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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 ZgN*m\l  
    +1e*>jE  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of I(<1-3~  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of |s|RJA1  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear j+s8V-7(  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 K":- zS  
    b%AYYk)d?  
    %fid=fopen('e21.dat','w'); Dt8eVWkN~  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) Oi7|R7NE  
    M1 =3000;              % Total number of space steps `,TPd ~#~  
    J =100;                % Steps between output of space 2H4+D)  
    T =10;                  % length of time windows:T*T0 |i1z47jN6P  
    T0=0.1;                 % input pulse width G.L4l|%W  
    MN1=0;                 % initial value for the space output location ucTkWqG  
    dt = T/N;                      % time step 0(teplo&P  
    n = [-N/2:1:N/2-1]';           % Index 594$X@ !v  
    t = n.*dt;   1298&C@  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 )5&Wt@7Kj`  
    u20=u10.*0.0;                  % input to waveguide 2 W.>yIA%  
    u1=u10; u2=u20;                 InRn!~_N  
    U1 = u1;   K{HdqmxL.I  
    U2 = u2;                       % Compute initial condition; save it in U x}72jJe`  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. O>H4hp  
    w=2*pi*n./T; ^ .>)*P  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @@}A\wA-  
    L=4;                           % length of evoluation to compare with S. Trillo's paper ;b(/PH!O  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ~ 5`Ngpp  
    for m1 = 1:1:M1                                    % Start space evolution )TG\P,H9  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ~KEnZa0  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; _)lK.5  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform sd Z=3)  
       ca2 = fftshift(fft(u2)); df}B:?Ew.  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation vrh}X[JEw'  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   $yRbo '-  
       u2 = ifft(fftshift(c2));                        % Return to physical space |)1"*`z  
       u1 = ifft(fftshift(c1)); i9w xP i  
    if rem(m1,J) == 0                                 % Save output every J steps. >[ywrB ?T  
        U1 = [U1 u1];                                  % put solutions in U array -K+grsb g  
        U2=[U2 u2]; R0{+Xd  
        MN1=[MN1 m1]; 3 nb3rHQ  
        z1=dz*MN1';                                    % output location 0s= GM|y  
      end PE+N5n2Tl  
    end Z$Qlr:7  
    hg=abs(U1').*abs(U1');                             % for data write to excel H~&9xtuHN  
    ha=[z1 hg];                                        % for data write to excel F^KoEWj[H  
    t1=[0 t'];  5Gg`+o  
    hh=[t1' ha'];                                      % for data write to excel file f H}`  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format rXvvJIbi  
    figure(1) Onby=Y o6  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn =v1s@5 ;~  
    figure(2) $O7>E!uVD  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn >L)Xyq  
    1,BtOzuRo  
    非线性超快脉冲耦合的数值方法的Matlab程序 Z3"f7l6  
    [BmondOx  
    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。   w ~Es,@  
    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  XW`&1qx  
    [G4#DP\t>p  
    [R6du*P  
    `<q{8  
    %  This Matlab script file solves the nonlinear Schrodinger equations O3B\K <l  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 7S),:Uy[\  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7RTp+FC]  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 *m2J$9q  
    z_CBOJl#C!  
    C=1;                           GXJJOy1"!  
    M1=120,                       % integer for amplitude bQEQHqY5  
    M3=5000;                      % integer for length of coupler rn U2EL  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) ad }^Dj/  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. `[/BG)4  
    T =40;                        % length of time:T*T0. f`P%aX'cBQ  
    dt = T/N;                     % time step B4_0+K H  
    n = [-N/2:1:N/2-1]';          % Index +*~?JT  
    t = n.*dt;   8BC}D+q  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. |_ E)2b:h  
    w=2*pi*n./T; \*1pFX#  
    g1=-i*ww./2; G)iV  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Q_qc_IcM y  
    g3=-i*ww./2; -i7W|X"  
    P1=0; ^~8l|d_  
    P2=0; @R(6w{h9  
    P3=1; Sh}AGNE'  
    P=0; T'0Ot3m`  
    for m1=1:M1                 s 3Y \,9\  
    p=0.032*m1;                %input amplitude !$f@j6.  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 $yHlkd`Y  
    s1=s10; YjoN: z`b  
    s20=0.*s10;                %input in waveguide 2 #*1\h=bzmW  
    s30=0.*s10;                %input in waveguide 3 )nTOIfP2  
    s2=s20; R/A40i  
    s3=s30; >Ix)jSNLgo  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ZSU;>&>%v  
    %energy in waveguide 1 Ri"3o  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ]7fqVOiOu  
    %energy in waveguide 2 N@)tU;U3O  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   % )?$82=2  
    %energy in waveguide 3 83Bp_K2\  
    for m3 = 1:1:M3                                    % Start space evolution ;HgV(d#X  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS r[JgCj+$&  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; [#$z.BoEo  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ie=tM'fb  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform b_z;^y~  
       sca2 = fftshift(fft(s2)); >jq~5HN  
       sca3 = fftshift(fft(s3)); $:t;WXc.<  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   V2V^*9(wu@  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 4JT9EKo  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); |*e >hk  
       s3 = ifft(fftshift(sc3)); GadQ \>  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 9Psy$  
       s1 = ifft(fftshift(sc1)); Yhb=^)@))  
    end \:'=ccf  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); P}KyT?X:  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); }pTy mAN  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ZBB^?FF  
       P1=[P1 p1/p10]; =pF 6  
       P2=[P2 p2/p10]; 5NZob<<  
       P3=[P3 p3/p10]; OGzth$7A  
       P=[P p*p]; K\`L>B. 1  
    end 8~u#?xs6  
    figure(1) Ir_K8 3VM  
    plot(P,P1, P,P2, P,P3); ?Xx,[Z&  
    kViX FPW  
    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~!~