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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 nlebFDb7  
    sK%Hx`  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of [x<6v}fRn  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of  AMD?LjY~  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear r%,H*DOu  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 "c/s/$k//  
    +e8>?dkq  
    %fid=fopen('e21.dat','w'); d[]p_oIQq  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) fEw=I7{Y  
    M1 =3000;              % Total number of space steps H[7cA9FI  
    J =100;                % Steps between output of space 4iv]N 4  
    T =10;                  % length of time windows:T*T0 |^PLZ>  
    T0=0.1;                 % input pulse width <@e+-$  
    MN1=0;                 % initial value for the space output location jfY{z=*]u  
    dt = T/N;                      % time step k<Tez{<  
    n = [-N/2:1:N/2-1]';           % Index J/x@$'  
    t = n.*dt;   HD:%Yv  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 +|?|8"Qg  
    u20=u10.*0.0;                  % input to waveguide 2 r[v-?W'  
    u1=u10; u2=u20;                 %]<RRH.w  
    U1 = u1;   5{FM#@  
    U2 = u2;                       % Compute initial condition; save it in U uPFHlT  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. .b#9q6F-/  
    w=2*pi*n./T; PNJe&q0*  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T &=-e`=qJ'6  
    L=4;                           % length of evoluation to compare with S. Trillo's paper $,;S\JmWP  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 \|~?x#aA  
    for m1 = 1:1:M1                                    % Start space evolution T")i+v  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS <4Q12:  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; lkg"'p{  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform fi&uB9hc  
       ca2 = fftshift(fft(u2)); TmYP_5g:  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 7V=MRf&xQ  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Xn/ n|[  
       u2 = ifft(fftshift(c2));                        % Return to physical space \o B'  
       u1 = ifft(fftshift(c1)); g%\$ !b  
    if rem(m1,J) == 0                                 % Save output every J steps. *"5N>F[L  
        U1 = [U1 u1];                                  % put solutions in U array f]ue#O  
        U2=[U2 u2]; skI(]BDf  
        MN1=[MN1 m1]; 5c]}G.NV  
        z1=dz*MN1';                                    % output location 3ximNQ} S  
      end Q54r?|'V  
    end ?Q96,T-) c  
    hg=abs(U1').*abs(U1');                             % for data write to excel (LRM~5KVg  
    ha=[z1 hg];                                        % for data write to excel CZyz;Jtk  
    t1=[0 t']; ^Ti_<<X  
    hh=[t1' ha'];                                      % for data write to excel file P{S\pWZkk  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format _~;&)cn,0  
    figure(1) 2$ |]Vj*Zs  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn j2 }  
    figure(2) zJ;>.0  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn E.J 0fwyT  
    !/j,hO4Z4  
    非线性超快脉冲耦合的数值方法的Matlab程序 }!%JYG^!D  
    bo@,4xw  
    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。   :K~rvv\L7  
    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 3`A>j"  
    p^1zIC>F  
    q^ a|wTC  
    F$Im9T6  
    %  This Matlab script file solves the nonlinear Schrodinger equations qKdS7SoS  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of +VCo$o  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear , 3X: )  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 M18qa,fK{  
    NunV8atn:  
    C=1;                           >Mvka;T]  
    M1=120,                       % integer for amplitude <4bz/^  
    M3=5000;                      % integer for length of coupler qoj^_s6  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) EntF@ln!  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. :dP~.ZY7  
    T =40;                        % length of time:T*T0. e~{^oM  
    dt = T/N;                     % time step B%tIwUE2  
    n = [-N/2:1:N/2-1]';          % Index {L@+(I  
    t = n.*dt;   '>j<yaD'  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 7}be>(  
    w=2*pi*n./T; Rj[ hhSx 2  
    g1=-i*ww./2; 2_;]  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; hv* >%p  
    g3=-i*ww./2; 6HoqEku/Q  
    P1=0; EM=w?T  
    P2=0; ~U6" ?  
    P3=1; CjZZm^O  
    P=0; n*Q`g@`  
    for m1=1:M1                 P|e`^Frxt  
    p=0.032*m1;                %input amplitude OJAx:&]3  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 CI`N8 f=v  
    s1=s10; 5Go0}'*%  
    s20=0.*s10;                %input in waveguide 2 #HeM,;Xp  
    s30=0.*s10;                %input in waveguide 3 !;%y$$gxh  
    s2=s20; kG/X"6pZ  
    s3=s30; b'i'GJBQ+$  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   dUS  ZNY  
    %energy in waveguide 1 aG%kmS&fv  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   pb#mg^8  
    %energy in waveguide 2 7K&}C;+  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   LP:nba :  
    %energy in waveguide 3 No) m/17y  
    for m3 = 1:1:M3                                    % Start space evolution nH@(Y&S  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS >1 @Ltvm  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; C.~ j'5N  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; x?"#gK`3;  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform e}A&V+  
       sca2 = fftshift(fft(s2)); mwh{"FL(  
       sca3 = fftshift(fft(s3)); f/}  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Wta]BX  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Cq>6rn  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); fXO_g  
       s3 = ifft(fftshift(sc3)); z8HsYf(!  
       s2 = ifft(fftshift(sc2));                       % Return to physical space V<8K@/n@  
       s1 = ifft(fftshift(sc1)); Vtb1[cnna  
    end y4@gGC=  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 8eluO ?p  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); =m7H)z)i*J  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); B5ea(j  
       P1=[P1 p1/p10]; $X \va?(  
       P2=[P2 p2/p10]; ]H ~Y7\N-v  
       P3=[P3 p3/p10]; ju|]Qlek  
       P=[P p*p]; W|MWXs5'1*  
    end m@jge)O&D  
    figure(1) whye)w  
    plot(P,P1, P,P2, P,P3); s)zJT  
    vE%s, E,  
    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~!~