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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 'r'=%u$1C  
    gx\V)8Zr  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 0%xktf  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of V[ UOlJ  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear D5zc{) /  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 k-$Acv(  
    e\)%<G5  
    %fid=fopen('e21.dat','w'); b:1B >  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) [*%lm9 x  
    M1 =3000;              % Total number of space steps T! }G51  
    J =100;                % Steps between output of space <Qq {&,Le  
    T =10;                  % length of time windows:T*T0 )Rr6@o  
    T0=0.1;                 % input pulse width #rHMf%0  
    MN1=0;                 % initial value for the space output location <5Vf3KoC&  
    dt = T/N;                      % time step v}>g* @  
    n = [-N/2:1:N/2-1]';           % Index DksYKv  
    t = n.*dt;   g5BL"Dn  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 [[T7s(3  
    u20=u10.*0.0;                  % input to waveguide 2 oKGH|iVEe  
    u1=u10; u2=u20;                 r$<!?Z  
    U1 = u1;   |:)Bo<8  
    U2 = u2;                       % Compute initial condition; save it in U iBE|6+g~Cj  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 'O%*:'5k  
    w=2*pi*n./T; k_g@4x1y*  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T osc8;B/  
    L=4;                           % length of evoluation to compare with S. Trillo's paper tmGhJZ2j  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 /.:1Da  
    for m1 = 1:1:M1                                    % Start space evolution 74_?@Z(  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS $$AZ)#t[  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Fd8nR9A  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform n'rq  
       ca2 = fftshift(fft(u2)); yf{\^^ i(  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation U=v>gNba  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   lU 9o"2  
       u2 = ifft(fftshift(c2));                        % Return to physical space "t2T*'j{  
       u1 = ifft(fftshift(c1));  hyxv+m[  
    if rem(m1,J) == 0                                 % Save output every J steps. e_-g|ukC  
        U1 = [U1 u1];                                  % put solutions in U array #kQ! GMZH  
        U2=[U2 u2]; ~#g c{ C@  
        MN1=[MN1 m1]; &UDbH* !4=  
        z1=dz*MN1';                                    % output location qJ" (:~  
      end zDg*ds\  
    end R/u0,  
    hg=abs(U1').*abs(U1');                             % for data write to excel 4n#u?)  
    ha=[z1 hg];                                        % for data write to excel Iq|h1ie m+  
    t1=[0 t']; {UH45#Ua  
    hh=[t1' ha'];                                      % for data write to excel file ?`TQ!m6y  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ]xf89[;0  
    figure(1) :F d1k Jm  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn QXI~Toddj  
    figure(2) [KUkv  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn t{,$?}  
    1uo |a  
    非线性超快脉冲耦合的数值方法的Matlab程序 58?WO}  
    7L+Wj }m  
    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。   \Vv)(/q{  
    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 $d1ow#ROgy  
    }51QUFhL0  
    }[%F  
    ]:ca=&>  
    %  This Matlab script file solves the nonlinear Schrodinger equations 9f['TG,"  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of aT/2rMKPF  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear zt2#K  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 DN9x<%/-  
    d% @0xsU1  
    C=1;                           6rS ? FG=  
    M1=120,                       % integer for amplitude W}F~vx.  
    M3=5000;                      % integer for length of coupler  [6@bsXiw  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) eDo4>k"5  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. *K>2B99TXu  
    T =40;                        % length of time:T*T0. F_u ?.6e]  
    dt = T/N;                     % time step bSM|"  
    n = [-N/2:1:N/2-1]';          % Index W)`>'X`  
    t = n.*dt;   |yNyk7~  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 4 JBfA,  
    w=2*pi*n./T; oCwep^P(v  
    g1=-i*ww./2; $_%  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ?:q"qwt$F  
    g3=-i*ww./2; gISA13  
    P1=0; H/f}t w  
    P2=0; zt((TD2  
    P3=1; mj9|q8v{+  
    P=0; 4o''C |ND  
    for m1=1:M1                 WKr4S<B8mr  
    p=0.032*m1;                %input amplitude ;[zZI~wh  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 @#"K6  
    s1=s10; qHrIs-NR  
    s20=0.*s10;                %input in waveguide 2 ?,v@H$)3_  
    s30=0.*s10;                %input in waveguide 3 J bima>  
    s2=s20; >$<Q:o}^  
    s3=s30; sS)tSt{C  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   T5@t_D>8  
    %energy in waveguide 1 vr>J$(F  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   3F6'3NvVc2  
    %energy in waveguide 2 AzGbvBI&V  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Z(E .F,k  
    %energy in waveguide 3 9( &$Gwi  
    for m3 = 1:1:M3                                    % Start space evolution aF=;v*  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 1_~'?'&^  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; E?0RR'  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; /|Gz<nSc  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Q<osYO{l  
       sca2 = fftshift(fft(s2)); }k1[Fc|  
       sca3 = fftshift(fft(s3)); 7|m{hSc  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   9Up> e  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); .Gno K?  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); e mq%" ;.  
       s3 = ifft(fftshift(sc3)); =0@o(#gM  
       s2 = ifft(fftshift(sc2));                       % Return to physical space }Ny~.EV5^  
       s1 = ifft(fftshift(sc1)); IxP$ lx  
    end (_q&QI0{  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); QK~>KgVi  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); '?|.#D#-c  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 5o|u!#6  
       P1=[P1 p1/p10]; ~"~uXNd  
       P2=[P2 p2/p10]; bF@iO316H  
       P3=[P3 p3/p10]; {-IRX)m*  
       P=[P p*p]; R[lA@q:  
    end m<9W#  
    figure(1) z Hj_q%A  
    plot(P,P1, P,P2, P,P3); 4_eFc$^  
    {XS2<!D  
    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~!~