[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 y{&{=1#  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 0{U]STj  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of df21t^0/  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear X-*KQ+?  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :JTRRv  

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%fid=fopen('e21.dat','w'); vkNZ -`+I  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ;:8jxkx6%  
M1 =3000;              % Total number of space steps eE#81]'6a  
J =100;                % Steps between output of space 7>W+Uq  
T =10;                  % length of time windows:T*T0 ?vL^:f["  
T0=0.1;                 % input pulse width 5~ *'>y  
MN1=0;                 % initial value for the space output location >h/)r6  
dt = T/N;                      % time step it/C y\f  
n = [-N/2:1:N/2-1]';           % Index )|59FOWg  
t = n.*dt;   F| ,Vw{  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 0
s+rd&  
u20=u10.*0.0;                  % input to waveguide 2 ~,M;+T}[r  
u1=u10; u2=u20;                 $@ T6g  
U1 = u1;   fed[^wW  
U2 = u2;                       % Compute initial condition; save it in U R"8})a gw  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ?=|)n%  
w=2*pi*n./T; E:dT_x<Y  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T CwH)6uA  
L=4;                           % length of evoluation to compare with S. Trillo's paper <Vr]2mw  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Hjo:;s  
for m1 = 1:1:M1                                    % Start space evolution ^}Dv$\;6  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS LzEE]i  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; $+)x)1  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform {
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   ca2 = fftshift(fft(u2)); 6"rFfdns  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation BHRrXC\  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   #IL~0t  
   u2 = ifft(fftshift(c2));                        % Return to physical space
([4{n  
   u1 = ifft(fftshift(c1)); CpP$HrQ  
if rem(m1,J) == 0                                 % Save output every J steps. ]>S$R&a  
    U1 = [U1 u1];                                  % put solutions in U array 8'g*}[  
    U2=[U2 u2]; ]mJAKycE%  
    MN1=[MN1 m1]; CB{k;H  
    z1=dz*MN1';                                    % output location B#Oc8`1Y  
  end +=29y@c  
end ?XTg%U  
hg=abs(U1').*abs(U1');                             % for data write to excel |]]pHC_/W  
ha=[z1 hg];                                        % for data write to excel ay7+H7^|hZ  
t1=[0 t']; NdED8 iRc  
hh=[t1' ha'];                                      % for data write to excel file ,{mf+ 3&$,  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format \PtC  
figure(1) _>:=<xyOq  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn q%=7<( w  
figure(2) v,x%^gv0  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn (1r>50Ge  
nF!_q;+Vp  
非线性超快脉冲耦合的数值方法的Matlab程序 !\D]\|Bo  
Pi]s<3PL  
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。   oE|{|27X  
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 (j"~]T!)1  
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%Cbc@=k  
XKPt[$ab  
%  This Matlab script file solves the nonlinear Schrodinger equations Y[8co<p  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of JXR/K=<^  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear oe_[h]Hgl  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8Q)mmkI\=  
K&a]pL6D  
C=1;                           RxDxLU2kt  
M1=120,                       % integer for amplitude (Ss77~W7  
M3=5000;                      % integer for length of coupler gJ[q {b  
N = 512;                      % Number of Fourier modes (Time domain sampling points) }zfLm`vJ  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. I>4Tbwy.-  
T =40;                        % length of time:T*T0. a518N*]j  
dt = T/N;                     % time step ]zR;%p  
n = [-N/2:1:N/2-1]';          % Index {HJ`%xN|  
t = n.*dt;   [{!j9E?(  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Er+3S@sfq,  
w=2*pi*n./T; ThqfZl=V  
g1=-i*ww./2; *$Wx*Jo  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; )eGu4iEPM  
g3=-i*ww./2; ^9V8M9  
P1=0; @aPu}Hi  
P2=0; 9oau_Q#  
P3=1; [@?.}!  
P=0; ][K8\  
for m1=1:M1                 g}og@UY7#  
p=0.032*m1;                %input amplitude eRqexqO!  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 tS/APSY  
s1=s10; ^)P5(fJ  
s20=0.*s10;                %input in waveguide 2 <IkD=X  
s30=0.*s10;                %input in waveguide 3 K}*p(1$u  
s2=s20; 1X_!%Z  
s3=s30; U!UX"r  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   H=SMDj)s+  
%energy in waveguide 1 VS@W.0/  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ZYt"=\_  
%energy in waveguide 2 .+~kJ0~Y  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   @_:?N(%(  
%energy in waveguide 3 zSv
Hvs  
for m3 = 1:1:M3                                    % Start space evolution \]:NOmI^'  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS +z?f,`.*  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ]` Gz_e  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ?j$8Uy$$  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform UU~;B  
   sca2 = fftshift(fft(s2)); n)7$x
YuH  
   sca3 = fftshift(fft(s3)); R\=\6("  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   z8[|LF-dx  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); l{SPV8[i  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); %1d6j<7  
   s3 = ifft(fftshift(sc3)); ~ilBw:L-3  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 2X|jq4  
   s1 = ifft(fftshift(sc1)); -#z'A  
end P*=3$-`  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); zSufU2  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); <y/AEY1  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); f6A['<%o  
   P1=[P1 p1/p10]; 00x^zu?N  
   P2=[P2 p2/p10]; !_z>w6uR  
   P3=[P3 p3/p10]; {'bkU9+  
   P=[P p*p]; b6M)qt9R  
end Q6<Uuiw  
figure(1) =@/^1.`  
plot(P,P1, P,P2, P,P3); JWjp<{Q;1  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~