[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 37ll8  
Bo`fy/x#  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Ufv{6"sH  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of NRcg~Nu  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !__f  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 !.+iA=K{  
`tVBV:4\  
%fid=fopen('e21.dat','w'); K^J;iu4  
N = 128;                       % Number of Fourier modes (Time domain sampling points) H$Q$3Q!`  
M1 =3000;              % Total number of space steps BNyDEFd  
J =100;                % Steps between output of space 1|;WaO1Q  
T =10;                  % length of time windows:T*T0 s$C;31k  
T0=0.1;                 % input pulse width S"|D!}@-  
MN1=0;                 % initial value for the space output location 8hQ"rrj+  
dt = T/N;                      % time step `
.MM|6  
n = [-N/2:1:N/2-1]';           % Index c500:OSB  
t = n.*dt;   w6Dysg:  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 KAgiY4  
u20=u10.*0.0;                  % input to waveguide 2 |QAmN>7U  
u1=u10; u2=u20;                 z:+Xs
!S  
U1 = u1;   \Wt&z,  
U2 = u2;                       % Compute initial condition; save it in U ;1NZY.pyc  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Xvi{A]V  
w=2*pi*n./T; plsf` a  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Uk S86`.  
L=4;                           % length of evoluation to compare with S. Trillo's paper 
%a5Sc|&-  
dz=L/M1;                       % space step, make sure nonlinear<0.05 IB}.J,=  
for m1 = 1:1:M1                                    % Start space evolution PaMi5Pq  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS T(a*d7  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 4J!1$  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform xO/44D  
   ca2 = fftshift(fft(u2)); g[8VfIe  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation &4O"Xs`ka  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   qlPjz*<h"H  
   u2 = ifft(fftshift(c2));                        % Return to physical space np=m~k  
   u1 = ifft(fftshift(c1)); cn<9!2a  
if rem(m1,J) == 0                                 % Save output every J steps. Y91TF'  
    U1 = [U1 u1];                                  % put solutions in U array *%B%BJnX  
    U2=[U2 u2]; GY@Np^>[a  
    MN1=[MN1 m1]; Kl(}s{YFn.  
    z1=dz*MN1';                                    % output location A~*Wr+pv  
  end SK;f#quUQ  
end A |NX"  
hg=abs(U1').*abs(U1');                             % for data write to excel |1J "r.K  
ha=[z1 hg];                                        % for data write to excel DSd 5?  
t1=[0 t']; g|)e3q{M  
hh=[t1' ha'];                                      % for data write to excel file *fSa8CV  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format \M:,Vg  
figure(1)
u+(e,t  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6XFO@c}d  
figure(2) FE M_7M  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn $N,9e  
bTO$
B2eh|  
非线性超快脉冲耦合的数值方法的Matlab程序 ~+
l%}4RZ  
xS,):R  
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。   um&N|5lHb  
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
@m6pAo4P  
:".!6~:2  
*$`r)pV%AK  
]Y;$~qQ  
%  This Matlab script file solves the nonlinear Schrodinger equations %{zM> le9  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of _'2r=a#`  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear tE>3.0U0Q  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 JC>}(yQA  
,LcMNPr  
C=1;                           S:Yo9~  
M1=120,                       % integer for amplitude pC5-,Z;8  
M3=5000;                      % integer for length of coupler KgAc0pz{7H  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Kh$L~4l  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. b<=K@I.=  
T =40;                        % length of time:T*T0. dN\pe@#lKP  
dt = T/N;                     % time step 
9FWn  
n = [-N/2:1:N/2-1]';          % Index | @di<d@  
t = n.*dt;    [POy"O  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 1/HPcCsHb  
w=2*pi*n./T; >x!N@G  
g1=-i*ww./2; p,kJ#I  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; M{~eI  
g3=-i*ww./2; V#3VRh  
P1=0; zYls>fbp,  
P2=0; Bm~>w`1wK  
P3=1; ?KS9Dh  
P=0; 9]AKNQq m  
for m1=1:M1                 !u7WCw.Dm  
p=0.032*m1;                %input amplitude f3v/Y5)  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 >vP^l {SD  
s1=s10; N3x}YHFF  
s20=0.*s10;                %input in waveguide 2 K.X%
Q,XD  
s30=0.*s10;                %input in waveguide 3 k{@z87+&  
s2=s20; SxOM@A  
s3=s30; vP,WV9Q1u  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   [oKB1GkA  
%energy in waveguide 1 =#y&xWxL  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   |/p^e  
%energy in waveguide 2 rbP.N ?YU%  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   (TnYUyFP`  
%energy in waveguide 3 "QiUuD=  
for m3 = 1:1:M3                                    % Start space evolution *&5G+d2
 
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS OW #pBeX99  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; r@ejU'uz  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; P!]DV$
o  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform kV(?u_ R  
   sca2 = fftshift(fft(s2)); jkD5Z`D  
   sca3 = fftshift(fft(s3)); -Tz9J4xU&  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   :;7qup  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Ge97e/CY  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); aZBaIl6I  
   s3 = ifft(fftshift(sc3)); [2&Fnmjk}X  
   s2 = ifft(fftshift(sc2));                       % Return to physical space .6/[X`*  
   s1 = ifft(fftshift(sc1)); pl7!O9bo  
end 7L]fCw p[  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); DtZkrj)D/  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); TF{ xFb)  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); d[O.UzQ  
   P1=[P1 p1/p10]; Zu+Z7@$}/  
   P2=[P2 p2/p10]; @Z|cUHo  
   P3=[P3 p3/p10]; qbT].,?!U  
   P=[P p*p]; "` 9W"A=  
end RrRCT.+E  
figure(1) <X;y 4lPZ  
plot(P,P1, P,P2, P,P3); M)|}Vn;!  
ap=M$9L'  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~