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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 7Hgn/b[?b  
    cg17e  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of c ^.^5@  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of XM w6b*O  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear h$6'9rL&i  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Haekr*1%  
    dg|x(p#  
    %fid=fopen('e21.dat','w'); J@E]Fl  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) :l!sKT?:d!  
    M1 =3000;              % Total number of space steps t!6uz  
    J =100;                % Steps between output of space ]BjY UTNm  
    T =10;                  % length of time windows:T*T0 b$fmU"%&|  
    T0=0.1;                 % input pulse width YlGUd~$`"+  
    MN1=0;                 % initial value for the space output location . !Z5A9^  
    dt = T/N;                      % time step ipp`99  
    n = [-N/2:1:N/2-1]';           % Index q0Q[]|L  
    t = n.*dt;   R%\3[  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 3Wbd=^hRvq  
    u20=u10.*0.0;                  % input to waveguide 2 4dCXBTT  
    u1=u10; u2=u20;                 F+Qnf'at1  
    U1 = u1;   hZL!%sL7  
    U2 = u2;                       % Compute initial condition; save it in U f'(F'TE  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. qK#"uU8B  
    w=2*pi*n./T; z _\L@b  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T !-470J  
    L=4;                           % length of evoluation to compare with S. Trillo's paper :f39)g5>  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ~/-SKGzo-  
    for m1 = 1:1:M1                                    % Start space evolution ('C)S)98C  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS DzE^FY  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; V*Fy@  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform hLgX0QV  
       ca2 = fftshift(fft(u2)); #-G@p  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation R=E4Sh  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   iJOG"gI&  
       u2 = ifft(fftshift(c2));                        % Return to physical space uj.$GAtO)  
       u1 = ifft(fftshift(c1)); (_@5V_U  
    if rem(m1,J) == 0                                 % Save output every J steps. ?&eS}skL  
        U1 = [U1 u1];                                  % put solutions in U array { >[ ]iX  
        U2=[U2 u2]; JWg.0d$hM  
        MN1=[MN1 m1]; #iv4L  
        z1=dz*MN1';                                    % output location t`|Rn9-  
      end , otXjz  
    end [qRww]g;P|  
    hg=abs(U1').*abs(U1');                             % for data write to excel @#t<!-8d  
    ha=[z1 hg];                                        % for data write to excel nKr'cb  
    t1=[0 t']; ^" g?m  
    hh=[t1' ha'];                                      % for data write to excel file ]J!#"m-]  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format yGt [Qvx#  
    figure(1) +[uh);vD`G  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn @Q2E1Uu%  
    figure(2) v@[3R7|4  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn juWXB+d2Y  
    9D=X3{be#  
    非线性超快脉冲耦合的数值方法的Matlab程序 ^ [m-PS(  
    L v/}&'\(  
    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。   l9eTghLi  
    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 Nh^I{%.x  
    8WP"~Js!  
    JJWP te/  
    4vG-d)"M2  
    %  This Matlab script file solves the nonlinear Schrodinger equations kjV>\e  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ">1wPq&  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear "'Fvt-<^S7  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 dazML|1ow  
    9ETdO,L)f  
    C=1;                           h'h8Mm  
    M1=120,                       % integer for amplitude `V V >AA5  
    M3=5000;                      % integer for length of coupler O^-QqCZE  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) ?r&~(<^z  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ll$mRC  
    T =40;                        % length of time:T*T0. t/O^7)%  
    dt = T/N;                     % time step T|S-?X,  
    n = [-N/2:1:N/2-1]';          % Index 7i xG{yu  
    t = n.*dt;   n5A|Zjk;  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. v}t{*P  
    w=2*pi*n./T; _/>I-\xWA  
    g1=-i*ww./2; ,WOCG 2h  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; P8dMfD*"E  
    g3=-i*ww./2; zFO0l).  
    P1=0; } #e=*8F7  
    P2=0; 7lwI]/ZH*  
    P3=1; I$+=Fb'N0  
    P=0; )#\3c,<Y  
    for m1=1:M1                 $=E4pb4Y  
    p=0.032*m1;                %input amplitude x2)WiO/As  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Gd\/n*j  
    s1=s10; 8h|}Q_  
    s20=0.*s10;                %input in waveguide 2 ^znUf4N1  
    s30=0.*s10;                %input in waveguide 3 $04lL/;  
    s2=s20; }15&<s  
    s3=s30; b1IAp>*2l  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   GOA dhh-  
    %energy in waveguide 1 ;7qzQ{Km  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   JP\jhkn  
    %energy in waveguide 2 3 I%N4K4  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   g]z k`R5  
    %energy in waveguide 3 8 NNh8k#6  
    for m3 = 1:1:M3                                    % Start space evolution cOpe6H6,bz  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 1:T"jsWw  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; !f AvxR  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; HX| p4-L  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform I(BJ1 8F$  
       sca2 = fftshift(fft(s2)); 0#Ug3_dfr  
       sca3 = fftshift(fft(s3)); -WyB2$!(  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   r>bgCQ#-n  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); _,K[kVn  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 3A"TpR4f`  
       s3 = ifft(fftshift(sc3)); ol_\ "  
       s2 = ifft(fftshift(sc2));                       % Return to physical space /O.q4p  
       s1 = ifft(fftshift(sc1)); [vb#W!M&|  
    end QwFA0  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); =eW4?9Uq  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Y}.f&rLe  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 1nvT={'R  
       P1=[P1 p1/p10]; Er@xrhH  
       P2=[P2 p2/p10]; {GCp5  
       P3=[P3 p3/p10]; I'{Ctc  
       P=[P p*p]; Oz(=%oS  
    end A~>B?Wijqg  
    figure(1) hUvA;E(qD  
    plot(P,P1, P,P2, P,P3); &DYC3*)Jih  
    ='kCY}dkO  
    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~!~