[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 {3V%  
BbCt_z'  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of <W$Ig@4[.d  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of c UJUZ@ol  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Y$tgz)  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {'(1c)q>  
^ W/,Z`  
%fid=fopen('e21.dat','w'); ,B^NH7A:  
N = 128;                       % Number of Fourier modes (Time domain sampling points) C3m](%?  
M1 =3000;              % Total number of space steps kaKV{;UM  
J =100;                % Steps between output of space \W^+aNbv=8  
T =10;                  % length of time windows:T*T0 d5b \kRr  
T0=0.1;                 % input pulse width Yh^~4S?  
MN1=0;                 % initial value for the space output location y2XeD=_'  
dt = T/N;                      % time step BkZmE,  
n = [-N/2:1:N/2-1]';           % Index cwe@W
PE2  
t = n.*dt;   HizMjJ|  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 {9 PeBc  
u20=u10.*0.0;                  % input to waveguide 2 x+mfQcSD&  
u1=u10; u2=u20;                 ;JNI$DR  
U1 = u1;   k3:8T#N>!O  
U2 = u2;                       % Compute initial condition; save it in U vocXk_  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 
yP&SA+  
w=2*pi*n./T; a.oZ}R7'Y  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T QH?}uX'x)G  
L=4;                           % length of evoluation to compare with S. Trillo's paper OJ2O?Te8  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Glt%%TJb  
for m1 = 1:1:M1                                    % Start space evolution z3 zN^ZT  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS !'yl
h8}  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; hM":?Rx  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform SI/@Bbd=  
   ca2 = fftshift(fft(u2)); nWrknm  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation k1EAmA l  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Wa/&H$d\u@  
   u2 = ifft(fftshift(c2));                        % Return to physical space "q-,140_  
   u1 = ifft(fftshift(c1)); yUZ;keQ_Tw  
if rem(m1,J) == 0                                 % Save output every J steps. '[XtARtY`  
    U1 = [U1 u1];                                  % put solutions in U array !W^b:qjJ  
    U2=[U2 u2]; ?2;gmZd7  
    MN1=[MN1 m1]; upD2vtU  
    z1=dz*MN1';                                    % output location =z=$S]qN  
  end (3H'!P7|~  
end 3,7SGt r  
hg=abs(U1').*abs(U1');                             % for data write to excel dc ]+1 A  
ha=[z1 hg];                                        % for data write to excel 8Z^9r/%*Z  
t1=[0 t']; AbWnDqv  
hh=[t1' ha'];                                      % for data write to excel file (|(#W+l~  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format W~TT`%[  
figure(1) 'dnTu@mUT  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn (l|:$%[0  
figure(2) .x 1& 
  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn c[/h7
!/aH  
\~3g*V  
非线性超快脉冲耦合的数值方法的Matlab程序 c4T8eTKU  
\xQ10\u  
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。   @0XqUcV  
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 4h|48</  
r306`)kX  
> xc7Hr~  
G=[=[o\  
%  This Matlab script file solves the nonlinear Schrodinger equations q~3dbj  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of **zh>Y}6  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 8veYs`  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Jgf73IX[  
{}vB#!  
C=1;                          
UuNcBzB2d  
M1=120,                       % integer for amplitude %T.4Aj  
M3=5000;                      % integer for length of coupler ]cz*k/*0  
N = 512;                      % Number of Fourier modes (Time domain sampling points) n1X.]|6'  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. rv(Qz|K@  
T =40;                        % length of time:T*T0. 7~t,Pt)  
dt = T/N;                     % time step mP1EWh|  
n = [-N/2:1:N/2-1]';          % Index t+R8{9L-  
t = n.*dt;   S{v [65  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. i.0}d5Y  
w=2*pi*n./T; +) pO82  
g1=-i*ww./2; sC8C><y  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rPK)=[MZ  
g3=-i*ww./2; Z#-:zD7_  
P1=0; '?q \mi  
P2=0; {=(GY@yU/  
P3=1; 1LgzqRq  
P=0; O23dtH  
for m1=1:M1                 \6UK:'5{  
p=0.032*m1;                %input amplitude eiL  ;  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 rek
89.p  
s1=s10; rt\i@}  
s20=0.*s10;                %input in waveguide 2 {Jv m *  
s30=0.*s10;                %input in waveguide 3 [SluYmW  
s2=s20; KL2#Bm_  
s3=s30; .A: #l?  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   {x3"/sF  
%energy in waveguide 1 DEGEr-  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   D[.;-4"_  
%energy in waveguide 2 *x^W`i   
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   `@8QQB  
%energy in waveguide 3 ";jj`  
for m3 = 1:1:M3                                    % Start space evolution '
USol<  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 3SRz14/W_R  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; -}liG  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 5jj
<sj!S  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform .%{3#\  
   sca2 = fftshift(fft(s2)); !n<vN@V*3d  
   sca3 = fftshift(fft(s3)); V~V_+  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   9{gY|2R_  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); _z:7Dj#  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ;\N{z6  
   s3 = ifft(fftshift(sc3)); "3kIQsD|j  
   s2 = ifft(fftshift(sc2));                       % Return to physical space {uO=Wkp~7  
   s1 = ifft(fftshift(sc1)); LwpO_/qV  
end @M[t|  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 3BBw:)V  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); M.|@|If4?  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); nLn3kMl4  
   P1=[P1 p1/p10]; C_SJ
4Sh  
   P2=[P2 p2/p10]; HZp}<7NR(7  
   P3=[P3 p3/p10]; 2}Ga  
   P=[P p*p]; I]HrtI  
end t'msgC6=>u  
figure(1) c/fU0cA@  
plot(P,P1, P,P2, P,P3); n H)6mOYp  
X.u&4SH  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~