计算脉冲在非线性耦合器中演化的Matlab 程序 N "Mw1R4 lk`, s % This Matlab script file solves the coupled nonlinear Schrodinger equations of
nr>Os@\BU % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
9W +RUh^W % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
[Z$ E^QAP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
l0G sY.~, AttS?TZr %fid=fopen('e21.dat','w');
"GY/2; N = 128; % Number of Fourier modes (Time domain sampling points)
WO<a^g
{ M1 =3000; % Total number of space steps
B>Xfs ZS J =100; % Steps between output of space
q{E44
eQ7F T =10; % length of time windows:T*T0
G iGXV @dq T0=0.1; % input pulse width
RI</T3%~ MN1=0; % initial value for the space output location
(// f"c]/ dt = T/N; % time step
\;F_QV n = [-N/2:1:N/2-1]'; % Index
/lqVMlz\77 t = n.*dt;
O[RivHCY u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@M_p3[c\ u20=u10.*0.0; % input to waveguide 2
DSX.84 u1=u10; u2=u20;
OD~B2MpM> U1 = u1;
e_Un:r@) U2 = u2; % Compute initial condition; save it in U
m2h@* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
6tKCY(#oO+ w=2*pi*n./T;
<yw(7 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
MeMSF8zS Q L=4; % length of evoluation to compare with S. Trillo's paper
io^ L [ dz=L/M1; % space step, make sure nonlinear<0.05
{ M& Vh] for m1 = 1:1:M1 % Start space evolution
0<'Q;'2* L u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
fq,LXQ#G u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
.{ +Ob i ca1 = fftshift(fft(u1)); % Take Fourier transform
;I@@PUnR ca2 = fftshift(fft(u2));
~+OAAkJ9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
?Q #yf8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
[ :*Jn} u2 = ifft(fftshift(c2)); % Return to physical space
eemw
I u1 = ifft(fftshift(c1));
f9FEH7S68 if rem(m1,J) == 0 % Save output every J steps.
bxR6@ U1 = [U1 u1]; % put solutions in U array
JT(6Uf U2=[U2 u2];
Z36C7 kw MN1=[MN1 m1];
.m/$ku{/J z1=dz*MN1'; % output location
|'ML
)`c[ end
5N.-m;s end
SNl% ?j|
f hg=abs(U1').*abs(U1'); % for data write to excel
HJ ^SqSm ha=[z1 hg]; % for data write to excel
TP R$oO2 t1=[0 t'];
P|' eM% hh=[t1' ha']; % for data write to excel file
eF=cMC %dlmwrite('aa',hh,'\t'); % save data in the excel format
u zgQ_ figure(1)
OJ!=xTU%h waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
+$y%H figure(2)
BWG*UjP
M waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
qGVf! R %!X9>i> 非线性超快脉冲耦合的数值方法的Matlab程序 X" m0|| 97 eEqI$# 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。
0tb%h[%,M 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
QMAineO Lfsq tQ=J` B3C%**~:e RM|2PG1m % This Matlab script file solves the nonlinear Schrodinger equations
P#o"T4 > % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
ewrs
D'? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ta+MH, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
F :p9y_W %pG^8Q()
C=1;
0s'h2={iI M1=120, % integer for amplitude
`G0GWh)`x M3=5000; % integer for length of coupler
68 \73L = N = 512; % Number of Fourier modes (Time domain sampling points)
8Z[YcLy"({ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
[ @;q#.}Z T =40; % length of time:T*T0.
l.nd Wv dt = T/N; % time step
{ i#z <ttu n = [-N/2:1:N/2-1]'; % Index
hteAuz4H t = n.*dt;
!!:mjq<0 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
J1UG}, -h w=2*pi*n./T;
3LW_qX g1=-i*ww./2;
+, |aIF g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
>h3m/aeNC g3=-i*ww./2;
)sZJH9[K P1=0;
w Sd|-e P2=0;
A2 9R5 P3=1;
SPN5H;{[]K P=0;
[L ?^+p> for m1=1:M1
;lP/hG;` p=0.032*m1; %input amplitude
A~) # s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
h"3 Mj*s s1=s10;
sD ,=_q@ s20=0.*s10; %input in waveguide 2
RIdh],- s30=0.*s10; %input in waveguide 3
s~'"& 0Gz s2=s20;
4^(aG7 s3=s30;
FKBI.}A?!' p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
VS jt|F)t %energy in waveguide 1
f"R S,] p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
H ]z83:Z %energy in waveguide 2
O;lGh1. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
[jEZ5]% %energy in waveguide 3
cNl NJ for m3 = 1:1:M3 % Start space evolution
Us2I eR s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
K;Fs5|gFU s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
4&kC8
[ r s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
c:I %jm sca1 = fftshift(fft(s1)); % Take Fourier transform
38#Zlc f sca2 = fftshift(fft(s2));
u *=8s5Q[ sca3 = fftshift(fft(s3));
H! P$p-*. sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
_)kTlX:, sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
!9t,#?! sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
^_gH}~l+U s3 = ifft(fftshift(sc3));
XY^]nm-{I s2 = ifft(fftshift(sc2)); % Return to physical space
.]w=+~ h s1 = ifft(fftshift(sc1));
.+(R,SvN%< end
^D8~s; ? p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
'\M]$`Et p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
alH6~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
?[< #>,W P1=[P1 p1/p10];
cDIZkni= P2=[P2 p2/p10];
FD al;T
P3=[P3 p3/p10];
+Ly@5y" P=[P p*p];
G e7Uety end
WZM figure(1)
tj4/x7 ! plot(P,P1, P,P2, P,P3);
HtV 8=.^ |*$0~ mA 转自：
http://blog.163.com/opto_wang/
