[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 w%F~4|F  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of =REMSej  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ))m\d*  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear y(/"DUx  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 v&Xsyb0CaM  
y,'M3GGl  
%fid=fopen('e21.dat','w'); +*&bgGhT  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Z$ q{!aY  
M1 =3000;              % Total number of space steps ?e( y/  
J =100;                % Steps between output of space *YH5kX  
T =10;                  % length of time windows:T*T0 mU@pRjq=  
T0=0.1;                 % input pulse width _wMxKM  
MN1=0;                 % initial value for the space output location A)6xEeyR  
dt = T/N;                      % time step +l'l*<  
n = [-N/2:1:N/2-1]';           % Index Kv(2x3("  
t = n.*dt;   [Z~h!}  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 !YX$4_I  
u20=u10.*0.0;                  % input to waveguide 2 mY6d+  
u1=u10; u2=u20;                 WOBLgM,|  
U1 = u1;   fNR2(8;}  
U2 = u2;                       % Compute initial condition; save it in U Wk<heF  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. C:z+8wt  
w=2*pi*n./T; wJc~AP)I%z  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Y$JGpeq8w  
L=4;                           % length of evoluation to compare with S. Trillo's paper A#NJ8_  
dz=L/M1;                       % space step, make sure nonlinear<0.05 N8*6sK.  
for m1 = 1:1:M1                                    % Start space evolution 9~3;upWu!  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS s4V-brCM$|  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 6!F@?3qCyg  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform T($d3Nn1  
   ca2 = fftshift(fft(u2)); 0QJ :  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation h&5b
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   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   K|^PHe  
   u2 = ifft(fftshift(c2));                        % Return to physical space fv@mA--  
   u1 = ifft(fftshift(c1));
FTu6%~M/  
if rem(m1,J) == 0                                 % Save output every J steps. 1,Ams  
    U1 = [U1 u1];                                  % put solutions in U array a ]~Rp  
    U2=[U2 u2]; >-S?rXO  
    MN1=[MN1 m1]; jGm`Qg{<  
    z1=dz*MN1';                                    % output location SXqWq  
  end P}"=67$  
end zEM c)  
hg=abs(U1').*abs(U1');                             % for data write to excel d `MTc  
ha=[z1 hg];                                        % for data write to excel rF@njw@  
t1=[0 t']; D;?
cf+6$  
hh=[t1' ha'];                                      % for data write to excel file '%Fg+cZN\  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format K Eda6zZH  
figure(1) .4CCR[Het  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn y~ 2C2'7  
figure(2) F#b^l}  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn c/Dk*.xy<  
T'^ Do/  
非线性超快脉冲耦合的数值方法的Matlab程序 x."R_>  
8NF93tqD6  
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。   ztS:1\  
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 |.#G G7F^S  
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jmORKX+)  
%  This Matlab script file solves the nonlinear Schrodinger equations mV>l`&K=  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of W(4Mvd  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear cMU"SO  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 s78MXS?py  
[,bra8f[C  
C=1;                           @5RbMf{  
M1=120,                       % integer for amplitude uqot
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M3=5000;                      % integer for length of coupler hr@kU x  
N = 512;                      % Number of Fourier modes (Time domain sampling points) #Vy8<Vy&w  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. AONEUSxJ  
T =40;                        % length of time:T*T0. .#q]{j@Ot  
dt = T/N;                     % time step `{KdmWhW  
n = [-N/2:1:N/2-1]';          % Index 8
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t = n.*dt;   olv0w;s  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Cg8
s9qE?  
w=2*pi*n./T; :kMF.9U:  
g1=-i*ww./2; AAXlBY6Y-  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; \V(w=  
g3=-i*ww./2; FG:t2ea  
P1=0; IRknD3LX  
P2=0; oNEjlV*  
P3=1; +dG3/vV  
P=0; +^<s'  
for m1=1:M1                 {1eW*9  
p=0.032*m1;                %input amplitude <rihi:4K  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 \Ota~A  
s1=s10; Z g.La<#  
s20=0.*s10;                %input in waveguide 2 h`n) b  
s30=0.*s10;                %input in waveguide 3 y9Q#%a8V  
s2=s20; 9,?7mgZp  
s3=s30; rD;R9b"J  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ]*Cq'<h$  
%energy in waveguide 1 ^qY?x7mx1  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   S[;d\Z]~  
%energy in waveguide 2 XiL[1JM  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   G"F)t(iX  
%energy in waveguide 3 6}cN7wnm j  
for m3 = 1:1:M3                                    % Start space evolution uXouN$&  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS |}o6N5)  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; im3BQIPR  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ^)E
# c  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform
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   sca2 = fftshift(fft(s2)); +;ylld  
   sca3 = fftshift(fft(s3)); M<nH  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   w{WEYS
 
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); gX|We}H  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Y 8n*o3jM  
   s3 = ifft(fftshift(sc3)); $(]E$ek  
   s2 = ifft(fftshift(sc2));                       % Return to physical space :+_  
   s1 = ifft(fftshift(sc1)); ~f:"Q(f+  
end y 2C Jk~  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); h e[2,  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); iv ~<me0F  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); "-Yj~  
   P1=[P1 p1/p10]; 1)#dgsa  
   P2=[P2 p2/p10]; }60/5HNr  
   P3=[P3 p3/p10]; | Rj"}SC  
   P=[P p*p]; CjGQ  
end /PKu",Azj  
figure(1) F!<!)_8Q  
plot(P,P1, P,P2, P,P3); /5Sd?pW;  
!'#GdRstv  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~