计算脉冲在非线性耦合器中演化的Matlab 程序 WIghP5% W L_~G`Rb3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
n&fV3[m`2 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
n*1UNQp@]O % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
jDnh/k0{d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7Av]f3Zr \5Jv;gc\\ %fid=fopen('e21.dat','w');
Yem\`; * N = 128; % Number of Fourier modes (Time domain sampling points)
pI`Ke " M1 =3000; % Total number of space steps
oW_WW$+N J =100; % Steps between output of space
*+AP}\p0F T =10; % length of time windows:T*T0
L:<'TXsRA T0=0.1; % input pulse width
c>g%oE MN1=0; % initial value for the space output location
".\(A f2 dt = T/N; % time step
qha<.Ro n = [-N/2:1:N/2-1]'; % Index
7Tbk ti; t = n.*dt;
D H^^$) u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
9 V&LJhDQ u20=u10.*0.0; % input to waveguide 2
RB" rx\u7K u1=u10; u2=u20;
!S:@x.n@iR U1 = u1;
D 4\I;M^ U2 = u2; % Compute initial condition; save it in U
%c0;Bb- ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
UQFuEI<1- w=2*pi*n./T;
R4/@dA0
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
0TpA3K L=4; % length of evoluation to compare with S. Trillo's paper
2XtQ"` ) dz=L/M1; % space step, make sure nonlinear<0.05
iCS/~[ for m1 = 1:1:M1 % Start space evolution
= N
c`hP u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
5 5,-1tWs u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
0 Yp;?p^ ca1 = fftshift(fft(u1)); % Take Fourier transform
UU/|s>F ca2 = fftshift(fft(u2));
?<;<# JN c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
`9-Zg??8r c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
wOOPWwk u2 = ifft(fftshift(c2)); % Return to physical space
b ~gF,^w u1 = ifft(fftshift(c1));
`Nn?G if rem(m1,J) == 0 % Save output every J steps.
wu')Q/v U1 = [U1 u1]; % put solutions in U array
Z ux2VepT U2=[U2 u2];
s<b7/ ;w' MN1=[MN1 m1];
#"_MY- z1=dz*MN1'; % output location
oB9m\o7$ end
Q 1Ao65 end
X\%3u PQ hg=abs(U1').*abs(U1'); % for data write to excel
e ?>suIB ha=[z1 hg]; % for data write to excel
WQx; tX t1=[0 t'];
H JiP:{ hh=[t1' ha']; % for data write to excel file
w.f [) %dlmwrite('aa',hh,'\t'); % save data in the excel format
Vd4osBu{fY figure(1)
%*OJRL` waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
i"xDQ$0G6 figure(2)
7W"menw waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
bSLj-vp 6K}=K?3Z 非线性超快脉冲耦合的数值方法的Matlab程序 N3p3"4_]fy &/9oi_r%r 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
K dm5O@tq Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vEGK{rMA R`q!~8u
Dfia=1A sLIP |i % This Matlab script file solves the nonlinear Schrodinger equations
cmI#R1\ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
s`RJl V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}c%y0)fL % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
aehMLl9cl ".f:R9- C=1;
3G^Ed)JvE M1=120, % integer for amplitude
t;Om9 M3=5000; % integer for length of coupler
n~j[ P w N = 512; % Number of Fourier modes (Time domain sampling points)
q;.]e#wvh dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
K8Zk{on T =40; % length of time:T*T0.
6^;!9$G|D* dt = T/N; % time step
+`-a*U94 n = [-N/2:1:N/2-1]'; % Index
mNoqs&UB t = n.*dt;
->=++ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
AW5g ( w=2*pi*n./T;
b_ yXM g1=-i*ww./2;
+;;%Atgn g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
6/ipdi[
_ g3=-i*ww./2;
oE1]v X P1=0;
KTt$Pt/. P2=0;
z D<9A6AB P3=1;
Q%Q?q)x P=0;
& Q>'U6"% for m1=1:M1
yXg1N
N p=0.032*m1; %input amplitude
rJp6d :M
s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2j1v.% s1=s10;
]xEE7H]\h s20=0.*s10; %input in waveguide 2
^1=| (Z/ s30=0.*s10; %input in waveguide 3
Tj5@OcA$ s2=s20;
P1 stL, s3=s30;
4uAafQ`@H p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
!!% [JR)cS %energy in waveguide 1
IQe[ CcM p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
i0Q
_f!j %energy in waveguide 2
5KE%@,k k p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
O7'3}P; %energy in waveguide 3
2 _n*u^X:_ for m3 = 1:1:M3 % Start space evolution
Z[ u,1l .T s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Gj`Y2X2r s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
A 5<Z&Y[ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
myOX:K* sca1 = fftshift(fft(s1)); % Take Fourier transform
^jjJM| a sca2 = fftshift(fft(s2));
D*'M ^k|1 sca3 = fftshift(fft(s3));
x9A
ZS#e)[ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
O>M*mT M sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
7u5\# |yL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
zy6(S_j s3 = ifft(fftshift(sc3));
9w;J7jgOT! s2 = ifft(fftshift(sc2)); % Return to physical space
{JCz^0DV s1 = ifft(fftshift(sc1));
p6*a1^lU6 end
gzCMJ<3!D p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
"4uUI_E9F; p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
U4l*;od p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
=z1o}ga=EA P1=[P1 p1/p10];
9$V_=Bo P2=[P2 p2/p10];
uf'P9MA}> P3=[P3 p3/p10];
[j]J_S9jJ P=[P p*p];
i z>y u[ | end
y{Y+2}Dv/ figure(1)
J:Y|O-S! plot(P,P1, P,P2, P,P3);
.4re0:V \*!%YTZ~ 转自：
http://blog.163.com/opto_wang/
