计算脉冲在非线性耦合器中演化的Matlab 程序 I4 ^}C;p0? E cW$'> ^ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
|{H-PH*Iz % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
\i$WXW ]| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
do(komP<\ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5\$ 8"/H o%\ pI% %fid=fopen('e21.dat','w');
j{u! /FD N = 128; % Number of Fourier modes (Time domain sampling points)
kKR Z79"7s M1 =3000; % Total number of space steps
- g]g J =100; % Steps between output of space
M /mUY T =10; % length of time windows:T*T0
CJu3h&Rp T0=0.1; % input pulse width
9K5[a^q|My MN1=0; % initial value for the space output location
naoH 685R4 dt = T/N; % time step
BKQI |i n = [-N/2:1:N/2-1]'; % Index
_o-D},f*e t = n.*dt;
~wsD g[ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
{Jl W1;Jc7 u20=u10.*0.0; % input to waveguide 2
79 ZBVe(} u1=u10; u2=u20;
'Nbae- p f U1 = u1;
)pA N_e" U2 = u2; % Compute initial condition; save it in U
C4~`3Mk ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
RZeU{u<O w=2*pi*n./T;
4_w+NI,; g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
;f7;U=gl, L=4; % length of evoluation to compare with S. Trillo's paper
,pz^ 8NJAI dz=L/M1; % space step, make sure nonlinear<0.05
+ B#3! for m1 = 1:1:M1 % Start space evolution
)m Uc
!TP u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
:5`BhFAd u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
A+lP]Oy0S ca1 = fftshift(fft(u1)); % Take Fourier transform
4^0L2BVcv ca2 = fftshift(fft(u2));
R1DXi c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Xbb('MoI63 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
PDnwa K u2 = ifft(fftshift(c2)); % Return to physical space
OO:^#Mvv5 u1 = ifft(fftshift(c1));
-
zQ if rem(m1,J) == 0 % Save output every J steps.
P]@m0f U1 = [U1 u1]; % put solutions in U array
'e4 ;,m U2=[U2 u2];
\e/'d~F MN1=[MN1 m1];
IP` ;hC z1=dz*MN1'; % output location
% :eep G| end
9
1r"-%(r end
Jy x6{O j hg=abs(U1').*abs(U1'); % for data write to excel
(f 0p ha=[z1 hg]; % for data write to excel
q.OkZI0n t1=[0 t'];
8h#/b1\ hh=[t1' ha']; % for data write to excel file
U'st\Dt %dlmwrite('aa',hh,'\t'); % save data in the excel format
pOn>m1| figure(1)
q=5#t~? waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
x-5X OqD{' figure(2)
&\$l%ic uo waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
/
W} Za&] K>TdN+Z}= 非线性超快脉冲耦合的数值方法的Matlab程序 9 T 4x1{mO |-hzvuSX 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。
@t 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
.ya^8gM byYdX'd. tVZj tGz= J>P{8Aw % This Matlab script file solves the nonlinear Schrodinger equations
9tVA.:FOZ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
LX e { % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K
YFumR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;wfzlUBC Z4Nl{
6 C=1;
-i@1sNx&' M1=120, % integer for amplitude
GQTMQXn( M3=5000; % integer for length of coupler
zQ$*!1FmN N = 512; % Number of Fourier modes (Time domain sampling points)
xS` %3+| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
;/W;M> ^ T =40; % length of time:T*T0.
}Lx?RU+@= dt = T/N; % time step
M`ETH8Su= n = [-N/2:1:N/2-1]'; % Index
b]s*z<|% t = n.*dt;
2B7X~t>8a ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Z@= 1-l w=2*pi*n./T;
}!\ZJo a g1=-i*ww./2;
cjU * g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Da!A1|" g3=-i*ww./2;
u0^:
XwZ! P1=0;
e uS"C* P2=0;
&,xN$ P3=1;
5Cd>p< P=0;
&inu mc for m1=1:M1
1O1/P,u+ p=0.032*m1; %input amplitude
,
e{kC s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2l#Ogn`k s1=s10;
}u&.n
pc s20=0.*s10; %input in waveguide 2
"_JGe#= s30=0.*s10; %input in waveguide 3
*M5 =PQfb s2=s20;
N. C<Mo s3=s30;
;}{%|UAsx p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
| eIN<RY5 %energy in waveguide 1
mHo}, | p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
~#dNGWwG %energy in waveguide 2
p6]4YGw*^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
<k'=_mC_ %energy in waveguide 3
5 fjeBfy for m3 = 1:1:M3 % Start space evolution
w:
~66 TCI s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
eOjoxnD-$ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
a&~d ,vC s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Z VuHO7' sca1 = fftshift(fft(s1)); % Take Fourier transform
|k:MXI sca2 = fftshift(fft(s2));
TmG$Cjf84 sca3 = fftshift(fft(s3));
}.Ht =E] sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
_e$15qW+ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
q4<3 O"c1 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
L,| 60* s3 = ifft(fftshift(sc3));
[!4p5; s2 = ifft(fftshift(sc2)); % Return to physical space
/c~z(wv s1 = ifft(fftshift(sc1));
S,m)yh . end
1`N q
K p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
dJM)~A y- p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
z iR} p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9hEIf,\ P1=[P1 p1/p10];
@Hj5ZJ
3 P2=[P2 p2/p10];
./LD P3=[P3 p3/p10];
2e zQX2q P=[P p*p];
pw*<tXH! end
TU{^/-l figure(1)
Od70w*, plot(P,P1, P,P2, P,P3);
^4_)a0Kcm, 1u7Kc'.xc 转自：
http://blog.163.com/opto_wang/
