计算脉冲在非线性耦合器中演化的Matlab 程序 vo(?[[ p$%h!.~99T % This Matlab script file solves the coupled nonlinear Schrodinger equations of
sw@2
?+ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
r?+u}uH % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
PvB?57wkF % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
i ('EBO
mcX akWmi %fid=fopen('e21.dat','w');
}-Ma ~/ N = 128; % Number of Fourier modes (Time domain sampling points)
aw4+1.xy M1 =3000; % Total number of space steps
.>nd@oU J =100; % Steps between output of space
-*Pt781 T =10; % length of time windows:T*T0
1*jL2P]D T0=0.1; % input pulse width
%7@H7 ^s}9 MN1=0; % initial value for the space output location
i|O7nB@ dt = T/N; % time step
B*AMo5 n = [-N/2:1:N/2-1]'; % Index
w:LCm `d t = n.*dt;
.5yc O u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
[ O )Z of u20=u10.*0.0; % input to waveguide 2
2Ee1mbZVw8 u1=u10; u2=u20;
$ P@cS1sB U1 = u1;
xq)/ QR U2 = u2; % Compute initial condition; save it in U
, Ex\\p- ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hpyre B w=2*pi*n./T;
0EB '! g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
stG& (M L=4; % length of evoluation to compare with S. Trillo's paper
8WGM%n#q dz=L/M1; % space step, make sure nonlinear<0.05
^0
lPv!2 for m1 = 1:1:M1 % Start space evolution
iL gt_@g u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
D6 oby*_w u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
I7_D $a= ca1 = fftshift(fft(u1)); % Take Fourier transform
Mfr#IzNHN ca2 = fftshift(fft(u2));
//,'oh~W c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
MB 5[Js| c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
_Xv/S_yW u2 = ifft(fftshift(c2)); % Return to physical space
zLqp@\sT u1 = ifft(fftshift(c1));
79x9<,a) if rem(m1,J) == 0 % Save output every J steps.
Ft rw3OxN U1 = [U1 u1]; % put solutions in U array
A(p U2=[U2 u2];
1c"m$)a4 MN1=[MN1 m1];
h3IkOh4|h z1=dz*MN1'; % output location
eM"mP&TTL end
pi}H.iF end
1Qu,]i` hg=abs(U1').*abs(U1'); % for data write to excel
Uh Tr<(@ ha=[z1 hg]; % for data write to excel
nQHd\/B
t1=[0 t'];
-c?wEqa~2 hh=[t1' ha']; % for data write to excel file
wg.fo:Q %dlmwrite('aa',hh,'\t'); % save data in the excel format
n1 >nnH]G figure(1)
')-(N
um waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
7uxPkZbb figure(2)
[\
YP8^.. waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
\>`$x: ^z; ,deoGh 非线性超快脉冲耦合的数值方法的Matlab程序 Hc%\9{zH ,O)\,t g 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。
<xjv7`G7 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
05 Q8` RT"2Us]* \=V[ba:q BQ:Kx _
% This Matlab script file solves the nonlinear Schrodinger equations
4Z9 3 g { % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
] *VF Ws % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
I=y j % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
KAcri<^G }n%R l\p C=1;
ydqmuZ%2h# M1=120, % integer for amplitude
G)Bq?=P
M3=5000; % integer for length of coupler
o>-v?Ug N = 512; % Number of Fourier modes (Time domain sampling points)
e=UVsYNx dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
v@uaf=x- T =40; % length of time:T*T0.
mh7sY;SvM dt = T/N; % time step
%N>NOk) n = [-N/2:1:N/2-1]'; % Index
Zt2@?w; t = n.*dt;
=G F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
+()t8,S, w=2*pi*n./T;
O\Mq< ;|7m g1=-i*ww./2;
[Um4\QvU x g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
j~*Z7iu g3=-i*ww./2;
kz;_f P1=0;
:U. )YHY P2=0;
`h9)`* P3=1;
iq uTT~ P=0;
i;hc]fYb=K for m1=1:M1
n`z+ w* p=0.032*m1; %input amplitude
_6UAeZ*M s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Wejwj/EU% s1=s10;
e_c;D2' F s20=0.*s10; %input in waveguide 2
G6 8Nv: s30=0.*s10; %input in waveguide 3
[&q bc#L s2=s20;
1uS-Tx s3=s30;
zL},`:(. p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
/3[ 9{r %energy in waveguide 1
M 1^C8cz p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
51M^yG&M %energy in waveguide 2
1: x nD p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
V}|v!h[O8 %energy in waveguide 3
{rvbo1t for m3 = 1:1:M3 % Start space evolution
uo4$rf7 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
# >:(#^Uu s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
yD"0=\ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Lkl|4L sca1 = fftshift(fft(s1)); % Take Fourier transform
^~6] 0$yJ sca2 = fftshift(fft(s2));
x]R(twi sca3 = fftshift(fft(s3));
?S&w0}R sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
U7"BlT!V\ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@\T;PTD- sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
J/x@$' s3 = ifft(fftshift(sc3));
HD:%Yv s2 = ifft(fftshift(sc2)); % Return to physical space
3K#mF7)a s1 = ifft(fftshift(sc1));
zzfn0g end
t+ S~u^ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
_+*/~E p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Sc'c$/ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
U$A7 EFK' P1=[P1 p1/p10];
!/nx=vg p P2=[P2 p2/p10];
mUt,Z^ l` P3=[P3 p3/p10];
i2:+h}o$e P=[P p*p];
Sc/`=h]T end
>I d!I figure(1)
NY jS plot(P,P1, P,P2, P,P3);
nQ642i%RQ dm2CA0 转自：
http://blog.163.com/opto_wang/
