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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 U:n~S  
    kc P ZIP:  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of iQ8{N:58DN  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of %7aJSuQN%  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <3@nv%  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9"+MZ$  
    %N ~c9B  
    %fid=fopen('e21.dat','w'); @-\=`#C**  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) +p Ywc0~  
    M1 =3000;              % Total number of space steps rA B=H*|6  
    J =100;                % Steps between output of space {nUmlP=mS  
    T =10;                  % length of time windows:T*T0 YjTr49Af0  
    T0=0.1;                 % input pulse width % H"  
    MN1=0;                 % initial value for the space output location Fs $FR-x  
    dt = T/N;                      % time step fx(8 o+  
    n = [-N/2:1:N/2-1]';           % Index 2#lpIj  
    t = n.*dt;   ]w;t0Bk  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 3!gz^[!?EN  
    u20=u10.*0.0;                  % input to waveguide 2 m[2[9 bQ0  
    u1=u10; u2=u20;                 | |pOiR5  
    U1 = u1;   qp6'n&^&  
    U2 = u2;                       % Compute initial condition; save it in U uKM` umE  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Ea<\a1Tl43  
    w=2*pi*n./T;  =5B5  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T $3>Rw/,  
    L=4;                           % length of evoluation to compare with S. Trillo's paper \:1$E[3v  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 bF_0',W  
    for m1 = 1:1:M1                                    % Start space evolution IO"P /Q  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS T5ky:{Y(  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; m)pHCS  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform h~Z &L2V  
       ca2 = fftshift(fft(u2)); JcmMbd&B  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 3I( n];  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ^$O(oE(D  
       u2 = ifft(fftshift(c2));                        % Return to physical space 5Wa)_@qI)`  
       u1 = ifft(fftshift(c1)); *f;$5B#^  
    if rem(m1,J) == 0                                 % Save output every J steps. ">t^jt{  
        U1 = [U1 u1];                                  % put solutions in U array w/( T  
        U2=[U2 u2]; L3wj vq^  
        MN1=[MN1 m1]; ';Nc;9  
        z1=dz*MN1';                                    % output location HP[B%  
      end  wk8fa  
    end R"O%##Ws  
    hg=abs(U1').*abs(U1');                             % for data write to excel 4To$!=  
    ha=[z1 hg];                                        % for data write to excel T?!SEblP]  
    t1=[0 t']; WR#h~N 9c  
    hh=[t1' ha'];                                      % for data write to excel file OQ_< Vxz  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Y#V(CIDe  
    figure(1) H#hpaP;  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn iz/CC V L  
    figure(2) #'%ii,;w Q  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn AU`z.Isf  
    "A~dt5GJ  
    非线性超快脉冲耦合的数值方法的Matlab程序 ~Uv#)  
    2'M5+[8y8  
    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。   i7h^L)M  
    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 !\%JOf}  
    H'YKj'  
    8w[O%  
    1/:vFX  
    %  This Matlab script file solves the nonlinear Schrodinger equations *lLCH,  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of =#9#unvE!  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear RbxQTM_:M  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 <HRPloVKo  
    ]$ s)6)kW  
    C=1;                           ]Bf1p  
    M1=120,                       % integer for amplitude 2RNee@!JJP  
    M3=5000;                      % integer for length of coupler 2Q@n a @s  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) [O_5`X9|  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 6<S-o|Xw  
    T =40;                        % length of time:T*T0. 6q>iPK Jt  
    dt = T/N;                     % time step ]SU)L5Dt;  
    n = [-N/2:1:N/2-1]';          % Index 2@Nd02v|  
    t = n.*dt;   ~gZ1*8 s`  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. <$A/ ('  
    w=2*pi*n./T; vS5}OV  
    g1=-i*ww./2; aDX&j2/  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; h~ _i::vg  
    g3=-i*ww./2; zB+e;x f|  
    P1=0; [|*7"Q(  
    P2=0; lW#2ox  
    P3=1; ceks~[rP  
    P=0; ~1*37w~  
    for m1=1:M1                 RE4#a 2  
    p=0.032*m1;                %input amplitude H'!OEZ  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ) aMiT  
    s1=s10; k^K76mB  
    s20=0.*s10;                %input in waveguide 2 [>p!*%m  
    s30=0.*s10;                %input in waveguide 3 z0ufLxq  
    s2=s20; \^y~w~g?  
    s3=s30; xh#_K@8  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   C "@>NC_  
    %energy in waveguide 1 OMjPC_  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   b+whZtNk7  
    %energy in waveguide 2 _IU5HT}2  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   TeZu*c  
    %energy in waveguide 3 ^hZ0"c  
    for m3 = 1:1:M3                                    % Start space evolution .c<U5/  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS }I}GA:~$%  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; +[n#{;]<  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =m (u=|N3  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform rf+}J_  
       sca2 = fftshift(fft(s2)); 'M?ptu?f  
       sca3 = fftshift(fft(s3)); `:r-&QdU o  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   lAA6tlc#C  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Iy*Q{H3[  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); j&S.k  
       s3 = ifft(fftshift(sc3)); *HV_$^)=  
       s2 = ifft(fftshift(sc2));                       % Return to physical space &*O'qOO<2  
       s1 = ifft(fftshift(sc1)); M9Sj@ww  
    end mz<,nR\  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 8_`C&vx  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); =$#5Ge]b  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); N&k\X]U  
       P1=[P1 p1/p10]; SufM ~9Ll  
       P2=[P2 p2/p10]; #;8VBbc\^  
       P3=[P3 p3/p10]; B!)9 >  
       P=[P p*p]; mhU=^/X  
    end ;IPk+,hpmi  
    figure(1) .@;5"  
    plot(P,P1, P,P2, P,P3); T&S=/cRBK}  
    6f#Mi+"  
    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~!~