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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 FN^FvQ  
    /*rhtrS)  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of k'3Wt*i  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of t ^SzqB  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 0 n vSvk  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 (zcLx;N  
    |E)aT#$f'  
    %fid=fopen('e21.dat','w'); {38bv. 3'  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) sa&) #Z:  
    M1 =3000;              % Total number of space steps . iwZ*b{  
    J =100;                % Steps between output of space j/!H$0PN  
    T =10;                  % length of time windows:T*T0 /)L 0`:I#  
    T0=0.1;                 % input pulse width `T&jPA9eY  
    MN1=0;                 % initial value for the space output location y 1\'( 1  
    dt = T/N;                      % time step oBQm05x"  
    n = [-N/2:1:N/2-1]';           % Index v]VWDT `  
    t = n.*dt;   jZ*WN|FK?  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 |j~lkzPnV  
    u20=u10.*0.0;                  % input to waveguide 2 5&!c7$K0  
    u1=u10; u2=u20;                 $XnPwOj  
    U1 = u1;   s1j{x&OSq  
    U2 = u2;                       % Compute initial condition; save it in U #0Ds'pE-  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. +^|iZbZKx  
    w=2*pi*n./T; #UP~iHbt\  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T %; "@Ah  
    L=4;                           % length of evoluation to compare with S. Trillo's paper s Be7"^  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 EnVuD 9  
    for m1 = 1:1:M1                                    % Start space evolution {KL5GowH  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ci9R.U)  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; |CFRJN-J"  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform @.C{OSH E  
       ca2 = fftshift(fft(u2)); ca<"  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ]/X(V|t  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   f58?5(Dc|  
       u2 = ifft(fftshift(c2));                        % Return to physical space /0MDISQy9  
       u1 = ifft(fftshift(c1)); @R|'X  
    if rem(m1,J) == 0                                 % Save output every J steps. 0%`4px4J  
        U1 = [U1 u1];                                  % put solutions in U array /iaf ^ >  
        U2=[U2 u2]; 5e8AmY8;  
        MN1=[MN1 m1]; q8P.,%   
        z1=dz*MN1';                                    % output location }iB|sl2J  
      end [^YA=K hu  
    end SkQswH  
    hg=abs(U1').*abs(U1');                             % for data write to excel wf.T3  
    ha=[z1 hg];                                        % for data write to excel BqK(DH^9N  
    t1=[0 t']; ^Q<mV*~  
    hh=[t1' ha'];                                      % for data write to excel file ~nLN`H d  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format !U%T&?E l  
    figure(1) KJn!Ap  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn O`1!  
    figure(2) ),:c+~@@kT  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn V N{NA+I  
    k44Q):ncY7  
    非线性超快脉冲耦合的数值方法的Matlab程序 bPK Ow<  
    oPf)be| #  
    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。   OPJ: XbG  
    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 hB;VCg8  
    l\0w;:N3  
    Elj_,z  
    x\e;+ubt}  
    %  This Matlab script file solves the nonlinear Schrodinger equations uP $ Cj  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of g^Yl TB  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear `O?T.p)   
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 y m,H@~  
    75T_Dx(H  
    C=1;                           -ezY= 0Q&  
    M1=120,                       % integer for amplitude g>0XxjP4  
    M3=5000;                      % integer for length of coupler W1Lr_z6  
    N = 512;                      % Number of Fourier modes (Time domain sampling points)  YpAg  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. dC e4u<so\  
    T =40;                        % length of time:T*T0. [H\:pP8t  
    dt = T/N;                     % time step <:FP4e "(  
    n = [-N/2:1:N/2-1]';          % Index Jb)#fH$L  
    t = n.*dt;   j:T/iH!YF  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. `O?TUQGR  
    w=2*pi*n./T; WO4=Mte?  
    g1=-i*ww./2; G|w=ez  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; yH 9!GS#  
    g3=-i*ww./2; /v|"0  
    P1=0; kd:$oS_*s  
    P2=0; W%2 80\h  
    P3=1; 1% F?B-k  
    P=0; jCAC `  
    for m1=1:M1                 >SN|?|2U/  
    p=0.032*m1;                %input amplitude HmfG$Z  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 87%*+n:?*  
    s1=s10; v8gdU7Ll,  
    s20=0.*s10;                %input in waveguide 2 $8USyGi3J  
    s30=0.*s10;                %input in waveguide 3 OH^N" L  
    s2=s20; jN-vY<?h]  
    s3=s30; {qW~"z*  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   :WI.LKlo~  
    %energy in waveguide 1 > oA? 6x  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Om'+]BBN  
    %energy in waveguide 2 [ xOzzp4  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   bPD`+: A_  
    %energy in waveguide 3 cfox7FmW  
    for m3 = 1:1:M3                                    % Start space evolution tkQH\5  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS KTvzOI8  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; J89Dul l  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; |4mpohX  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 9][(Iu]h7  
       sca2 = fftshift(fft(s2)); fP tm0.r  
       sca3 = fftshift(fft(s3)); i&njqK!wS  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   >&g}7d%  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); )15Z#`x  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 7"7rmZ   
       s3 = ifft(fftshift(sc3)); $@d9<83=  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ; Sd\VR  
       s1 = ifft(fftshift(sc1)); !3i Gz_y  
    end svelYe#9z  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); PiV7*F4qI.  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); }>^Q'BW;65  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); l$K,#P<)  
       P1=[P1 p1/p10]; +$xeoxU>;  
       P2=[P2 p2/p10]; 2oa#0`{  
       P3=[P3 p3/p10]; O20M[_S  
       P=[P p*p]; Tmh(= TB'  
    end _A<u#.yd  
    figure(1) a9n^WOJ6  
    plot(P,P1, P,P2, P,P3); VL[R(a6c <  
    ;fw1  
    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~!~