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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 \c}_!.xj"  
    ,1/O2aQ%\0  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of W*S}^6ZT`  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of } I>68dS[  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !q\MXS($#u  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \ vn!SO7  
    ypU-/}Cf,  
    %fid=fopen('e21.dat','w'); >[}lC7 z,  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) B@cC'F#G  
    M1 =3000;              % Total number of space steps j9gn7LS  
    J =100;                % Steps between output of space /]j^a:#"6t  
    T =10;                  % length of time windows:T*T0 ]%M&pc3U  
    T0=0.1;                 % input pulse width DW( /[jo\  
    MN1=0;                 % initial value for the space output location &O +?#3  
    dt = T/N;                      % time step 8;6j  
    n = [-N/2:1:N/2-1]';           % Index YI+ clh;%9  
    t = n.*dt;   n*A?>NV  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Hjhgu=  
    u20=u10.*0.0;                  % input to waveguide 2  :o~]FVf  
    u1=u10; u2=u20;                 UE9RrfdN  
    U1 = u1;   ;~D$ rT  
    U2 = u2;                       % Compute initial condition; save it in U {zX]4 1T  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. e"oTlB  
    w=2*pi*n./T; o|:c{pwq  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T dG&^M ".(  
    L=4;                           % length of evoluation to compare with S. Trillo's paper :HW| mqKd  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 /!Ay12lKE}  
    for m1 = 1:1:M1                                    % Start space evolution mR|L'[l  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS !3F3E8%  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 6am g*=]  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform :FTx#cZ  
       ca2 = fftshift(fft(u2)); (+yH   
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ziDvDu=  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   GY>G}bfh  
       u2 = ifft(fftshift(c2));                        % Return to physical space @C-03`JWuK  
       u1 = ifft(fftshift(c1)); NSawD.9mV  
    if rem(m1,J) == 0                                 % Save output every J steps. {N3&JL5\"E  
        U1 = [U1 u1];                                  % put solutions in U array {Qi J-[q  
        U2=[U2 u2]; CvHE7H|-{  
        MN1=[MN1 m1]; 3 Fb9\2<H  
        z1=dz*MN1';                                    % output location &(7=NAQsE  
      end Gv[s86AP,  
    end pMHF u/|Pr  
    hg=abs(U1').*abs(U1');                             % for data write to excel p}oGhO&=  
    ha=[z1 hg];                                        % for data write to excel 1 |  
    t1=[0 t']; 4#CHX^De  
    hh=[t1' ha'];                                      % for data write to excel file X+1Mv  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Rh}}8 sv  
    figure(1) 5?MaKNm}  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ]_BH"ng}  
    figure(2) 2HUw^ *3  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Ul_ 5"3ze  
    (xfh 9=.  
    非线性超快脉冲耦合的数值方法的Matlab程序 ,,SV@y;  
    V408u y-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。   [ *Dj7z t:  
    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 #f [}a  
    @U3:9~Q  
    E!'6v DVC:  
    Ur]/kij  
    %  This Matlab script file solves the nonlinear Schrodinger equations jDb"|l  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of TjDtNE  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear JK`$/l|7  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 uu9IUqEq2  
    l?QA;9_R'  
    C=1;                           j]FK.G'  
    M1=120,                       % integer for amplitude l\F71pwSI  
    M3=5000;                      % integer for length of coupler ,z<1:st]<  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 3.@LAF  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. R# T 6]  
    T =40;                        % length of time:T*T0. 2}=@n*8*d  
    dt = T/N;                     % time step dB6['z)2  
    n = [-N/2:1:N/2-1]';          % Index *Y?oAVkz  
    t = n.*dt;   &r.M~k >  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. -#v1/L/=  
    w=2*pi*n./T; 99.F'Gz  
    g1=-i*ww./2; %ufh  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; =&6sU{j*  
    g3=-i*ww./2; |.,]0CRg  
    P1=0; {nXygg J  
    P2=0; ?"*JV1 9  
    P3=1; }toe'6  
    P=0; d)S`.Q  
    for m1=1:M1                 $[}EV(#y  
    p=0.032*m1;                %input amplitude gyMHC{l/B  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 j g//I<D  
    s1=s10; u7^(?"x  
    s20=0.*s10;                %input in waveguide 2 ~|9VVeE  
    s30=0.*s10;                %input in waveguide 3 7UY4* j|[C  
    s2=s20; (8aj`> y  
    s3=s30; hf]m'5pb  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   %59uR}\  
    %energy in waveguide 1 ]/kpEx  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   y+T[="W  
    %energy in waveguide 2 ;}iB9 Tl  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   "!D y[J  
    %energy in waveguide 3 'AX5V-t  
    for m3 = 1:1:M3                                    % Start space evolution 9Q^cE\j  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS l_/(J)|a  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ^P^%Q)QXl  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; @J&korU  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform W^H3=hZ  
       sca2 = fftshift(fft(s2));  *<W8j[?  
       sca3 = fftshift(fft(s3)); /zt M'  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   PWyf3  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); CxeW5qc  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); (T0MWp0  
       s3 = ifft(fftshift(sc3)); oWL_Hh%-f`  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 5LB{b]w7m  
       s1 = ifft(fftshift(sc1)); }mXYS|{  
    end ?!&%-R6*  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); t+}w Tis  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); | bz%SB  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 3PGAUQR#"q  
       P1=[P1 p1/p10]; ^l|b>z"0ao  
       P2=[P2 p2/p10]; 6_4 B!  
       P3=[P3 p3/p10]; BH1h2OEe#  
       P=[P p*p]; w+>+hq  
    end RzjUrt  
    figure(1) *9"x0bth  
    plot(P,P1, P,P2, P,P3); HB8s[]A:D  
    Hl0" zS[  
    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~!~