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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 正序阅读 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 I A%ZCdA;  
    r.q*S4IS.m  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of t zShds  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ;Rlf[](iL  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear (_%l[:o6  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 x2,;ar\D  
    J!Q #xs  
    %fid=fopen('e21.dat','w'); 0u;a*#V@  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) #iKPp0`K*  
    M1 =3000;              % Total number of space steps })+iAxR  
    J =100;                % Steps between output of space wz..  
    T =10;                  % length of time windows:T*T0 0q4P hxR`e  
    T0=0.1;                 % input pulse width .p =OAh<  
    MN1=0;                 % initial value for the space output location 2`^6``  
    dt = T/N;                      % time step P{L S +.  
    n = [-N/2:1:N/2-1]';           % Index +Wl]1 c/  
    t = n.*dt;   ) &DsRA7v  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 8J#xB  
    u20=u10.*0.0;                  % input to waveguide 2 p()q)P  
    u1=u10; u2=u20;                 * >/w,E]  
    U1 = u1;   ~:L5Ar<  
    U2 = u2;                       % Compute initial condition; save it in U @d5$OpL$%  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ihJ!]#Fbm  
    w=2*pi*n./T; O>N/6Z  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 2TG2<wqvE  
    L=4;                           % length of evoluation to compare with S. Trillo's paper mGDy3R90  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 Sp6==(:.  
    for m1 = 1:1:M1                                    % Start space evolution .]H/u "d  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS <BIQc,)2}  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; kbL7Xjk  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform b<!' WpY-  
       ca2 = fftshift(fft(u2)); \2!.  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation qnHjwMi  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   sSf;j,7V  
       u2 = ifft(fftshift(c2));                        % Return to physical space T6b~uE  
       u1 = ifft(fftshift(c1)); lN&+<>a  
    if rem(m1,J) == 0                                 % Save output every J steps. ,PoG=W  
        U1 = [U1 u1];                                  % put solutions in U array |"PS e~ u  
        U2=[U2 u2]; $EHF f$M  
        MN1=[MN1 m1];  ?H!jKX  
        z1=dz*MN1';                                    % output location s2( 7z9jR  
      end H | C3{9  
    end /0cm7[a?  
    hg=abs(U1').*abs(U1');                             % for data write to excel _M&n~ r  
    ha=[z1 hg];                                        % for data write to excel n*ROlCxV  
    t1=[0 t']; mU(v9Jpf7  
    hh=[t1' ha'];                                      % for data write to excel file z;?ztpa@  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format )3A+Ell`  
    figure(1) E2 FnC}#W  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn '%ByFZ zi  
    figure(2) <& 3[|Ca  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Y}xM&%  
    r@zs4N0WP  
    非线性超快脉冲耦合的数值方法的Matlab程序 Zn0a)VH%  
    uF|Up]Z G  
    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。   Tay$::V  
    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^/KB=  
    t^Lb}A#$4  
    q sUBvq  
    #6 ni~d&0  
    %  This Matlab script file solves the nonlinear Schrodinger equations O8A(OfX  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of &^K(9"  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear #'},/Lm@  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =>lX brJ  
    Nmd{C(^o  
    C=1;                           @ ;@~=w  
    M1=120,                       % integer for amplitude S(U9Dlyarg  
    M3=5000;                      % integer for length of coupler  j'Jb+@W?  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) YD@Z}NE v"  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. `mW~{)x  
    T =40;                        % length of time:T*T0. ~NPhVlT  
    dt = T/N;                     % time step ev0>j4Q  
    n = [-N/2:1:N/2-1]';          % Index IA&V?{OE@I  
    t = n.*dt;   qdy(C^(fa  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. $m~&| s  
    w=2*pi*n./T; T{^P  
    g1=-i*ww./2; "wcw`TsK  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ',!jYh}Uxk  
    g3=-i*ww./2; pH.&C 5kA  
    P1=0; d>mT+{3  
    P2=0; PNd'21N  
    P3=1;  @)0  
    P=0;  Qe7=6<  
    for m1=1:M1                 -"S94<Y  
    p=0.032*m1;                %input amplitude h)fsLzn]Tf  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 y$bY 8L  
    s1=s10; Q"U%]2@=  
    s20=0.*s10;                %input in waveguide 2 fVgN8b|&'  
    s30=0.*s10;                %input in waveguide 3 ]cv|dc=  
    s2=s20; F-b]>3r  
    s3=s30; wkPjMmW+!  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   9_d# F'#F  
    %energy in waveguide 1 f8SO:ihXL  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ]" e'z  
    %energy in waveguide 2 cr<j<#(Z}  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ^&C/,,U  
    %energy in waveguide 3 ^n<YO=|u  
    for m3 = 1:1:M3                                    % Start space evolution ZA. S X|m  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Cse`MP  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; fMUh\u3  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; u=qaz7E  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform rr2 !H%:  
       sca2 = fftshift(fft(s2)); 6it [i@*"  
       sca3 = fftshift(fft(s3)); [<{r~YFjWW  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   NOwd'iU  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 9G2rVk  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); q2J |koT  
       s3 = ifft(fftshift(sc3)); Q0Do B  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ;,6C&|n]w  
       s1 = ifft(fftshift(sc1)); Dn J `]r  
    end y\uBVa<B  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 8f[ztT0`g  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); G1w$lc  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); !wQ?+ :6  
       P1=[P1 p1/p10]; QEbf]U=  
       P2=[P2 p2/p10]; 7S 8X)  
       P3=[P3 p3/p10]; ]UEA"^  
       P=[P p*p]; gED|2%BXb  
    end -C(Yl=  
    figure(1) _EP]|DTfr  
    plot(P,P1, P,P2, P,P3); `JDZR:bMaT  
    <XG]aYBR  
    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~!~