计算脉冲在非线性耦合器中演化的Matlab 程序 /q\_&@ *pzq.# % This Matlab script file solves the coupled nonlinear Schrodinger equations of
l_/C65 %.: % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
%m{U&
-(l@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
s,*c@1f? % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
w' 7R4 lo&# (L+2 %fid=fopen('e21.dat','w');
W</n=D<,I N = 128; % Number of Fourier modes (Time domain sampling points)
|r RG=tG_' M1 =3000; % Total number of space steps
T:asm1BC[ J =100; % Steps between output of space
\n rP$ T =10; % length of time windows:T*T0
1+y" i<3) T0=0.1; % input pulse width
IO.<q,pP!_ MN1=0; % initial value for the space output location
3b [jwCt dt = T/N; % time step
~<qt%W? n = [-N/2:1:N/2-1]'; % Index
_DPOyR2 t = n.*dt;
e yw'7 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
m:Go-tk u20=u10.*0.0; % input to waveguide 2
'_+9y5 u1=u10; u2=u20;
ts9pM~_~ U1 = u1;
O';ew)tI
U2 = u2; % Compute initial condition; save it in U
"L & k)J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
B`#h{ )[ w=2*pi*n./T;
x ;BbTBc > g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'3l$al:H^ L=4; % length of evoluation to compare with S. Trillo's paper
mZ0J!QYk dz=L/M1; % space step, make sure nonlinear<0.05
xcCl
(M]+ for m1 = 1:1:M1 % Start space evolution
T9y;OG u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
oholt/gb+0 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
q$ghLGz ca1 = fftshift(fft(u1)); % Take Fourier transform
jkrx]`A{~ ca2 = fftshift(fft(u2));
BZ+-p 5]- c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
=
Rc"^oS c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
D>T],3U(H u2 = ifft(fftshift(c2)); % Return to physical space
ySN V^+ u1 = ifft(fftshift(c1));
=)<3pG O if rem(m1,J) == 0 % Save output every J steps.
J>S3sP U1 = [U1 u1]; % put solutions in U array
&w~Xa( uu U2=[U2 u2];
=F%RLpNU4 MN1=[MN1 m1];
;\)=f6N z1=dz*MN1'; % output location
uf) Oy7FQ end
Nofu7xiDw[ end
ZKbDp~ hg=abs(U1').*abs(U1'); % for data write to excel
CVKnTEs ha=[z1 hg]; % for data write to excel
/nB'kg[h\ t1=[0 t'];
ddpl Pzm# hh=[t1' ha']; % for data write to excel file
)GB`*M[ %dlmwrite('aa',hh,'\t'); % save data in the excel format
89eq[ |G_ figure(1)
^3I'y
UsY waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
]YD(`42 x figure(2)
jD< pIHau waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
E)' 8U wgd<3 X 非线性超快脉冲耦合的数值方法的Matlab程序 cz.3|Lby x6yW:tUG5 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。
R ZcH+?7 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
b 6W#SpCF [Z }B" a>Re^GT+z z& 'f/w8 % This Matlab script file solves the nonlinear Schrodinger equations
EnCU4CU` % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
B%b_/F]e % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
# 3.)H9
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
E3\ZJjG N=ifI V c C=1;
m4**>!I M1=120, % integer for amplitude
QPg2Y<2 M3=5000; % integer for length of coupler
X= _Z(;<& N = 512; % Number of Fourier modes (Time domain sampling points)
:0Te4UE;P7 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
O3_B<Em T =40; % length of time:T*T0.
m 6so]xr dt = T/N; % time step
KR k~w] n = [-N/2:1:N/2-1]'; % Index
<?|6*2_= t = n.*dt;
D!l8l49hLu ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
STT2o= w=2*pi*n./T;
k EAhTh&g* g1=-i*ww./2;
_ g6wQdxT g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
fA
XE~ g3=-i*ww./2;
fPE ? hG<x P1=0;
Mvof%I P2=0;
iSd?N}2,I P3=1;
z> :U{!5k P=0;
c^-YcG wa for m1=1:M1
i_Ar<9a~ p=0.032*m1; %input amplitude
=J.EH| s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
<9 },M s1=s10;
wznn #j s20=0.*s10; %input in waveguide 2
F E6C6dW{ s30=0.*s10; %input in waveguide 3
R~c1)[[E s2=s20;
TzY!D *%z s3=s30;
u 9}!Gq p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
+ U5U.f% %energy in waveguide 1
3/tJDb5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
twv
lQ| %energy in waveguide 2
cs5ix"1A p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
w
a.f![ %energy in waveguide 3
(HSw% e for m3 = 1:1:M3 % Start space evolution
uHrb: X!q s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
q] ZSj J s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
W"O-L s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ohTd' +Lm sca1 = fftshift(fft(s1)); % Take Fourier transform
Z!)f* sca2 = fftshift(fft(s2));
0.(M l5&e sca3 = fftshift(fft(s3));
T{;=#rG < sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
5 ZUy: sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
vTcZ8|3 e sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
b6Xi s3 = ifft(fftshift(sc3));
& G=0 s2 = ifft(fftshift(sc2)); % Return to physical space
#fzw WP s1 = ifft(fftshift(sc1));
&:#A +4& end
u2,H ]- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
]c,l5u}A$ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
V
Q h/ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
pg5&= P1=[P1 p1/p10];
eEie?# Z/6 P2=[P2 p2/p10];
N 4 +g(" P3=[P3 p3/p10];
x!`KhTu`_A P=[P p*p];
:5<#X 8>d end
@:IL/o* figure(1)
M)tv;!eQ plot(P,P1, P,P2, P,P3);
EFv4=OWB AA_@\: w^ 转自：
http://blog.163.com/opto_wang/
