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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 J]|S0JC`  
    o3HS|  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of !L)yI#i4C  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of jV' tcFr4  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 0oo_m6ie&  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 G{0f* cH)  
    W=4|ahk$  
    %fid=fopen('e21.dat','w'); [Vj|fy4  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) tDtqTB}  
    M1 =3000;              % Total number of space steps zKGr(9I  
    J =100;                % Steps between output of space  /UtSZ(  
    T =10;                  % length of time windows:T*T0 n +dRAIqB  
    T0=0.1;                 % input pulse width *}Rd%'  
    MN1=0;                 % initial value for the space output location :AyZe7:(D  
    dt = T/N;                      % time step c+jnQM'  
    n = [-N/2:1:N/2-1]';           % Index \3whM6tK  
    t = n.*dt;   Fl++rUT  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 %3T:W\h  
    u20=u10.*0.0;                  % input to waveguide 2 ,&jjp eZP  
    u1=u10; u2=u20;                 Y^gIvX  
    U1 = u1;   ;V^I>-fnm  
    U2 = u2;                       % Compute initial condition; save it in U ^ ?T,>ZI  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. \>+BvF  
    w=2*pi*n./T; `!.c_%m2  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T \$ :)Ka  
    L=4;                           % length of evoluation to compare with S. Trillo's paper Tx/KL%X  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 kS_3 7-;  
    for m1 = 1:1:M1                                    % Start space evolution kp*BAQ  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ~HXZ-*  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; M+lI,j+  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform dq3"L!0u  
       ca2 = fftshift(fft(u2)); z_a7HCG2  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation >2tosxH M  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   y|Y hDO  
       u2 = ifft(fftshift(c2));                        % Return to physical space rm,h\  
       u1 = ifft(fftshift(c1)); =%wBC;  
    if rem(m1,J) == 0                                 % Save output every J steps. l6!a?C[2T  
        U1 = [U1 u1];                                  % put solutions in U array ||.Ve,<:  
        U2=[U2 u2]; #}xPOz7:  
        MN1=[MN1 m1]; >IHf5})R  
        z1=dz*MN1';                                    % output location #DcK{|ty  
      end ~PCS_  
    end i(kr#XsU  
    hg=abs(U1').*abs(U1');                             % for data write to excel DkBVk+  
    ha=[z1 hg];                                        % for data write to excel <@=w4\5j9  
    t1=[0 t']; c1StA  
    hh=[t1' ha'];                                      % for data write to excel file < !]7Gt  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format kYkck]|  
    figure(1) KQ.cd]6  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn rE\.[mFI  
    figure(2) IeBb#Qedz  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Xj21:IMR  
    n/IDq$/P  
    非线性超快脉冲耦合的数值方法的Matlab程序 I)4NCjcCw  
    Fi"TY^-E;  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ooT~R2u  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 n:YA4t7S  
    el,n5O Z7  
    SMh[7lU`  
    YQ5d!a.  
    %  This Matlab script file solves the nonlinear Schrodinger equations fh e%5#3  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of k!m9 l1x  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear H/Ov8|  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ^os|yRzV*M  
    ,T7(!)dR  
    C=1;                           SL>0_  
    M1=120,                       % integer for amplitude jVdB- y/r  
    M3=5000;                      % integer for length of coupler U`ELd:  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) !,PoH  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 7 *HBb-  
    T =40;                        % length of time:T*T0. z>W'Ra6  
    dt = T/N;                     % time step R~(_m#6`:  
    n = [-N/2:1:N/2-1]';          % Index )9>E} SU/  
    t = n.*dt;   '>r"+X^W  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. o^~KAB7  
    w=2*pi*n./T; Sc&p*G  
    g1=-i*ww./2; NeY,Of|  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 04R-}  
    g3=-i*ww./2; u\|Ys  
    P1=0; >zB0+l  
    P2=0; j0[9Cj^%c  
    P3=1; )NS& 1$  
    P=0; !Ql&Ls  
    for m1=1:M1                 I;Bcim;  
    p=0.032*m1;                %input amplitude \}mn"y  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 JD$;6Jv3P  
    s1=s10; f}F   
    s20=0.*s10;                %input in waveguide 2 &sJ%ur+G  
    s30=0.*s10;                %input in waveguide 3 a,*~wmg  
    s2=s20; 2u'h,on?  
    s3=s30; $qj||zA  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ?BnjtefIe  
    %energy in waveguide 1 4 g^oy^~  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ?]u=5gqUU  
    %energy in waveguide 2 %1VfTr5  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   -dsE9)&8DX  
    %energy in waveguide 3 ZtqN8$[6n  
    for m3 = 1:1:M3                                    % Start space evolution 0^rDf L  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS B>W!RyH8o  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; FrryZe=  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; _m|Tr*i8  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform U49 `!~b7  
       sca2 = fftshift(fft(s2)); \Lu] %}  
       sca3 = fftshift(fft(s3)); -|~tZuf  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   4Fpu68y  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 'w5g s}1D  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Y:} !W  
       s3 = ifft(fftshift(sc3)); (}LLk +  
       s2 = ifft(fftshift(sc2));                       % Return to physical space AjA.="3  
       s1 = ifft(fftshift(sc1)); 73OYHp_j  
    end <v =T31aS  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); B7!dp`rPp  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ;nB.f.e`  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); j:6VWdgq  
       P1=[P1 p1/p10]; r*t\\2  
       P2=[P2 p2/p10]; 1ti4 ZM  
       P3=[P3 p3/p10]; y6S:[Z{~A  
       P=[P p*p]; t!,GI&  
    end c$HZvv  
    figure(1) Y^@Nvt$<K  
    plot(P,P1, P,P2, P,P3); Iz[T.$9  
    Xm! ;  
    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~!~