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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 ym]12PAU5  
    7_=7 ;PQ<  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ]* #k|>Fl  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 9s.x%m,  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear T?DX|?2X  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Yn~N;VUA  
    CnXl 7"  
    %fid=fopen('e21.dat','w'); - &7\do<  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) ~Z{IdE  
    M1 =3000;              % Total number of space steps ]Qu.-F#g  
    J =100;                % Steps between output of space g?9IS,Gp  
    T =10;                  % length of time windows:T*T0 I6.!0.G  
    T0=0.1;                 % input pulse width AZHZUd4  
    MN1=0;                 % initial value for the space output location #W]4aZ1  
    dt = T/N;                      % time step Uo~-^w}  
    n = [-N/2:1:N/2-1]';           % Index dF`\ewRFn  
    t = n.*dt;   e@`"V,i  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 US.7:S-r"  
    u20=u10.*0.0;                  % input to waveguide 2 &*e(  
    u1=u10; u2=u20;                 CyWMr/'  
    U1 = u1;   2#XYR>[  
    U2 = u2;                       % Compute initial condition; save it in U `Z' h[-2`  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. b3vPGR  
    w=2*pi*n./T; 2_i9 q>I  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 6Hh\ys  
    L=4;                           % length of evoluation to compare with S. Trillo's paper  gZg5On  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 /uNgftj  
    for m1 = 1:1:M1                                    % Start space evolution #+Pk_?  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS (b*PDhl`+  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 3= q,k<=L  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 'G#T 6B!  
       ca2 = fftshift(fft(u2)); fPA5]a9  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation C&1()U  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ^z^zsNx  
       u2 = ifft(fftshift(c2));                        % Return to physical space ov9+6'zya  
       u1 = ifft(fftshift(c1)); r](%9Y  
    if rem(m1,J) == 0                                 % Save output every J steps. P@xb  
        U1 = [U1 u1];                                  % put solutions in U array 8NUVHcB6  
        U2=[U2 u2]; z2 m(<zb  
        MN1=[MN1 m1]; HT% =o}y  
        z1=dz*MN1';                                    % output location 2C &G' @>  
      end lG>,&(  
    end h,palP6^  
    hg=abs(U1').*abs(U1');                             % for data write to excel jMAZ4M  
    ha=[z1 hg];                                        % for data write to excel X9S` #N  
    t1=[0 t']; ~CRd0T[^  
    hh=[t1' ha'];                                      % for data write to excel file *Bm7>g6  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format w Jr5[p*M  
    figure(1) kLfk2A;'i  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn YTk"'q-  
    figure(2) oR1HJ2>Z1  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6 o!*bWh  
    dln1JZ!  
    非线性超快脉冲耦合的数值方法的Matlab程序 ;WqWD-C  
    d OYEl<!J  
    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。   })#SjFq<V  
    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 fK?/o]vq  
    c(j|xQ\pE  
    Af`qe+0E  
    +5k^-  
    %  This Matlab script file solves the nonlinear Schrodinger equations 7%0V?+]P  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of %p(!7FDE2n  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear #sRkKl|  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ih[!v"bv  
    <=g{E-  
    C=1;                            L#>^R   
    M1=120,                       % integer for amplitude 6A ;,Ph2  
    M3=5000;                      % integer for length of coupler {}A1[ Y|  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) xaw)iC[gI{  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. hUo}n>Aa  
    T =40;                        % length of time:T*T0. u;/5@ADW  
    dt = T/N;                     % time step }NgevsV>;  
    n = [-N/2:1:N/2-1]';          % Index 9()d7Y#d/`  
    t = n.*dt;   v*[oe  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. |vUjoa'.7E  
    w=2*pi*n./T; Zai:?%^  
    g1=-i*ww./2; 1I#]OY#>  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 8rEUZk  
    g3=-i*ww./2; \v]esIP5R'  
    P1=0; 5IJm_oy  
    P2=0; +~{Honj[  
    P3=1; |3SM  
    P=0; d&x #9ka  
    for m1=1:M1                 gT&s &0_7  
    p=0.032*m1;                %input amplitude t"Tv(W?_  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 " R5! VV  
    s1=s10; .gP}/dj  
    s20=0.*s10;                %input in waveguide 2 sWKe5@-o0  
    s30=0.*s10;                %input in waveguide 3 HVLj(_ A  
    s2=s20; AS-%I+ A  
    s3=s30; <u Kd)l  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   O>tz;RU  
    %energy in waveguide 1 g-8D1.U  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   cqSo%a2  
    %energy in waveguide 2 (l_/ HQ32  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   vP. ^j7wB  
    %energy in waveguide 3 A(84cmq!q  
    for m3 = 1:1:M3                                    % Start space evolution Py^fWQ5I~%  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Ss$/Bh>hN  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 6!T9VL\=H  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; "IuHSjP  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform A}l+BIt  
       sca2 = fftshift(fft(s2)); |1/UC"f  
       sca3 = fftshift(fft(s3)); SF. Is=b  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ZT d)4f  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 3I.0jA#T&/  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); G}V5PEF]`  
       s3 = ifft(fftshift(sc3)); L}hc|(:  
       s2 = ifft(fftshift(sc2));                       % Return to physical space >X58 zlxk  
       s1 = ifft(fftshift(sc1)); NfsF'v  
    end @ i*It Hk  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ?qJt4Om  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); , #nYHD  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); jnzOTS   
       P1=[P1 p1/p10]; J-U5_>S  
       P2=[P2 p2/p10]; !l|fzS8g  
       P3=[P3 p3/p10]; ZFFKv  
       P=[P p*p]; .EB'n{zxd  
    end 4^3lG1^YY  
    figure(1) duq(K9S  
    plot(P,P1, P,P2, P,P3); N% !TFQf  
    ;_iDiLC;  
    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~!~