计算脉冲在非线性耦合器中演化的Matlab 程序 2itJD1; B `` ) % This Matlab script file solves the coupled nonlinear Schrodinger equations of
(sXR@Ce$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
(4 hCT* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K!JXsdHK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
nkv+O$LXP 'T8(md299 %fid=fopen('e21.dat','w');
.+;;-]}) N = 128; % Number of Fourier modes (Time domain sampling points)
Stzv M1 =3000; % Total number of space steps
g3} K J =100; % Steps between output of space
?gp:uxq, . T =10; % length of time windows:T*T0
.ykCmznf* T0=0.1; % input pulse width
y@5{.jsr_ MN1=0; % initial value for the space output location
:{(` ;fJ dt = T/N; % time step
U]aH 4 N n = [-N/2:1:N/2-1]'; % Index
]dx6E6 A,
t = n.*dt;
baD`k?]( u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
x*Lm{c5+ u20=u10.*0.0; % input to waveguide 2
K,!"5W rX* u1=u10; u2=u20;
<vMdfw"( U1 = u1;
O% 1X[ U2 = u2; % Compute initial condition; save it in U
eQiK \iDS ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mHm"QBa! w=2*pi*n./T;
3kTOWIX g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
yX^/Oc@j L=4; % length of evoluation to compare with S. Trillo's paper
b6 @(UneVM dz=L/M1; % space step, make sure nonlinear<0.05
W[+=_B for m1 = 1:1:M1 % Start space evolution
8f\sG:$ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
#s 4v0auK u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
9`A}-YA ! ca1 = fftshift(fft(u1)); % Take Fourier transform
(1t b ca2 = fftshift(fft(u2));
d]89DdZk c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
| f :1Br c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
k>2tC< u2 = ifft(fftshift(c2)); % Return to physical space
j9V*f
HK u1 = ifft(fftshift(c1));
R-L *N$@! if rem(m1,J) == 0 % Save output every J steps.
jkzC^aG U1 = [U1 u1]; % put solutions in U array
8PR1RC J U2=[U2 u2];
s+EJXox w MN1=[MN1 m1];
:`pgdn z1=dz*MN1'; % output location
p\"WX end
Sk ~ ( t end
$.7 Ov| hg=abs(U1').*abs(U1'); % for data write to excel
O|5Z-r0< ha=[z1 hg]; % for data write to excel
i`FskEoijq t1=[0 t'];
0q@U># hh=[t1' ha']; % for data write to excel file
*dTI4k %dlmwrite('aa',hh,'\t'); % save data in the excel format
cZ<@1I5QK figure(1)
4i DlBs+ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
3 NLC~CJ figure(2)
1x"S^j
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
%, Pwo{SH k*?Axk# 非线性超快脉冲耦合的数值方法的Matlab程序 o
0-3[W'x< U2l DTRt 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
q|;Sn Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-Um|: [*I F$| Ec9 -n aj.omG| F!LVyY"w % This Matlab script file solves the nonlinear Schrodinger equations
rJ@yOed["b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
i*T>, z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
wDL dmrB % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
xE[CNJ%t^, +2ZBj6 e9 C=1;
I^CK q?V?: M1=120, % integer for amplitude
rA">< pH M3=5000; % integer for length of coupler
B. J_(V+ N = 512; % Number of Fourier modes (Time domain sampling points)
!oJ226>WI dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
v0d<P2ix T =40; % length of time:T*T0.
ZRK1 UpP dt = T/N; % time step
KMhEU** n = [-N/2:1:N/2-1]'; % Index
FL, av>mV t = n.*dt;
{<p-/| Z52 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'ot,6@~x> w=2*pi*n./T;
:k- (%E]( g1=-i*ww./2;
#S*@RKSE|7 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
voD0 u g3=-i*ww./2;
"EE=j$8u+ P1=0;
uT X0lu ; P2=0;
EYsf<8cl P3=1;
l rE| >R P=0;
h=1cD\^|qw for m1=1:M1
'&|]tu:q p=0.032*m1; %input amplitude
"F$0NYb]I s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-UhSy>m s1=s10;
No '^] r s20=0.*s10; %input in waveguide 2
a2z1/Nh s30=0.*s10; %input in waveguide 3
09r0Rb s2=s20;
SviGLv;oR s3=s30;
hPM:=@ N$ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=L UDg7P %energy in waveguide 1
dV:vM9+x p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
DaK 2P;WP %energy in waveguide 2
r
N.<S[ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Xyf7sHQ %energy in waveguide 3
W,g0n=2 V for m3 = 1:1:M3 % Start space evolution
W{{{c2 . s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
]xYm@%>6 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
N Y& |:F s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
LHS^[}x^1 sca1 = fftshift(fft(s1)); % Take Fourier transform
<f')] sca2 = fftshift(fft(s2));
5W(S ~} sca3 = fftshift(fft(s3));
WN_i-A1G/h sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
_ i-(` 5 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
E>|xv#:~DV sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
UP*\p79oO s3 = ifft(fftshift(sc3));
(16U]s s2 = ifft(fftshift(sc2)); % Return to physical space
\N?,6;%xB s1 = ifft(fftshift(sc1));
.2si[:_(p end
C8J3^ ?7E p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
W8/8V, p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
cl4Vi% p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
)(Z)yz P1=[P1 p1/p10];
Z Rjqjx P2=[P2 p2/p10];
B!#F!Wk" P3=[P3 p3/p10];
W $l%= / P=[P p*p];
Y?^1=9?6 end
ZgXn8O[a figure(1)
i l)LkZ@ plot(P,P1, P,P2, P,P3);
JLZ[sWP=' RyxEZ7dC<y 转自：
http://blog.163.com/opto_wang/
