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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 ,T&B.'cq  
    ]4z?sk@  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of W&bh&KzCW  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of _v2FXm   
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear (5G^"Srw  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 pOH_ CXw  
    BT#'<!7!  
    %fid=fopen('e21.dat','w'); Pi+,y  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) Q3oVl^q  
    M1 =3000;              % Total number of space steps Q'Q+mt8u5  
    J =100;                % Steps between output of space (V e[FhA  
    T =10;                  % length of time windows:T*T0 /3+7a\|mKr  
    T0=0.1;                 % input pulse width W*U\79H  
    MN1=0;                 % initial value for the space output location vkBngsS  
    dt = T/N;                      % time step ?"sk"{  
    n = [-N/2:1:N/2-1]';           % Index 2!" N9Adt  
    t = n.*dt;   Keof{>V=CA  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 UTs0=:+,t  
    u20=u10.*0.0;                  % input to waveguide 2 ]Ff&zBJ  
    u1=u10; u2=u20;                 `+* Mr  
    U1 = u1;   IS'=%qhC`  
    U2 = u2;                       % Compute initial condition; save it in U 0Y!Bb2 m  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. l|N1u=Z  
    w=2*pi*n./T; \" .3x PkE  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T iY*Xm,#  
    L=4;                           % length of evoluation to compare with S. Trillo's paper -{L[Wt{1  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 $f C=v  
    for m1 = 1:1:M1                                    % Start space evolution *AxKV5[H  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS },[j+wx  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; XM8C{I1  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform y4shW|>5_  
       ca2 = fftshift(fft(u2)); %C)U F  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Q) FL|   
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Xb;CY9&  
       u2 = ifft(fftshift(c2));                        % Return to physical space "t\rjFw  
       u1 = ifft(fftshift(c1)); gQ/zk3?k  
    if rem(m1,J) == 0                                 % Save output every J steps. YTYYb#"Q  
        U1 = [U1 u1];                                  % put solutions in U array U'lrdc"Q  
        U2=[U2 u2]; y l3iU:+V  
        MN1=[MN1 m1]; J-I7K !B  
        z1=dz*MN1';                                    % output location RHB>svT^K>  
      end Ye1P5+W(  
    end `9 $?g|rB  
    hg=abs(U1').*abs(U1');                             % for data write to excel i>e75`9  
    ha=[z1 hg];                                        % for data write to excel S!g&&RDx  
    t1=[0 t']; XPX{c|]>.  
    hh=[t1' ha'];                                      % for data write to excel file O'5(L9,  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 'VF9j\a  
    figure(1) T]E$H, p  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Vwv O@G7A  
    figure(2) @rVmr{UE  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1 k H  
    >xH3*0 Lp  
    非线性超快脉冲耦合的数值方法的Matlab程序 9prG@  
    J.O;c5wL  
    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。   1` 9/[2z  
    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 q .?D{[2  
    y)(@  
    >GZF \ER  
    "w_(p|cm=  
    %  This Matlab script file solves the nonlinear Schrodinger equations zHx?-Q&3  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of &G'R{s&"  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear c"0CHrd  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 !TG"AW  
    z2,rnm)Q  
    C=1;                           kW/ksz0)  
    M1=120,                       % integer for amplitude wePMBL1P*  
    M3=5000;                      % integer for length of coupler *W i(%  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) g\6(ezUF*  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. A 7TP1  
    T =40;                        % length of time:T*T0. lUWjm%|  
    dt = T/N;                     % time step Y3-15:-  
    n = [-N/2:1:N/2-1]';          % Index ~[,E i k  
    t = n.*dt;   /+66y=`UJ  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. U;{VL!  
    w=2*pi*n./T;  T>LtN  
    g1=-i*ww./2; Xv'64Nc!;  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; qP]Gl--q{  
    g3=-i*ww./2; &, K;F'  
    P1=0; !X#=Pt[,  
    P2=0; +LX&1GX  
    P3=1; LTJ|EXYA  
    P=0; V:IoeQ]-  
    for m1=1:M1                 ,',fO?Qv'  
    p=0.032*m1;                %input amplitude h3JIiwv0!  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 }*+ca>K  
    s1=s10; UkeW2l`:  
    s20=0.*s10;                %input in waveguide 2 )DoY*'Cl  
    s30=0.*s10;                %input in waveguide 3 gE8>5_R|  
    s2=s20; 242lR0#aY  
    s3=s30; =P2T&Gb  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   v'Lckw@G4  
    %energy in waveguide 1 6i&WF<%D  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   zzPgLE55  
    %energy in waveguide 2 g:OVAA  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   BeplS  
    %energy in waveguide 3 `cVG_= 2  
    for m3 = 1:1:M3                                    % Start space evolution /~AajLxu3W  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS @3b0hi4  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; i;Gl-b\_h  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; D4 e)v%  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform BDcl1f T  
       sca2 = fftshift(fft(s2)); (+T|B E3*#  
       sca3 = fftshift(fft(s3)); TNiF l hq  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ^8We}bs-c  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); b/<n:*$   
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); GKm)wOb(*S  
       s3 = ifft(fftshift(sc3)); hX[hR  
       s2 = ifft(fftshift(sc2));                       % Return to physical space >5XE*9  
       s1 = ifft(fftshift(sc1)); od-N7lp#  
    end q?\3m3GM  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); v`no dI  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); =SLJkw&w6  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); u QCQ$  
       P1=[P1 p1/p10]; u*PN1E  
       P2=[P2 p2/p10]; ;2& (]1X  
       P3=[P3 p3/p10]; !_zmm$bR  
       P=[P p*p]; [?]s((A~B  
    end }X}fX#[  
    figure(1) a}%>i~v<  
    plot(P,P1, P,P2, P,P3); uv._N6mj  
    BcA:M\dK%  
    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~!~