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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 pm-SDp>s  
    =U6%Wdth  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of l;I)$=={=  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ==[a7|q  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 2\xv Yf-  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 +6=2B0$ r  
    Gu-*@C:^&  
    %fid=fopen('e21.dat','w'); LV'@JFT-  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) LCrE1Q%VP  
    M1 =3000;              % Total number of space steps ydCVG,"  
    J =100;                % Steps between output of space a sDq(J`sQ  
    T =10;                  % length of time windows:T*T0 K +oFu%  
    T0=0.1;                 % input pulse width +`_I !  
    MN1=0;                 % initial value for the space output location ,7m Rb-*p  
    dt = T/N;                      % time step m]yt6b4  
    n = [-N/2:1:N/2-1]';           % Index J Cu3,O!q  
    t = n.*dt;   I<q=lK  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 x<'(b7{U0  
    u20=u10.*0.0;                  % input to waveguide 2 *TpzX y  
    u1=u10; u2=u20;                 R6ynL([xh  
    U1 = u1;   }nDKSC/[V!  
    U2 = u2;                       % Compute initial condition; save it in U u.wm;eK[  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 1sL#XB$@N  
    w=2*pi*n./T; E$-u:Z<-  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T h)EHaaf  
    L=4;                           % length of evoluation to compare with S. Trillo's paper E\V-< ]o  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 "5]Fl8c?  
    for m1 = 1:1:M1                                    % Start space evolution I*/?*p/I  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Th&* d;  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; S4j`=<T,  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform b_&;i4[  
       ca2 = fftshift(fft(u2)); ?*}^xXI/  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation B5>1T[T'-  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   yJx{6  
       u2 = ifft(fftshift(c2));                        % Return to physical space i2ap]  
       u1 = ifft(fftshift(c1)); jXEuK:exQ  
    if rem(m1,J) == 0                                 % Save output every J steps. ({#9gTP2b  
        U1 = [U1 u1];                                  % put solutions in U array 6N}>@Y5  
        U2=[U2 u2]; ~+1t3M e  
        MN1=[MN1 m1]; *xEcX6ZHX  
        z1=dz*MN1';                                    % output location 6&p I{  
      end olNgtSX  
    end uqy b  
    hg=abs(U1').*abs(U1');                             % for data write to excel %RE-_~GF  
    ha=[z1 hg];                                        % for data write to excel d, fX3  
    t1=[0 t']; O2|[g8(_F  
    hh=[t1' ha'];                                      % for data write to excel file |wASeZMO2  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format \Kph?l9Ww  
    figure(1) `I(#.*  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn sd;J(<Ofh  
    figure(2) {shf\pm!o  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn RbUhLcG5  
    box(FjrZE  
    非线性超快脉冲耦合的数值方法的Matlab程序 ?*i qg[:  
    vEJ2d&  
    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。   tAfdbt  
    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 #}50oWE  
    usb.cE3 z  
    ;[*jLi,uc  
    }cK<2J#  
    %  This Matlab script file solves the nonlinear Schrodinger equations <eU28M?\  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 8}m bfu o1  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear kG:,Ff>  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @SREyqC4  
    VeixwGZ.  
    C=1;                           a+$WlG/x  
    M1=120,                       % integer for amplitude / ,3,l^kZ  
    M3=5000;                      % integer for length of coupler >[ r TUn;  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) O$}p}%%y7  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. r<]Db&k   
    T =40;                        % length of time:T*T0. Qe=,EXf  
    dt = T/N;                     % time step MWv_BXQ  
    n = [-N/2:1:N/2-1]';          % Index 6"^Yn.  
    t = n.*dt;   S Rs~p  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. N&`VMEB)k  
    w=2*pi*n./T; ,3_;JT"5  
    g1=-i*ww./2; x{Y}1+Y4  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; j4wcxZYY~  
    g3=-i*ww./2; )i&z!|/2  
    P1=0; %T]NM3|U  
    P2=0; mQmn&:R  
    P3=1; J/3qJst  
    P=0; D}|PBR  
    for m1=1:M1                 zzsQfI#  
    p=0.032*m1;                %input amplitude 0-H!\IB  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 IUco 8  
    s1=s10; yT Pi/=G  
    s20=0.*s10;                %input in waveguide 2 ^06f\7A  
    s30=0.*s10;                %input in waveguide 3 8d9&LPv  
    s2=s20; H`/Q hE  
    s3=s30; rrK&XP&  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   5y7rY!]Bf  
    %energy in waveguide 1 9-;ujl?{  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   k9j_#\E[  
    %energy in waveguide 2 8H4"mxO  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   jEj#|w  
    %energy in waveguide 3 gakmg#ki  
    for m3 = 1:1:M3                                    % Start space evolution u.( WW(/N  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS av>c  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ea3;1-b:  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; uGm~ Oo  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform y:Xs/RS  
       sca2 = fftshift(fft(s2)); RXa&*Jtr -  
       sca3 = fftshift(fft(s3)); |cpBoU  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   (4_7ICFI  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); -x~h.s,  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); >r%L=22+  
       s3 = ifft(fftshift(sc3)); &V7@ TZ  
       s2 = ifft(fftshift(sc2));                       % Return to physical space QjH;'OVt  
       s1 = ifft(fftshift(sc1)); 70NQ9*AAy  
    end r\7F}ZW/  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); yX%T-/XJ  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); o JC-?  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); K8NoY6  
       P1=[P1 p1/p10]; j .Ro(0%  
       P2=[P2 p2/p10]; ,Y&LlB 2  
       P3=[P3 p3/p10]; }X{#=*$GQ  
       P=[P p*p]; ,bT|:T@ny  
    end L3:dANG  
    figure(1) 7'wt/9  
    plot(P,P1, P,P2, P,P3); 2N_8ahc  
    n:JWu0,h  
    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~!~