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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 XhjH68S(  
    7<DlA>(oUX  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of h-<2N)>!  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of M \rW  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 'Y{fah  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 HM ;9%rtO  
    ).e_iE[&  
    %fid=fopen('e21.dat','w'); 'H- : >'k  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 6tBL?'pG  
    M1 =3000;              % Total number of space steps 5SKj% %B2,  
    J =100;                % Steps between output of space )e`$'y@L$  
    T =10;                  % length of time windows:T*T0 (<!Yw|~  
    T0=0.1;                 % input pulse width :G\f(2@  
    MN1=0;                 % initial value for the space output location ["VUSa  
    dt = T/N;                      % time step B*#lkMr  
    n = [-N/2:1:N/2-1]';           % Index uc4#giCD  
    t = n.*dt;   WVlyR\.  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 zX{K\yp  
    u20=u10.*0.0;                  % input to waveguide 2 dq[X:3i  
    u1=u10; u2=u20;                 ousvsP%'  
    U1 = u1;   ,;9byb  
    U2 = u2;                       % Compute initial condition; save it in U ~ {OBRC  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. FY h+G-Y#  
    w=2*pi*n./T; mb_*FJB-_  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T QyN<o{\FD!  
    L=4;                           % length of evoluation to compare with S. Trillo's paper 9M{z@H/  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ]G m"U!h*  
    for m1 = 1:1:M1                                    % Start space evolution H.#<&5f  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS eCHT) 35u  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; g9~>mJR  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform (F9U`1~4  
       ca2 = fftshift(fft(u2)); w3oh8NRs_  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation &' E(  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   YJi C}.4Q  
       u2 = ifft(fftshift(c2));                        % Return to physical space <RQ\nU  
       u1 = ifft(fftshift(c1)); Fy_D[g  
    if rem(m1,J) == 0                                 % Save output every J steps. J_) .Hd  
        U1 = [U1 u1];                                  % put solutions in U array CYD&#+o  
        U2=[U2 u2]; ha_&U@w  
        MN1=[MN1 m1]; ZdQt!  
        z1=dz*MN1';                                    % output location CtiTXDc_  
      end . AJ(nJ)  
    end 6S*L[zBnA\  
    hg=abs(U1').*abs(U1');                             % for data write to excel ;#a^M*e  
    ha=[z1 hg];                                        % for data write to excel zi M~V'  
    t1=[0 t']; Hxe!68{aR  
    hh=[t1' ha'];                                      % for data write to excel file Bg.~#H  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format {akSK  
    figure(1) >S\D+1PV  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn _Ec9g^I10  
    figure(2) V?x&.C2Z  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ft$@':F  
    CHxu%- g  
    非线性超快脉冲耦合的数值方法的Matlab程序 mOm_a9M L  
    AG ?cI@',  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   7mG/f  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 x,)|;HXm  
    3^NHV g  
    53>y<  
    P_Rh& gkuK  
    %  This Matlab script file solves the nonlinear Schrodinger equations yb{ud  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of k0[b4cr`  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear y>4r<Y ZQ  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 `r?xo7  
    NrQGoAOw  
    C=1;                           E8$k}I  
    M1=120,                       % integer for amplitude "N'|N.,  
    M3=5000;                      % integer for length of coupler O"%b@$p\L  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) .;),e#  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 2/[J<c\G  
    T =40;                        % length of time:T*T0.  hsYS<]  
    dt = T/N;                     % time step /K!&4mK  
    n = [-N/2:1:N/2-1]';          % Index of?hP1kl[  
    t = n.*dt;   s#phs `v  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 6k569c{7  
    w=2*pi*n./T; -B+Pl*  
    g1=-i*ww./2; \53(D7+  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; =v-qao7xCV  
    g3=-i*ww./2; ^g^R[8  
    P1=0; &~9'7 n!  
    P2=0; zn!H&!8&  
    P3=1; .K I6<k/  
    P=0; 'E_M, Y  
    for m1=1:M1                 dXwfOC\\  
    p=0.032*m1;                %input amplitude VTM*=5|c   
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 gXrXVv<)yw  
    s1=s10; kBF.TGT[l  
    s20=0.*s10;                %input in waveguide 2 "$@>n(w  
    s30=0.*s10;                %input in waveguide 3 e u{  
    s2=s20; V]4g- CS[  
    s3=s30; {0~ Sj%Ze  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   j.}@9  
    %energy in waveguide 1 p]z< 43O$  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   )(^L *  
    %energy in waveguide 2 mI$<+S1!  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   b-'T>1V  
    %energy in waveguide 3 c)L1@qdZ  
    for m3 = 1:1:M3                                    % Start space evolution nw.,`M,N  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS yf 7Sz$Eq  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 45?aV@  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; hU: 9zLe  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform h\]D:S  
       sca2 = fftshift(fft(s2)); $9~6M*  
       sca3 = fftshift(fft(s3)); "`va_Mk  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   l*l?aI  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); F},#%_4  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); *!mT#Vm^  
       s3 = ifft(fftshift(sc3)); n:TWZ.9  
       s2 = ifft(fftshift(sc2));                       % Return to physical space A(j9T,!  
       s1 = ifft(fftshift(sc1)); *F4"mr|\  
    end O1C| { M  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Y! 8 I  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Npr<{}ZE  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); s2IjZF{  
       P1=[P1 p1/p10]; seNJ6p=`  
       P2=[P2 p2/p10]; ET2^1X#j  
       P3=[P3 p3/p10]; LtJl\m.th  
       P=[P p*p]; `<cn b!]  
    end Un~ }M/  
    figure(1) !@.9>"FU  
    plot(P,P1, P,P2, P,P3); cPx] :sC  
    G8sxg&bf{  
    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~!~