[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 +jYO?uaT  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of }Uki)3(  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of /Y5I0Ko Uw  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 'E
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 c_c]0Tm  
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%fid=fopen('e21.dat','w'); wVkms  
N = 128;                       % Number of Fourier modes (Time domain sampling points) K y~ 9's  
M1 =3000;              % Total number of space steps W"S,~y  
J =100;                % Steps between output of space )~xL_yW_X  
T =10;                  % length of time windows:T*T0 H|;6K`O_  
T0=0.1;                 % input pulse width JbpKstc;  
MN1=0;                 % initial value for the space output location 6g4CUP'Y  
dt = T/N;                      % time step 4r#O._Z  
n = [-N/2:1:N/2-1]';           % Index 6la# 0U23  
t = n.*dt;   u\=gps/Z  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 _d6mf
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u20=u10.*0.0;                  % input to waveguide 2 loN!&YceW  
u1=u10; u2=u20;                 ='u'/g$'&  
U1 = u1;   f gI.q  
U2 = u2;                       % Compute initial condition; save it in U iz]Vb{5n%  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1.  v'i"Q  
w=2*pi*n./T; H
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g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T d,[.=Jqv[  
L=4;                           % length of evoluation to compare with S. Trillo's paper sj a;N
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dz=L/M1;                       % space step, make sure nonlinear<0.05 lnL&v'{  
for m1 = 1:1:M1                                    % Start space evolution RrKAgw  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS GjZ@fnF  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; mNN,}nHu  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform #3u3WTk+  
   ca2 = fftshift(fft(u2)); G~_5E]8  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation @_^QBw0  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ~-x8@ /   
   u2 = ifft(fftshift(c2));                        % Return to physical space UXD?
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   u1 = ifft(fftshift(c1)); Nge_ Ks  
if rem(m1,J) == 0                                 % Save output every J steps. Gir_.yc/  
    U1 = [U1 u1];                                  % put solutions in U array >0)E\_ u  
    U2=[U2 u2]; +*,rOK`C  
    MN1=[MN1 m1]; !+& NG&1  
    z1=dz*MN1';                                    % output location idnn%iO  
  end H^xrFXg~z  
end vW]Frb  
hg=abs(U1').*abs(U1');                             % for data write to excel G&:[G>iSm^  
ha=[z1 hg];                                        % for data write to excel SdC505m0*  
t1=[0 t']; N%;Q[*d@/  
hh=[t1' ha'];                                      % for data write to excel file GbUcNROr  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Q_QmyD~m  
figure(1) ]Vhhx`0  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn T[a1S?_*T  
figure(2) 6nt$o)[  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 8(ny^]v|  
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非线性超快脉冲耦合的数值方法的Matlab程序 7p3 ;b"'  
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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。   }D dg  
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 ;hF>iw  
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%  This Matlab script file solves the nonlinear Schrodinger equations Uo(\1&?  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Rg)\o(J  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g*t.g@B<2  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 +A W6 >yV`  
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C=1;                           FMY r6/I  
M1=120,                       % integer for amplitude As@~%0 S  
M3=5000;                      % integer for length of coupler X^%I 3  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ]]o7ej  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 1w+OnJI?  
T =40;                        % length of time:T*T0. Oz^+;P1  
dt = T/N;                     % time step 
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n = [-N/2:1:N/2-1]';          % Index G,{L=xOh  
t = n.*dt;   3Zsqx=w  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. tnqW!F~  
w=2*pi*n./T; \^EjE  
g1=-i*ww./2; X ~4^$x  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; RTA9CR)JP4  
g3=-i*ww./2; l1jS2O(  
P1=0; x)G/YUv76  
P2=0; yHQ.EZ~%  
P3=1; `@ qSDW!b  
P=0; Q9K Gf;  
for m1=1:M1                 8/b_4!5c  
p=0.032*m1;                %input amplitude 9L%&4V}BIS  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 }n=Tw92g  
s1=s10; \ :})R{  
s20=0.*s10;                %input in waveguide 2 Y~=5umNSX  
s30=0.*s10;                %input in waveguide 3 y>2v 9;Qp  
s2=s20; [lS'GszA  
s3=s30; aEXV^5;,pJ  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   tRbZ^5x\@  
%energy in waveguide 1 dcU|y%k%  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   WSDNTfpI  
%energy in waveguide 2 f:7Y  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   F xFK  
%energy in waveguide 3 ~
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for m3 = 1:1:M3                                    % Start space evolution TW3
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS PG<N\  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; n$`Nx\v  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; HLYM(Pz  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform \Zoo9Wy  
   sca2 = fftshift(fft(s2)); NXeo&+F  
   sca3 = fftshift(fft(s3)); SKLQAE5  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ZI}m~7  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 5`x9+XvoN  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); iCAd7=o  
   s3 = ifft(fftshift(sc3)); b@1QE  
   s2 = ifft(fftshift(sc2));                       % Return to physical space dUb(C1h  
   s1 = ifft(fftshift(sc1)); 6ap,XFRMh  
end Z|8f7@k{|+  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); \vQ_:-A  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); lS?f?n^  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); `9K'I-hv<8  
   P1=[P1 p1/p10]; ::TUSz2/2  
   P2=[P2 p2/p10]; 7Fy^K;V"  
   P3=[P3 p3/p10]; Tj:+:B(HB  
   P=[P p*p]; q<hN\kBs  
end r{%NMj  
figure(1) a$aI%  
plot(P,P1, P,P2, P,P3); {B\.8)&8  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~