[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序 :A,V<Es}I"  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of h7-!q@  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of #cBt@SEL'  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >69+e+|I  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Hb3+$vJ^  
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%fid=fopen('e21.dat','w'); q9RCXo>Y+1  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ->oQ,ezB  
M1 =3000;              % Total number of space steps yWACIaj  
J =100;                % Steps between output of space g< cR/  
T =10;                  % length of time windows:T*T0 W%f:+s}cI  
T0=0.1;                 % input pulse width &t+  
MN1=0;                 % initial value for the space output location 0}YR=  
dt = T/N;                      % time step "-4V48ci  
n = [-N/2:1:N/2-1]';           % Index mN^92@eebC  
t = n.*dt;   ?gb"S,  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ?=]`X=g6  
u20=u10.*0.0;                  % input to waveguide 2 sD$ \!7:b  
u1=u10; u2=u20;                 :5G3uN+\  
U1 = u1;   J<Wz3}w6  
U2 = u2;                       % Compute initial condition; save it in U 8x jJ  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. W>Y8
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w=2*pi*n./T; K h9$  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ,epKt(vl  
L=4;                           % length of evoluation to compare with S. Trillo's paper w|x=^  
dz=L/M1;                       % space step, make sure nonlinear<0.05 S<f&?\wK=v  
for m1 = 1:1:M1                                    % Start space evolution AC=cz!3iB  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS I?v)>||Q  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; oh`I$  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform O`O{n_o^u  
   ca2 = fftshift(fft(u2)); OE-$P  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation n37C"qJ/i  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ~1pJQ)!zlq  
   u2 = ifft(fftshift(c2));                        % Return to physical space />XfK,c-  
   u1 = ifft(fftshift(c1)); :b;2
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if rem(m1,J) == 0                                 % Save output every J steps. _=jc%@]1y  
    U1 = [U1 u1];                                  % put solutions in U array .Lo$uKsW$l  
    U2=[U2 u2]; Qw^nN(K!>  
    MN1=[MN1 m1]; GBvB0kC)c  
    z1=dz*MN1';                                    % output location ^ 3LM%B  
  end xTX\%s|  
end ]nN']?{7PW  
hg=abs(U1').*abs(U1');                             % for data write to excel =1lKcA[z  
ha=[z1 hg];                                        % for data write to excel _Kx /z  
t1=[0 t']; {a9Z<
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hh=[t1' ha'];                                      % for data write to excel file 6rL'hB!!]*  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format cD8.rRyD  
figure(1) !&TbE@Xk  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn yw5MlZ4P=  
figure(2) ={b/s31H:  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn N{`-&8q;K  
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非线性超快脉冲耦合的数值方法的Matlab程序 it\{#rb=4  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   bslv_OxJ  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 KO<fN,DR  
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%  This Matlab script file solves the nonlinear Schrodinger equations JiP]FJ;  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of F&;g< SD  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear SxC$EQgL  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 x2/|i?ZO  
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C=1;                           Mq42^m:qe  
M1=120,                       % integer for amplitude wCe
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M3=5000;                      % integer for length of coupler *D F5sY  
N = 512;                      % Number of Fourier modes (Time domain sampling points) N2;T\xx,  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. |]DZc/  
T =40;                        % length of time:T*T0. 9M~EH?>+[  
dt = T/N;                     % time step `?r
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n = [-N/2:1:N/2-1]';          % Index E@"+w,x)  
t = n.*dt;   I1kx3CwJ{P  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. -hL8z
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w=2*pi*n./T; 0gHJ%m9s  
g1=-i*ww./2; P$.Azrl  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 29u"\f a  
g3=-i*ww./2; DyG3|5s1R  
P1=0; y ']>J+b0  
P2=0; > zh%CF$  
P3=1; ,Zzh.z::D  
P=0; 5h+g^{BE  
for m1=1:M1                 q>r9ooN  
p=0.032*m1;                %input amplitude C>N)~Ut  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 WDY,?  
s1=s10; l+bP48  
s20=0.*s10;                %input in waveguide 2 nWbe=z&y8[  
s30=0.*s10;                %input in waveguide 3 O\XN/R3  
s2=s20; TuBg4\V  
s3=s30; :74^?  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   w@nN3U+  
%energy in waveguide 1 @8|-
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p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   9Q^>.^~^  
%energy in waveguide 2 -'&MT :L  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   g$?B!!qT  
%energy in waveguide 3 Jm\'
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for m3 = 1:1:M3                                    % Start space evolution ep3_G\m  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS :Py/d6KK  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; JE9|;A  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; >6=yxCJ  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform %&4sHDP  
   sca2 = fftshift(fft(s2)); +G?4Wc1  
   sca3 = fftshift(fft(s3)); 8G1Tpn  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   5ts8o&|   
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Vg\EAs>f  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); KZ`d3ad  
   s3 = ifft(fftshift(sc3)); 7}%3Aw6]S  
   s2 = ifft(fftshift(sc2));                       % Return to physical space k:Uyez  
   s1 = ifft(fftshift(sc1)); \UGs_5OT  
end 4B<D.i ;}  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); xI<Dc*G  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); BGodrb1  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 4NQS'*%D  
   P1=[P1 p1/p10]; X/];*='Q  
   P2=[P2 p2/p10]; jWiB_8-6  
   P3=[P3 p3/p10]; m!|u{<,R  
   P=[P p*p]; ^lB1- ;ng  
end TWQf2  
figure(1) 6BFtY+.y  
plot(P,P1, P,P2, P,P3); G!8O*4+A  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~