计算脉冲在非线性耦合器中演化的Matlab 程序 y)e 8pPD G %d#h<e|,. % This Matlab script file solves the coupled nonlinear Schrodinger equations of
@is !VzE
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
R9`37(c9+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
h#7p&F % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
U^.kp# x# {gwJ>]z"e %fid=fopen('e21.dat','w');
~y.t amNW N = 128; % Number of Fourier modes (Time domain sampling points)
=7212('F M1 =3000; % Total number of space steps
&@h(6 J =100; % Steps between output of space
+ =N#6 # 1 T =10; % length of time windows:T*T0
(!B1} 5" T0=0.1; % input pulse width
)UgLs|G~ MN1=0; % initial value for the space output location
?(d<n dt = T/N; % time step
AeN$AqQd/ n = [-N/2:1:N/2-1]'; % Index
c Y(2}Ay t = n.*dt;
KJ;;825? u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
L|H:&|F u20=u10.*0.0; % input to waveguide 2
q71 ~Y:7f u1=u10; u2=u20;
2=/,9ka ~ U1 = u1;
l OuO~`,J U2 = u2; % Compute initial condition; save it in U
T z?0E"yx ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
BL^\"Xh$| w=2*pi*n./T;
-) Li L g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
`!A<XiAOmM L=4; % length of evoluation to compare with S. Trillo's paper
VW/ICX~"d dz=L/M1; % space step, make sure nonlinear<0.05
@n Oj6b for m1 = 1:1:M1 % Start space evolution
;bhD:$NB X u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
E6zSM l5b u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
7`_`V&3s ca1 = fftshift(fft(u1)); % Take Fourier transform
J70r` ca2 = fftshift(fft(u2));
o3OtG#g2 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
f5ttQ&@FF c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
GI _.[ u2 = ifft(fftshift(c2)); % Return to physical space
#l?E2
U4WL u1 = ifft(fftshift(c1));
#Li6RSeW if rem(m1,J) == 0 % Save output every J steps.
O-jpS?@ U1 = [U1 u1]; % put solutions in U array
l1I\khS U2=[U2 u2];
[;RO= MN1=[MN1 m1];
O=E?m=FR" z1=dz*MN1'; % output location
Hru~Y}V end
0Mu6R=s end
h1A Z+9 hg=abs(U1').*abs(U1'); % for data write to excel
?hh#@61
ha=[z1 hg]; % for data write to excel
x=%wP VJ t1=[0 t'];
mo( )l8 hh=[t1' ha']; % for data write to excel file
bD ADFitSo %dlmwrite('aa',hh,'\t'); % save data in the excel format
T1[B* R wC figure(1)
k(23Zt] waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
.:/[%q{k figure(2)
[wv;CUmgc waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
&cHA xker O@-|_N*;K 非线性超快脉冲耦合的数值方法的Matlab程序 k|D =Q }u?DK,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。
RHv|i jYy 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
'}BYMEd/m% rMEM$1vPU T7qE
2 ;*[ oi % This Matlab script file solves the nonlinear Schrodinger equations
K zW qHq % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
C=,O'U(ep % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
'D &[Y)f^ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ZXH{9hxd *pj ^d>< C=1;
PDN bhUAV M1=120, % integer for amplitude
s )9d\{ M3=5000; % integer for length of coupler
>\4"k4d} N = 512; % Number of Fourier modes (Time domain sampling points)
w e}G%09L dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
u%b. #! T =40; % length of time:T*T0.
ag{cm' . dt = T/N; % time step
Cr>YpWm n = [-N/2:1:N/2-1]'; % Index
SodYb t = n.*dt;
S\<nCkE^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T7# }& > w=2*pi*n./T;
y^[?F>wB g1=-i*ww./2;
o_R_ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
" rU
2g g3=-i*ww./2;
n =qu?xu P1=0;
A w"Y_S8. P2=0;
Hkzx(yTi P3=1;
>e M> Y@8= P=0;
Gph:'3
*X for m1=1:M1
`/RcE.5n\@ p=0.032*m1; %input amplitude
}!*CyO* s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
CX3yIe~u s1=s10;
d<_#Q7]I4 s20=0.*s10; %input in waveguide 2
p,K!'\ s30=0.*s10; %input in waveguide 3
W'" p:Uh q s2=s20;
UiQF4Uc" s3=s30;
m TgsvC p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
[5i }C
K_= %energy in waveguide 1
e]zd6{g[m p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Lpv,6#m`) %energy in waveguide 2
fV o7wp p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
ioJ|-@! #o %energy in waveguide 3
aW*8t'm;m' for m3 = 1:1:M3 % Start space evolution
;Z!x\{- L s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Zonr/sA ~ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
nh*hw[Ord s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
1
.Nfl@] sca1 = fftshift(fft(s1)); % Take Fourier transform
^u-;VoK sca2 = fftshift(fft(s2));
-=4{X
R3 sca3 = fftshift(fft(s3));
~djHtd> sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
m5
l,Lxj sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
.1YiNmW= sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
%4^NX@1jV s3 = ifft(fftshift(sc3));
<`")Zxf+ s2 = ifft(fftshift(sc2)); % Return to physical space
[m0G;%KR/ s1 = ifft(fftshift(sc1));
;!pSYcT, end
S1U>Q~ZPA p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
H6Q!~o\"H p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
p(fL'
J p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
ycj\5+ g P1=[P1 p1/p10];
Z3 O_K P2=[P2 p2/p10];
YckLz01jh P3=[P3 p3/p10];
kK_9I (7c P=[P p*p];
W0k7( v) end
a_(T9pr figure(1)
g). IF. plot(P,P1, P,P2, P,P3);
cceh`s=cU Ctx{rf_~ 转自：
http://blog.163.com/opto_wang/
