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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 4w5);x.  
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    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of I%:\"g"c  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of t>! Ok  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 74r$)\q  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 $f?GD<}?7r  
    &u2H^ j  
    %fid=fopen('e21.dat','w'); Z`<5SHQd  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) X;]I jha<*  
    M1 =3000;              % Total number of space steps B~B,L*kC2  
    J =100;                % Steps between output of space ezb*tN!  
    T =10;                  % length of time windows:T*T0 3Fw7q"  
    T0=0.1;                 % input pulse width N*+L'bO  
    MN1=0;                 % initial value for the space output location yV*jc`1  
    dt = T/N;                      % time step Rt>mAU$}  
    n = [-N/2:1:N/2-1]';           % Index k+BY3a  
    t = n.*dt;   @jCMQYR  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 4sq](! A  
    u20=u10.*0.0;                  % input to waveguide 2 o3$dl`'  
    u1=u10; u2=u20;                 {T-=&%||  
    U1 = u1;   ,N1pww?  
    U2 = u2;                       % Compute initial condition; save it in U !dq$qUl/  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. $0R5 ]]db)  
    w=2*pi*n./T; {)(Mkm +d  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T qP0UcG  
    L=4;                           % length of evoluation to compare with S. Trillo's paper @ZRg9M:N  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 Gz52^O :  
    for m1 = 1:1:M1                                    % Start space evolution f0879(,i  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 1 -$+@Xl  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Eh^gR`I  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform : { iK 5  
       ca2 = fftshift(fft(u2)); 5"y)<VLJX  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation g:Q:cSg<  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   +%H=+fJ2}  
       u2 = ifft(fftshift(c2));                        % Return to physical space #jJ0Mxg  
       u1 = ifft(fftshift(c1)); MOPHu O{^  
    if rem(m1,J) == 0                                 % Save output every J steps. %l,CJd5  
        U1 = [U1 u1];                                  % put solutions in U array $_3 )m  
        U2=[U2 u2]; h$mGaw vZ~  
        MN1=[MN1 m1]; *R}p9;dpO  
        z1=dz*MN1';                                    % output location m>|7&l_  
      end jvxCCYXR  
    end 0{ _6le]  
    hg=abs(U1').*abs(U1');                             % for data write to excel |ZC'a!  
    ha=[z1 hg];                                        % for data write to excel P%ThW9^vnj  
    t1=[0 t']; Y9I|s{~  
    hh=[t1' ha'];                                      % for data write to excel file KrR`A(=WL  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format @Ko#nDEq  
    figure(1) =KAN|5yn  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn F"cZ$TL]  
    figure(2) qHgzgS7a  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn R13V }yL  
    ~^'WHuz Py  
    非线性超快脉冲耦合的数值方法的Matlab程序 X#Ob^E%J  
    l[i1,4  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   D<:zw/IRE  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1/,~0N9  
    1;PI%++  
    *2fJdY  
    E62_k 0q  
    %  This Matlab script file solves the nonlinear Schrodinger equations M2;6Cz>,P  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of q6b&b^r+H  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 4 L 5$=V  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 _Fn`G .r<  
    Z?d][zGw  
    C=1;                           sgnc$x"  
    M1=120,                       % integer for amplitude `4?|yp.|L  
    M3=5000;                      % integer for length of coupler mN> (n+ly  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) NB5lxaL  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. F@HJ3O9  
    T =40;                        % length of time:T*T0. :Gzp (@<@e  
    dt = T/N;                     % time step GvvKM=1  
    n = [-N/2:1:N/2-1]';          % Index 6oFA=CjU{  
    t = n.*dt;   }#2(WHf =<  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. F(ZczwvR  
    w=2*pi*n./T;  3bJ|L3G  
    g1=-i*ww./2; 'vYt_T  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; q: X^V$`  
    g3=-i*ww./2; u%6b|M@P  
    P1=0; hd,O/-m#  
    P2=0; -r]L MQ  
    P3=1; 7G7"Zule*j  
    P=0; bR1Q77<G\  
    for m1=1:M1                 }: u-l3e  
    p=0.032*m1;                %input amplitude Bj"fUI!dK  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 <:&{c-f/  
    s1=s10; lauq(aD_C  
    s20=0.*s10;                %input in waveguide 2 ZD7qw*3+  
    s30=0.*s10;                %input in waveguide 3 ,b5vnW\  
    s2=s20; N7KG_o%  
    s3=s30; ^.  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   P RNq8nmxC  
    %energy in waveguide 1 sl(go^  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   K r<UPr  
    %energy in waveguide 2 yqtaQ0F~  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ];5Auh 0o  
    %energy in waveguide 3 r:Q=6j,  
    for m3 = 1:1:M3                                    % Start space evolution B9Wd '  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS G'';VoW=   
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; I~Qi):&x  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; |7Ab_  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform )D)4=LJ  
       sca2 = fftshift(fft(s2)); fU\;\  
       sca3 = fftshift(fft(s3)); 6#.9T;&  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ~=t9-AF-  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); a#x@ e?GvI  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); :h/v"2uDN  
       s3 = ifft(fftshift(sc3)); 1)qD)E5&cf  
       s2 = ifft(fftshift(sc2));                       % Return to physical space g[ uf e<  
       s1 = ifft(fftshift(sc1)); &}|`h8JA]K  
    end (_+ux1h6^  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); QAMcI:5  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); e 'F:LMX  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); V]"pM]>3X  
       P1=[P1 p1/p10]; GXNkl?#  
       P2=[P2 p2/p10]; d2)]6)z6  
       P3=[P3 p3/p10]; U.b|3E/^  
       P=[P p*p]; *UXa.kT@  
    end %o0H#7'  
    figure(1) ${}9/(x/^  
    plot(P,P1, P,P2, P,P3); 1'iQlnMO@  
    ( z F_<  
    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~!~