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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 q5S9C%b  
    \'j|BJ~L f  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 8q7b_Pq1U  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of e+K^A q  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear sDV Q#}a  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 }<:}XlwT%  
    g9F?z2^  
    %fid=fopen('e21.dat','w'); 2:ylv<\$  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) C7AUsYM  
    M1 =3000;              % Total number of space steps N{>n$ v}  
    J =100;                % Steps between output of space `r_/Wt{g  
    T =10;                  % length of time windows:T*T0 FVBYo%Ap  
    T0=0.1;                 % input pulse width Oow2>F%_#  
    MN1=0;                 % initial value for the space output location jc9y<{~x/  
    dt = T/N;                      % time step U m+8"W  
    n = [-N/2:1:N/2-1]';           % Index <a+Z;>  
    t = n.*dt;   %8x#rohP  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 0m ? )ROaJ  
    u20=u10.*0.0;                  % input to waveguide 2 E_LN]v  
    u1=u10; u2=u20;                 zx7{U8*`<  
    U1 = u1;   @lph)A Nk  
    U2 = u2;                       % Compute initial condition; save it in U T[A 69O]v  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. F6dP,(  
    w=2*pi*n./T; [ikOb8 G#  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T jZ; =so  
    L=4;                           % length of evoluation to compare with S. Trillo's paper "zy7C*)>r  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 gZ1?G-Q  
    for m1 = 1:1:M1                                    % Start space evolution @=kSo -SX  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS )dSi/  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; H>@+om  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform n(]-y@X0_  
       ca2 = fftshift(fft(u2)); uW3!Yg@  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ,7b[!#?8  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   >F&47Yn  
       u2 = ifft(fftshift(c2));                        % Return to physical space sp`Dvqx0  
       u1 = ifft(fftshift(c1)); S21,VpW\  
    if rem(m1,J) == 0                                 % Save output every J steps. X\ F|Tk3_  
        U1 = [U1 u1];                                  % put solutions in U array *uvQ\.  
        U2=[U2 u2]; \nqS+on]  
        MN1=[MN1 m1]; t&DEb_"De  
        z1=dz*MN1';                                    % output location WMg~Y"W  
      end KY] C6kh  
    end iG?[<1~  
    hg=abs(U1').*abs(U1');                             % for data write to excel sn>~O4"  
    ha=[z1 hg];                                        % for data write to excel O|UC ?]6  
    t1=[0 t']; &iVs0R  
    hh=[t1' ha'];                                      % for data write to excel file HUOj0T  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 7J&4akT{9  
    figure(1) M& CqSd  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn +d-NL?c  
    figure(2) GowH]MO  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 2)~> R  
    ei5~&  
    非线性超快脉冲耦合的数值方法的Matlab程序 D|#E9OQzs  
    da~],MN  
    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。   &YeA:i?  
    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 W+1^4::+  
    *4_Bd=5(U  
    /|#fejPh  
    D7qOZlX16  
    %  This Matlab script file solves the nonlinear Schrodinger equations :p6M=  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 0Fr?^3h  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear IdxzE_@  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 !$>R j  
    xi; `ecqS<  
    C=1;                           bK-N:8Z  
    M1=120,                       % integer for amplitude i(+p0:< 0  
    M3=5000;                      % integer for length of coupler _t}WsEQ+P  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) {2 "zVt#h  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. e64^ChCoV  
    T =40;                        % length of time:T*T0. h3@v+Z<}  
    dt = T/N;                     % time step m9}P9 ?  
    n = [-N/2:1:N/2-1]';          % Index w"&n?L  
    t = n.*dt;   J!7MZL b  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. m<2M4u   
    w=2*pi*n./T; !_Z&a  
    g1=-i*ww./2; 5.J.RE"M  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; vEz"xz1j!]  
    g3=-i*ww./2; 2T[9f;jM'  
    P1=0; t5IEQ2  
    P2=0; SOvF[,+  
    P3=1; 4|#WFLo@  
    P=0; QnX(V[  
    for m1=1:M1                 i<g-+Qs  
    p=0.032*m1;                %input amplitude CQDkFQq-dq  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 t9IW/Q  
    s1=s10; |)/aGZ+  
    s20=0.*s10;                %input in waveguide 2 =rX>1  
    s30=0.*s10;                %input in waveguide 3 yyy|Pw4:Z  
    s2=s20; KRKCD4  
    s3=s30; 3%=~) 7cF  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   `,*5wBC  
    %energy in waveguide 1 P J[`|  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   )IZ~G\Ra'  
    %energy in waveguide 2 }|5Pr(I  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   b9dLt6d  
    %energy in waveguide 3 ^@NU}S):yN  
    for m3 = 1:1:M3                                    % Start space evolution V,N%;iB}  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ! #2{hQRu  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Y% 5eZ=z  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 4)o  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 0h7r&t%YsV  
       sca2 = fftshift(fft(s2)); SGlNKA},A  
       sca3 = fftshift(fft(s3)); vd4ytC  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   l_%6  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 0>Z_*U~6  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); fXQNHZ|4  
       s3 = ifft(fftshift(sc3)); nwCrZW  
       s2 = ifft(fftshift(sc2));                       % Return to physical space sZF6h=67D  
       s1 = ifft(fftshift(sc1)); 3=]sLn0L  
    end W X6&oy>  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); /%A*aGyIc  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); UN<]N76!  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 'F#KM1s  
       P1=[P1 p1/p10]; $l&(%\pp  
       P2=[P2 p2/p10]; 2x0<&Xy#P  
       P3=[P3 p3/p10]; XAL1|] S  
       P=[P p*p]; -4_$ln w$  
    end WU=59gB+jL  
    figure(1) 3WIk  
    plot(P,P1, P,P2, P,P3); G {%LB}2  
    0F><P?5  
    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~!~