[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 
\#uqD\DE  
0\V\qAk  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of `DI{wqV9  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of )3k)2XF  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear J%:WLQo  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \7|s$ XQ\  
#rh0r`  
%fid=fopen('e21.dat','w'); zd?bHcW/h  
N = 128;                       % Number of Fourier modes (Time domain sampling points) c80 }1  
M1 =3000;              % Total number of space steps Rg%R/p)C  
J =100;                % Steps between output of space tfi2y]{A  
T =10;                  % length of time windows:T*T0 wlm3~B\64  
T0=0.1;                 % input pulse width j)6@q@P/  
MN1=0;                 % initial value for the space output location Q.j-C}a  
dt = T/N;                      % time step M3hy5j(b  
n = [-N/2:1:N/2-1]';           % Index sL!;hKK  
t = n.*dt;   ({*.!ty  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ,$hQ(yF  
u20=u10.*0.0;                  % input to waveguide 2 &>d:ewM\  
u1=u10; u2=u20;                 (1j(*
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U1 = u1;   @)aXNQY  
U2 = u2;                       % Compute initial condition; save it in U ,\|n=T,  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. &M!4]pow
 
w=2*pi*n./T; yC9:sQ'k  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T X;K8,A7`  
L=4;                           % length of evoluation to compare with S. Trillo's paper *T.={>HE8  
dz=L/M1;                       % space step, make sure nonlinear<0.05 uf{SxEa  
for m1 = 1:1:M1                                    % Start space evolution :d!i[W*  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Y}V)4j  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Ktg&G<%J0  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform D6C-x  
   ca2 = fftshift(fft(u2)); 9Q SUCN_  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation }M"-5K}  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   iqU.a/~y  
   u2 = ifft(fftshift(c2));                        % Return to physical space X}65\6  
   u1 = ifft(fftshift(c1)); K1m!S9d`x  
if rem(m1,J) == 0                                 % Save output every J steps. Y-}hNZn"{  
    U1 = [U1 u1];                                  % put solutions in U array TE*>a5C|  
    U2=[U2 u2]; ]1/W8
z%  
    MN1=[MN1 m1]; $5q{vy  
    z1=dz*MN1';                                    % output location Z'*G'/*  
  end 6E*Zj1KX  
end 1A,4Aw<  
hg=abs(U1').*abs(U1');                             % for data write to excel 'W<a54T?z  
ha=[z1 hg];                                        % for data write to excel GI'&g@?u  
t1=[0 t']; 30gZ_8C>}  
hh=[t1' ha'];                                      % for data write to excel file `4"y#Z  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format D{&+7C:8.  
figure(1) 0ER6cTo-t  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn uK"$=v6|  
figure(2) (HTk;vbZm  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn  d'**wh,  
.@x"JI>;  
非线性超快脉冲耦合的数值方法的Matlab程序 2vW,.]95M  
hc@;}a\Y  
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。   +e{d
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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 `9G$p|6  
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K>DnD0  

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%  This Matlab script file solves the nonlinear Schrodinger equations &CPe$'FYI  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of kBDe*K.V  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear #!<+:y'S?  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 g-TX;(  
5 \.TZMB  
C=1;                           j*3sjOoC  
M1=120,                       % integer for amplitude lHj7O&+  
M3=5000;                      % integer for length of coupler Wb}0-U{S'  
N = 512;                      % Number of Fourier modes (Time domain sampling points) *$WiJ3'(m  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ['9OGV\  
T =40;                        % length of time:T*T0. )Or:wFSMq  
dt = T/N;                     % time step <R]Wy}2-  
n = [-N/2:1:N/2-1]';          % Index SqT"/e]b'  
t = n.*dt;   .+yJh  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. FdK R{dX}  
w=2*pi*n./T; ggYIq*4  
g1=-i*ww./2; c,u$tnE)  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 5qODS_Eq  
g3=-i*ww./2; |'l* 
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P1=0; TTw~.
x,  
P2=0; ="[+6X  
P3=1; 0,
i+  
P=0; Y9(i}uTi  
for m1=1:M1                 (WU~e!}  
p=0.032*m1;                %input amplitude ">4[+'  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 J4R  
s1=s10; qLktMp_  
s20=0.*s10;                %input in waveguide 2 e\bF_ N2VA  
s30=0.*s10;                %input in waveguide 3 fb S.  
s2=s20; kY |=a  
s3=s30; uJAB)ti2I  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   khO<Z^wi[  
%energy in waveguide 1 y^Xxa'y  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   x:D<Mu#  
%energy in waveguide 2 <3]/ms  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   <pa];k(IQL  
%energy in waveguide 3 k3htHCf*G$  
for m3 = 1:1:M3                                    % Start space evolution 0%L$TJ.''  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS P^{`d_[K%  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; rq|czQ  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; `S!uj <-  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform  cB{;Nh6"  
   sca2 = fftshift(fft(s2)); >!ZyykAs  
   sca3 = fftshift(fft(s3)); "r `6c0Z  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   l#(g&x6J  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); F@*r%[S/  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); cqU/Y_%l'  
   s3 = ifft(fftshift(sc3)); U=*q;$L#  
   s2 = ifft(fftshift(sc2));                       % Return to physical space YUE1 '}  
   s1 = ifft(fftshift(sc1)); ]8j5Ou6#y  
end J,2v~Dq  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); cF>;f(X  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); p`V9+CA  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); iF2IR{h  
   P1=[P1 p1/p10]; .dq.F#2B;  
   P2=[P2 p2/p10]; V:$1o  
   P3=[P3 p3/p10]; _\V{X}ftqa  
   P=[P p*p]; kTe<1^,m  
end hQRc,d6x5  
figure(1) 3 mMdq*X5  
plot(P,P1, P,P2, P,P3); iegPEb  
<zWQ[^  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~