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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 F2yc&mXyk  
    6mr5`5~w  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of W8:?y*6  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of iX8& mUR  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ~U+SK4SK:o  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 eJ+V!K'H2  
    u%FG% j?C  
    %fid=fopen('e21.dat','w'); FWNO/)~t  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) {umdW x.*  
    M1 =3000;              % Total number of space steps )J&1uMp{  
    J =100;                % Steps between output of space F0O"rN{  
    T =10;                  % length of time windows:T*T0 R=jIVw'  
    T0=0.1;                 % input pulse width [bd fp a  
    MN1=0;                 % initial value for the space output location d(RSn|[0  
    dt = T/N;                      % time step ` V}e$  
    n = [-N/2:1:N/2-1]';           % Index `a}!t=~#w  
    t = n.*dt;   l$$N~FN  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 b&BSigrvou  
    u20=u10.*0.0;                  % input to waveguide 2 d5gYJ/Qv  
    u1=u10; u2=u20;                 Wpo:'?!(M^  
    U1 = u1;   ,/n<Qg"`  
    U2 = u2;                       % Compute initial condition; save it in U "G\OKt'Z  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 8<}f:9/  
    w=2*pi*n./T; ;h> s=D,r  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ?[>+'6  
    L=4;                           % length of evoluation to compare with S. Trillo's paper KD9Y  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 +$Q33@F5l  
    for m1 = 1:1:M1                                    % Start space evolution ^;0.P)yGA  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Xk[;MZ[  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; WyH2` xxX  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform "71@WLlN  
       ca2 = fftshift(fft(u2)); juPW!u  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 2x-67_BHY=  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   g3@Qn?(j!  
       u2 = ifft(fftshift(c2));                        % Return to physical space o*7`r~  
       u1 = ifft(fftshift(c1)); #Jt9U1WbF  
    if rem(m1,J) == 0                                 % Save output every J steps. ]r;-Lx{F  
        U1 = [U1 u1];                                  % put solutions in U array O-r,&W  
        U2=[U2 u2]; 5/<?Y&x  
        MN1=[MN1 m1]; %jKbRiz1u  
        z1=dz*MN1';                                    % output location f8um.Xnp6  
      end AyZL(  
    end zoYw[YP9  
    hg=abs(U1').*abs(U1');                             % for data write to excel V=}AFGC85  
    ha=[z1 hg];                                        % for data write to excel |IL..C  
    t1=[0 t']; Iuk!A?XV  
    hh=[t1' ha'];                                      % for data write to excel file (rV#EA+6[`  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format .du FMJl  
    figure(1) ..RCR_DIp  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn T/Q#V)Tp  
    figure(2) $OK}jSH*v)  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ~Aul 7[IH  
    #w3cImgp2  
    非线性超快脉冲耦合的数值方法的Matlab程序 YK Nz[x$|  
    < &[=,R0 @  
    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。   Q C?*O?~#  
    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 ;E0Xn-o_  
    yD6lzuk{X  
    5!Y51R^c  
    ydFZ$W_}w  
    %  This Matlab script file solves the nonlinear Schrodinger equations N<V,5  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Yhu 6QyRV  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear $ftcYBZa  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 "I.PV$Rxl  
    5(kRFb'31F  
    C=1;                           hawE2k0p(  
    M1=120,                       % integer for amplitude |U}al[  
    M3=5000;                      % integer for length of coupler / 0Z_$Q&e  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) FFGG6r  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 4O Lq  
    T =40;                        % length of time:T*T0. qE73M5L&  
    dt = T/N;                     % time step H2oAek(  
    n = [-N/2:1:N/2-1]';          % Index ][R#Q;y<  
    t = n.*dt;   o'S&YD  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ]DcQ8D  
    w=2*pi*n./T; fyat-wbb  
    g1=-i*ww./2; ghq#-N/t  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ki`7S  
    g3=-i*ww./2; <{U "0jY!9  
    P1=0; bN-ljw0&  
    P2=0; W ~sP7&sp  
    P3=1; &y-(UOqbkP  
    P=0; B=K& +  
    for m1=1:M1                 (vHB`@x  
    p=0.032*m1;                %input amplitude ZsjDe{TH  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 *3_@#Uu7  
    s1=s10; >*v!2=  
    s20=0.*s10;                %input in waveguide 2 ZujPk-  
    s30=0.*s10;                %input in waveguide 3 e-vwve  
    s2=s20; z)$X/v  
    s3=s30; v{7Jzjd  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Cf#[E~24  
    %energy in waveguide 1 `em}vdY  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   J)R;NYl  
    %energy in waveguide 2 >gNVL (  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   0. _)X  
    %energy in waveguide 3 m4FT^ ^3yE  
    for m3 = 1:1:M3                                    % Start space evolution % j4  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 5e^t;  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; U2  0@B`<  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;  +c@s  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform D;%(Z!  
       sca2 = fftshift(fft(s2)); at_~b Ox6X  
       sca3 = fftshift(fft(s3)); XI#1)  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   O=c^Ak   
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 7;H!F!K]  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Nrp0z:  
       s3 = ifft(fftshift(sc3)); RtZK2  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ~4HS 2\  
       s1 = ifft(fftshift(sc1)); u;$g1 3  
    end  [wS~.  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 4N&4TUIM  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); + k1|+zzS  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); rv/O^aL`Y  
       P1=[P1 p1/p10]; W10=SM}  
       P2=[P2 p2/p10]; tE"aNA#=  
       P3=[P3 p3/p10]; @"[xX}xK;  
       P=[P p*p]; )@"iWQ 3K  
    end (<RZZ{m  
    figure(1) ,1-n=eTQ  
    plot(P,P1, P,P2, P,P3); 1&_9 3  
    ;{xk[f m=  
    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~!~