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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 p  lnH  
    &/WM:]^?0)  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ;F"!$Z/  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Cj8&wz}ez  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear W34xrm  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 H u;"TG  
    !2Nk  
    %fid=fopen('e21.dat','w'); B-C$>H^  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 05FGfnq.8  
    M1 =3000;              % Total number of space steps /"gRyv  
    J =100;                % Steps between output of space xyGwYv>*KO  
    T =10;                  % length of time windows:T*T0 e`qrafa  
    T0=0.1;                 % input pulse width O0qG 6a  
    MN1=0;                 % initial value for the space output location bzNnEH`^]  
    dt = T/N;                      % time step Z2$_9.  
    n = [-N/2:1:N/2-1]';           % Index <x^$Fu  
    t = n.*dt;   fI)XV7,X  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 3s!6rT_=)d  
    u20=u10.*0.0;                  % input to waveguide 2 1PwtzH .w  
    u1=u10; u2=u20;                 dw<i)P^   
    U1 = u1;   s0?'mC+p  
    U2 = u2;                       % Compute initial condition; save it in U DPzW,aIgv  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. r V%6 8x9  
    w=2*pi*n./T; C{J5:ak  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T hUlRtt  
    L=4;                           % length of evoluation to compare with S. Trillo's paper gS +X%  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 pKc!sd C  
    for m1 = 1:1:M1                                    % Start space evolution G7 UUx+X  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS AhF@  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; _h-agn4[i  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform jV sH  
       ca2 = fftshift(fft(u2)); `}),wBq  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ; CCg]hX  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   k2D*`\ D  
       u2 = ifft(fftshift(c2));                        % Return to physical space *m"9F'(Sd  
       u1 = ifft(fftshift(c1)); ta)gOc)r R  
    if rem(m1,J) == 0                                 % Save output every J steps. gFTU9k<  
        U1 = [U1 u1];                                  % put solutions in U array ]%6%rq%9C  
        U2=[U2 u2]; )4ek!G]Rb  
        MN1=[MN1 m1]; oDA'$]UL  
        z1=dz*MN1';                                    % output location V|'@D#\  
      end SiaNL:  
    end 0vqH-)}  
    hg=abs(U1').*abs(U1');                             % for data write to excel u;q Q/Ftb  
    ha=[z1 hg];                                        % for data write to excel MeBTc&S<  
    t1=[0 t']; ]vQa~}  
    hh=[t1' ha'];                                      % for data write to excel file aH6j,R%  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format daKZ*B|  
    figure(1) #'&-S@/nQs  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn CB#2XS>V  
    figure(2) :g|.x  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6-wpR  
    ' bl9fO4v  
    非线性超快脉冲耦合的数值方法的Matlab程序 ;I*t5{  
    1!1JT;gG^9  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   jv~#'=T'  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 M$EF 8   
    m-O*t$6  
    jI8`trD  
    PL= v,NB  
    %  This Matlab script file solves the nonlinear Schrodinger equations K`N$nOw  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of bDvGFSAH  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g&g:H H :  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 viG=Ap.Th  
    AJ/Hw>>$?m  
    C=1;                           h/\v+xiF  
    M1=120,                       % integer for amplitude VjWJx^ZL#  
    M3=5000;                      % integer for length of coupler ^N<aHFF  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) [s^p P2  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. eW8cI)wU  
    T =40;                        % length of time:T*T0. .$-;`&0cZ  
    dt = T/N;                     % time step 9mD dX  
    n = [-N/2:1:N/2-1]';          % Index @M\JzV4 A[  
    t = n.*dt;   a^&"gGg  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Jzf+"%lv  
    w=2*pi*n./T; DL,R~  
    g1=-i*ww./2; z!6_u@^-  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; I '0[  
    g3=-i*ww./2; X{#^O/  
    P1=0; \/1~5mQ+  
    P2=0; `S((F|Ty=;  
    P3=1; 9q?knMt  
    P=0; AIOGa<^  
    for m1=1:M1                 YTTy6*\,_  
    p=0.032*m1;                %input amplitude s>G6/TTH6  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 g=D]=&H  
    s1=s10; ,$Fh^KNo]  
    s20=0.*s10;                %input in waveguide 2 RbUir185Y  
    s30=0.*s10;                %input in waveguide 3 -aJ(-Np$f  
    s2=s20; C3 "EZe[R  
    s3=s30; aN"YEL>w  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Z6gwAvf<  
    %energy in waveguide 1 `{YOl\d_  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ]Qe~|9I  
    %energy in waveguide 2 AT t.}-  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   D7pQWlN\  
    %energy in waveguide 3 eW.qMx#:od  
    for m3 = 1:1:M3                                    % Start space evolution wOL%otEf  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 5L6.7}B  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; aEdMZ+P.  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Jy:@&c  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Q']'KU.  
       sca2 = fftshift(fft(s2)); ){GJgk|P  
       sca3 = fftshift(fft(s3)); fQ~~%#z1  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   BpA7 z/  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 9hK8dJw  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); IJ.H/l}h  
       s3 = ifft(fftshift(sc3)); WClprSl8  
       s2 = ifft(fftshift(sc2));                       % Return to physical space v0WB.`rO  
       s1 = ifft(fftshift(sc1)); a.u{b&+9  
    end L' _%zO  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); bL<H$DB6  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Usht\<{  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); (Ajhf}zJ  
       P1=[P1 p1/p10]; <2j$P Y9  
       P2=[P2 p2/p10]; ZD50-w;  
       P3=[P3 p3/p10]; J8FzQ2  
       P=[P p*p]; mn1!A`$  
    end :fX61S6)  
    figure(1) ++w{)Io Z  
    plot(P,P1, P,P2, P,P3); Pi[]k]XA\  
    0F!Uai1  
    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~!~