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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 Q8i6kf!  
    O!tD1^O!1}  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 37Y]sJrs$  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of =ndKG5  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear qC1@p?8$  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]9Hy "#Fz  
    :~Y$\Ww(~  
    %fid=fopen('e21.dat','w'); ow "Xv  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 7/L7L5h<  
    M1 =3000;              % Total number of space steps 67?5Cv  
    J =100;                % Steps between output of space _!zY(9%  
    T =10;                  % length of time windows:T*T0 lH.2H  
    T0=0.1;                 % input pulse width $EF@x}h:A  
    MN1=0;                 % initial value for the space output location g=Di2j{A  
    dt = T/N;                      % time step |e\%pfZ   
    n = [-N/2:1:N/2-1]';           % Index _!7o   
    t = n.*dt;   9j`-fs@:  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 8vK&d>  
    u20=u10.*0.0;                  % input to waveguide 2 PQ>JoRs  
    u1=u10; u2=u20;                 -yeT$P&|  
    U1 = u1;   tw66XxE  
    U2 = u2;                       % Compute initial condition; save it in U jLSZ#H  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. _rd{cvdR  
    w=2*pi*n./T; iY-dM(_:]  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ,H*3_c&Q  
    L=4;                           % length of evoluation to compare with S. Trillo's paper s?Kn,6Y  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 P>|2~YxjU  
    for m1 = 1:1:M1                                    % Start space evolution 9&cZIP   
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS \BL9}5y  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; <=Qk^Y2k  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform jxvVp*-=<j  
       ca2 = fftshift(fft(u2)); 5oS\uX|  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation eAMT72_  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ,"o \_{<z  
       u2 = ifft(fftshift(c2));                        % Return to physical space "|if<hx+  
       u1 = ifft(fftshift(c1)); KXJHb{?  
    if rem(m1,J) == 0                                 % Save output every J steps. kN)ev?pQ[  
        U1 = [U1 u1];                                  % put solutions in U array (&(f`c@I  
        U2=[U2 u2]; JFZ p^{  
        MN1=[MN1 m1]; iweP3u##  
        z1=dz*MN1';                                    % output location W= !f  
      end #82B`y<<y/  
    end rzu^br9X  
    hg=abs(U1').*abs(U1');                             % for data write to excel T (qu~}  
    ha=[z1 hg];                                        % for data write to excel 9!LAAE`  
    t1=[0 t']; '' 6  
    hh=[t1' ha'];                                      % for data write to excel file J5k%  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format f@0`,  
    figure(1) &>o)7H];  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn (]:G"W8f  
    figure(2) Qxwe,:  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn a;K:~R+@,  
    XebCl{HHp  
    非线性超快脉冲耦合的数值方法的Matlab程序 y_6HQ:  
    S~T[*Z/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。   z2V!u\It  
    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 nFqMS|EN  
    -LyIu#  
    utr_fFu  
    Z(L>~+%  
    %  This Matlab script file solves the nonlinear Schrodinger equations {)mlXo(On  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of rhrlEf@  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <\5{R@A*6  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 3r\QLIr L8  
    g=)@yZ3>v  
    C=1;                           5M*p1^ >  
    M1=120,                       % integer for amplitude [Mi~4b  
    M3=5000;                      % integer for length of coupler :9<5GF(  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) {'1,JwSmb  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Nx99dr  
    T =40;                        % length of time:T*T0. 1 !sYd@iD@  
    dt = T/N;                     % time step M0|z^2  
    n = [-N/2:1:N/2-1]';          % Index "jSn`  
    t = n.*dt;   y.zW>Mfl  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. &b_duWs  
    w=2*pi*n./T; x RfX:3  
    g1=-i*ww./2; rZLMY M  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; .MKxHM7  
    g3=-i*ww./2; [(C lvGx  
    P1=0; FEkx&9]  
    P2=0; 4 QWHGh"  
    P3=1; q bo`E!K  
    P=0; Px<;-H`  
    for m1=1:M1                 R&?p^!`%  
    p=0.032*m1;                %input amplitude HkrNt/]  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ,q4Y N-3  
    s1=s10; W|:WAxJ*d  
    s20=0.*s10;                %input in waveguide 2 Q]8r72uSk  
    s30=0.*s10;                %input in waveguide 3 `!i>fo~  
    s2=s20; ~%]+5^Ka]  
    s3=s30; o\N),;LM  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ]]+"`t,-  
    %energy in waveguide 1 2'D2>^os  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   >">-4L17m  
    %energy in waveguide 2 .L}ar7  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   C`fQ` RL\  
    %energy in waveguide 3 /wQDcz  
    for m3 = 1:1:M3                                    % Start space evolution q N>j2~  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS dwRJ0D]&  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ~!I \{(  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; i9d.Ls  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform =dPrG=A   
       sca2 = fftshift(fft(s2)); &a V`u?'e  
       sca3 = fftshift(fft(s3)); &W1cc#(  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   T a_#Rg*!  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 5( 3tPbm{  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); $(BW |Pc  
       s3 = ifft(fftshift(sc3)); ~MOIrF  
       s2 = ifft(fftshift(sc2));                       % Return to physical space HM`;%0T0(  
       s1 = ifft(fftshift(sc1)); 'h$1vT  
    end 4g|}]K1s  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));  0y?bwxkc  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); YQ]W<0(  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |1#*`2j\=9  
       P1=[P1 p1/p10]; Ls( &.  
       P2=[P2 p2/p10]; J=  T!  
       P3=[P3 p3/p10]; b^0=X!bg  
       P=[P p*p]; d+8Sypv^4*  
    end 8/k* "^3  
    figure(1) m}rUc29cS,  
    plot(P,P1, P,P2, P,P3); |(]XZ!{  
    lwSA!W  
    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~!~