=+%6b)A  
       P=[P p*p]; q?qH7={,eu  
    end "QvTn=  
    figure(1) :O7n*lwx  
    plot(P,P1, P,P2, P,P3); OtbPr F5  
    [:zP]l.|  
    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~!~