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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 EWr8=@iU  
    App9um3:  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of S<-e/`p=H  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of gbl`_t/  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear \["'%8[:gR  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 "IvFkS=*Q  
    7e`ylnP!  
    %fid=fopen('e21.dat','w'); {dbPMx  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) ^xpiNP!?a  
    M1 =3000;              % Total number of space steps G(;C~kHX  
    J =100;                % Steps between output of space >=WlrmI  
    T =10;                  % length of time windows:T*T0 tlz+!>  
    T0=0.1;                 % input pulse width z-Ndv;:  
    MN1=0;                 % initial value for the space output location X=W.{?  
    dt = T/N;                      % time step v&8%t 7|  
    n = [-N/2:1:N/2-1]';           % Index 5 wT e?  
    t = n.*dt;   Oh|KbM*vS  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 TsvF~Gdp  
    u20=u10.*0.0;                  % input to waveguide 2 &2,0?ra2&  
    u1=u10; u2=u20;                 HqZ3]  
    U1 = u1;   ;:Yz7<>Y,  
    U2 = u2;                       % Compute initial condition; save it in U qkLp8/G>pO  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ISbhC!59  
    w=2*pi*n./T; Hl3%+f  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T I|SQhbi  
    L=4;                           % length of evoluation to compare with S. Trillo's paper _UqE -+&  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 E76#xsyhF  
    for m1 = 1:1:M1                                    % Start space evolution S 6|#9C&  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS IGtpL[.;/  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; _@gd9Fi7J  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform B F,8[|%#  
       ca2 = fftshift(fft(u2)); -%g$~MZ?'  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation DUAI  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   A\1X-Mm  
       u2 = ifft(fftshift(c2));                        % Return to physical space ):c)$$dn  
       u1 = ifft(fftshift(c1)); Hkv4^|  
    if rem(m1,J) == 0                                 % Save output every J steps. /3!c ;(  
        U1 = [U1 u1];                                  % put solutions in U array WcG}9)9  
        U2=[U2 u2]; @rV|7%u  
        MN1=[MN1 m1]; k|Syw ATr  
        z1=dz*MN1';                                    % output location n;F/}:c_a  
      end EV$$wrohQ`  
    end A0@E^bG  
    hg=abs(U1').*abs(U1');                             % for data write to excel 4dgo*9  
    ha=[z1 hg];                                        % for data write to excel 1c%ee$Q  
    t1=[0 t']; 3om_Z/k  
    hh=[t1' ha'];                                      % for data write to excel file k\NwH?ppu  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format u@{z xYn  
    figure(1) FD+y?UF  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn y;r{0lTB  
    figure(2) mk'$ |2O  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn A.%MrgOOX  
    :|V`QM  
    非线性超快脉冲耦合的数值方法的Matlab程序 t 5{Y'  
     u51%~  
    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`g)(*  
    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 3R=R k  
    TJhzyJ"t  
    n$03##pf  
    BS@x&DB  
    %  This Matlab script file solves the nonlinear Schrodinger equations {j!jm5  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of YWXY4*G  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Pcs62aE  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 &l0-0 T>  
    Q~y) V  
    C=1;                           l[P VWM  
    M1=120,                       % integer for amplitude B'kV.3t  
    M3=5000;                      % integer for length of coupler ylo/]pVs  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) c2,;t)%@E  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. K*]^0  
    T =40;                        % length of time:T*T0. \H -,^[G3  
    dt = T/N;                     % time step Ol@ssm  
    n = [-N/2:1:N/2-1]';          % Index MB:VACCr  
    t = n.*dt;   VOY#Y*)g  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. `-J$7)d@  
    w=2*pi*n./T; ^G*zFqa+`  
    g1=-i*ww./2; itpljh  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; G8Qo]E9-/  
    g3=-i*ww./2; @8;0p  
    P1=0; "+@>!U  
    P2=0; 8e:\T.)M  
    P3=1; uh8+Y%V p  
    P=0; .R<Ke\y/  
    for m1=1:M1                 (0c L! N;;  
    p=0.032*m1;                %input amplitude =ll{M{0Q]!  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 5YW.s   
    s1=s10; |LwW/>I  
    s20=0.*s10;                %input in waveguide 2 jb5nL`(j$  
    s30=0.*s10;                %input in waveguide 3 S7A[HG;  
    s2=s20; sgRD]SF  
    s3=s30; TSp;Vr OP  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   P_Bhec|#fT  
    %energy in waveguide 1 YcQ3 :i  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   /;K?Y#mf~j  
    %energy in waveguide 2 ?u)[xEx6}+  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   2!y%nkO*  
    %energy in waveguide 3 yE80*C~d  
    for m3 = 1:1:M3                                    % Start space evolution >e4w8Svcy  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS eLd7|*|  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; M10u?  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; [|NgrU_.  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform cfg_xrW0^  
       sca2 = fftshift(fft(s2)); \B$Q%\-PX  
       sca3 = fftshift(fft(s3)); -T  5$l  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   j. m(Z}  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); HJh9 <I  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ! 54(K6a[  
       s3 = ifft(fftshift(sc3)); >d{O1by=d9  
       s2 = ifft(fftshift(sc2));                       % Return to physical space #G/ _FRo`  
       s1 = ifft(fftshift(sc1)); L+b"d3!G&%  
    end ?d? cD  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); |iJ+e -_R  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); _s&sA2r<  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); !FhiTh:GCh  
       P1=[P1 p1/p10]; ,Z"l3~0\  
       P2=[P2 p2/p10]; [p%OIqC`pB  
       P3=[P3 p3/p10]; G3.MS7 J  
       P=[P p*p]; ti)4J2c,8  
    end T 5jZd@VT,  
    figure(1) HxgH*IMs  
    plot(P,P1, P,P2, P,P3); 3XeCaq'N  
    -54  
    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~!~