[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 6nSk,yE'hE  
@%cJjZ5y  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 
N$,)vb<  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of @x J^JcE  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Tx_(^K  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 17Gdu[E  
IKr7"`  
%fid=fopen('e21.dat','w'); D3lYy>~d5;  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ;q
k~>  
M1 =3000;              % Total number of space steps /+1Fa):  
J =100;                % Steps between output of space QBn>@jq  
T =10;                  % length of time windows:T*T0 O}f(h5!k  
T0=0.1;                 % input pulse width _0j}(Q>|H#  
MN1=0;                 % initial value for the space output location Zz&i0r  
dt = T/N;                      % time step ]D-4
8o0  
n = [-N/2:1:N/2-1]';           % Index O}D
8  
t = n.*dt;   CC-:dN
b  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 =K>Z{%i  
u20=u10.*0.0;                  % input to waveguide 2 -5 W0K}  
u1=u10; u2=u20;                 x[^A9  
U1 = u1;   835Upj>  
U2 = u2;                       % Compute initial condition; save it in U #f~a\}$I  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Y-c~"#  
w=2*pi*n./T; ;VFr5.*x  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T t5Mo'*j =  
L=4;                           % length of evoluation to compare with S. Trillo's paper W=\dsdnu*  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ,"VQ0Z1  
for m1 = 1:1:M1                                    % Start space evolution _~(Xd@c(  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS .XB] X  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ZAH<!@qh  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform n1/lE)  
   ca2 = fftshift(fft(u2)); G([vy#p  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation eztk$o  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   zB$6e!fc  
   u2 = ifft(fftshift(c2));                        % Return to physical space rWs5s!l,  
   u1 = ifft(fftshift(c1)); `^_:  
if rem(m1,J) == 0                                 % Save output every J steps. 66Xt=US  
    U1 = [U1 u1];                                  % put solutions in U array _dBU6U:V  
    U2=[U2 u2]; ^Q,/C8qeb  
    MN1=[MN1 m1]; f,a %@WT  
    z1=dz*MN1';                                    % output location F`Y<(]+   
  end ?mAw"Rb!  
end ?.4l1X6Ba  
hg=abs(U1').*abs(U1');                             % for data write to excel k0IU~y%  
ha=[z1 hg];                                        % for data write to excel V$%K=[  
t1=[0 t']; ,h._iO)I^  
hh=[t1' ha'];                                      % for data write to excel file  :Y
3?,  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format g\)z!DQ]  
figure(1) "'#Hh&Us  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn pzr-}>xrZ  
figure(2) 7&)F;;H  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn L>b,}w  
B~#@fI
L  
非线性超快脉冲耦合的数值方法的Matlab程序 W8NA.  
.Cus t  
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。   j[`?`RyU  
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 ~&:R\  
3Q}Y?rkJ5  
;LE @Ezx  
\^4$}@*]  
%  This Matlab script file solves the nonlinear Schrodinger equations &zcjU+n  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of o{LFXNcg[  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear SXz([Z{)  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 FO=1P7  
Y%l3SB,5L  
C=1;                           B
-|Zo_7  
M1=120,                       % integer for amplitude
rtx]dc1m  
M3=5000;                      % integer for length of coupler 2oG|l!C  
N = 512;                      % Number of Fourier modes (Time domain sampling points) |u;PU`
^-z  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. KgWT&^t  
T =40;                        % length of time:T*T0. l5ds`uR#  
dt = T/N;                     % time step *KH@u  
n = [-N/2:1:N/2-1]';          % Index 'e64%t  
t = n.*dt;   K>6k@okO  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. G9inNz*Cx  
w=2*pi*n./T; ji -1yX  
g1=-i*ww./2; # :w2Hf6Q  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; =+S3S{\CK  
g3=-i*ww./2; 9lJj/  
P1=0; ]/Qy1,  
P2=0;
xN8JrZE&  
P3=1; )N6[rw<  
P=0; D#1~]d  
for m1=1:M1                 QS*cd|7J;  
p=0.032*m1;                %input amplitude Wb)l8[=  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 C}'="g^=sl  
s1=s10; Q5n :f+  
s20=0.*s10;                %input in waveguide 2 >o#wP  
s30=0.*s10;                %input in waveguide 3 {taVAcb  
s2=s20; lkg*AAR?'  
s3=s30; b|o!&9Yyr  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   %H@76NvEz  
%energy in waveguide 1 p3FnYz-V  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   O:tX0<6  
%energy in waveguide 2 UH-uU~  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ]=VS~azZ5  
%energy in waveguide 3 /&as)  
for m3 = 1:1:M3                                    % Start space evolution n o+tVm|  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS /8t+d.r;/  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; fR%1FXpK&  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; %`1CE\f  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 1 3`0d  
   sca2 = fftshift(fft(s2)); 0(/D|  
   sca3 = fftshift(fft(s3)); yPh2P5}H>  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   >04>rn#},,  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); L2.`1Aag  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); UW[{d/.wC  
   s3 = ifft(fftshift(sc3)); D *I;|.=u  
   s2 = ifft(fftshift(sc2));                       % Return to physical space T) tZU?  
   s1 = ifft(fftshift(sc1)); Df
:7P>  
end 56SS >b  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); )QCM2  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); l()MYuLNV  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); qJXsf M6  
   P1=[P1 p1/p10]; pNE\@U|4E  
   P2=[P2 p2/p10]; k7|z$=zY  
   P3=[P3 p3/p10]; [7Lx
t
 
   P=[P p*p]; @U3foL2\  
end Oqpl2Y"/  
figure(1) 6$fnQcpJ  
plot(P,P1, P,P2, P,P3); O0wCb  
o;4e)tK  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~