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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 a/uo}[Y  
    2`= 6%s  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of D=)f )-u'  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of '?yCq$&  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear t=#Pya  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 5ZAb]F90  
    41 vL"P K  
    %fid=fopen('e21.dat','w'); AP\ofLmq  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) VZIR4J[\.  
    M1 =3000;              % Total number of space steps \BI/G  
    J =100;                % Steps between output of space =BZ?-mIU  
    T =10;                  % length of time windows:T*T0 mEuHl>  
    T0=0.1;                 % input pulse width Yp4c'Zk  
    MN1=0;                 % initial value for the space output location 5H:@ 8,B  
    dt = T/N;                      % time step "MiD8wX-  
    n = [-N/2:1:N/2-1]';           % Index )DUL)S  
    t = n.*dt;   fH8!YQG8$  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Gr(|Ra .  
    u20=u10.*0.0;                  % input to waveguide 2 uC]Z8&+obb  
    u1=u10; u2=u20;                 g9my=gY  
    U1 = u1;   ELh3 ^  
    U2 = u2;                       % Compute initial condition; save it in U n`;R pr&  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. i3 )xX@3  
    w=2*pi*n./T; -&[z\"T  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T *,\` o~  
    L=4;                           % length of evoluation to compare with S. Trillo's paper .%0ne:5  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 $rG<uO  
    for m1 = 1:1:M1                                    % Start space evolution YJ2ro-X  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS pyW u9  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ? 4)v`*  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform s([Wn)I  
       ca2 = fftshift(fft(u2)); twk&-:'  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation $~'Tf>e  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   =J |sbY"]  
       u2 = ifft(fftshift(c2));                        % Return to physical space M>_= "atI  
       u1 = ifft(fftshift(c1)); p#_[  
    if rem(m1,J) == 0                                 % Save output every J steps. I*1S/o_xI  
        U1 = [U1 u1];                                  % put solutions in U array %TK&)Q% h5  
        U2=[U2 u2]; G"S5ki`o  
        MN1=[MN1 m1]; C 7n Kk/r  
        z1=dz*MN1';                                    % output location ;>2#@QP  
      end mT_GrIl[  
    end U 0ZB^`  
    hg=abs(U1').*abs(U1');                             % for data write to excel |tG+iF@4  
    ha=[z1 hg];                                        % for data write to excel `% E9xcD%  
    t1=[0 t']; Uk-HP\C"7  
    hh=[t1' ha'];                                      % for data write to excel file @%@zH%b  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format j.QHkI1.  
    figure(1) R.7#zhC`4  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn .T3=Eq&"W  
    figure(2) TvrwVL)  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn =%h~/,  
    FpkXOj?*  
    非线性超快脉冲耦合的数值方法的Matlab程序 "]]q} O?  
    WaYO1*=  
    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。   bx(w :]2  
    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 _F8T\f |  
    }h~'AM  
    AQci,j"  
    J`Oy.Qu)  
    %  This Matlab script file solves the nonlinear Schrodinger equations Sa}D.SBg  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of {of]/ 3=  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pVOI5>f\  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 -fux2?8M  
    +?e}<#vd'?  
    C=1;                           YhgUCF#  
    M1=120,                       % integer for amplitude ULvVD6RQ47  
    M3=5000;                      % integer for length of coupler YMAQ+A!  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) `45d"B I  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Y(GW0\<  
    T =40;                        % length of time:T*T0. VC=6uB  
    dt = T/N;                     % time step <PD|_nZT  
    n = [-N/2:1:N/2-1]';          % Index q$^<zY  
    t = n.*dt;   uiK:*[  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Jn,w)Els  
    w=2*pi*n./T; {aJz. `u\  
    g1=-i*ww./2; kGD|c=K}  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; !3KPwI,  
    g3=-i*ww./2; *o|p)lH  
    P1=0; R]=SWE}U  
    P2=0; J<_1z':W)  
    P3=1; b]dxlj} <  
    P=0; ? -{IsF^  
    for m1=1:M1                 NS 5 49S  
    p=0.032*m1;                %input amplitude |E|T%i^}./  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 l\U*sro<  
    s1=s10; 3"B+xbe=  
    s20=0.*s10;                %input in waveguide 2 3*\8p6G  
    s30=0.*s10;                %input in waveguide 3 k6g|7^es2  
    s2=s20; e3rfXhp  
    s3=s30; nh|EZp]  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   -4`sqv ]  
    %energy in waveguide 1 2))t*9;h  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   'WzUu MCx  
    %energy in waveguide 2 u~)%tL  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   y7; 5xF?q  
    %energy in waveguide 3 s7Qyfe&>  
    for m3 = 1:1:M3                                    % Start space evolution Wy,"cT  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS *cy.*@d  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ;q&Z9 lm  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ,^!Zm^4,  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform $Q,n+ /  
       sca2 = fftshift(fft(s2)); 'Ix5,^M}B  
       sca3 = fftshift(fft(s3)); +cw{aI`a8  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ;;6\q!7`  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); rUvwpP"k  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); KPg[-d  
       s3 = ifft(fftshift(sc3)); ;<VR2U`  
       s2 = ifft(fftshift(sc2));                       % Return to physical space bN4d:0Y  
       s1 = ifft(fftshift(sc1)); Wb'*lT0=  
    end m^c%]5$  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); }*OD M6  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); j>V"hf  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); AYYRxhv_,  
       P1=[P1 p1/p10]; 0c-QIr}m  
       P2=[P2 p2/p10]; yx 7loy$[  
       P3=[P3 p3/p10]; 3v G  
       P=[P p*p]; =G[ H,;W  
    end wz)m{:b<  
    figure(1) cnC_#kp  
    plot(P,P1, P,P2, P,P3); `lvh\[3^  
    \c FAxL(  
    转自:http://blog.163.com/opto_wang/
     
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    离线ciomplj
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    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~