计算脉冲在非线性耦合器中演化的Matlab 程序 `/8@F j GJ ^c ^` % This Matlab script file solves the coupled nonlinear Schrodinger equations of
/ F0q8j0 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
idI w7hi4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+9_Y0<C % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^CkMk 1 I?e5h@u E %fid=fopen('e21.dat','w');
zHJCXTM N = 128; % Number of Fourier modes (Time domain sampling points)
+?_!8N8 M1 =3000; % Total number of space steps
G@8)3 @ J =100; % Steps between output of space
#H Un~r T =10; % length of time windows:T*T0
5ya9VZ5# T0=0.1; % input pulse width
vS gT36ZF MN1=0; % initial value for the space output location
]VI^ hhf dt = T/N; % time step
28MMH
Q n = [-N/2:1:N/2-1]'; % Index
Z
vysLHj t = n.*dt;
G Y~$<^AK u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
wI%M3XaBws u20=u10.*0.0; % input to waveguide 2
B~Sj#(WEa u1=u10; u2=u20;
cAWn*% U1 = u1;
|2(q 9j U2 = u2; % Compute initial condition; save it in U
fLDrit4_Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
oTw!#Re) w=2*pi*n./T;
v] m/$X2 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
]M?i: A$B L=4; % length of evoluation to compare with S. Trillo's paper
R N$vKJk dz=L/M1; % space step, make sure nonlinear<0.05
TGCB=e for m1 = 1:1:M1 % Start space evolution
<kn 2 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
pjeNBSu6 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
q}{E![ZTu ca1 = fftshift(fft(u1)); % Take Fourier transform
Xa q;d' ca2 = fftshift(fft(u2));
GP} ; ~ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
q
W(@p` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
QS#@xhH u2 = ifft(fftshift(c2)); % Return to physical space
T ,lM(2S[ u1 = ifft(fftshift(c1));
=2R4Z8G if rem(m1,J) == 0 % Save output every J steps.
;: ;E|{e U1 = [U1 u1]; % put solutions in U array
e5L+NPeM6v U2=[U2 u2];
&YhAB\Rw MN1=[MN1 m1];
j\y;~
V z1=dz*MN1'; % output location
8`4M4" lj end
pBsb>wvej end
3?93Pj3oPt hg=abs(U1').*abs(U1'); % for data write to excel
!<[+ u ha=[z1 hg]; % for data write to excel
'Y?-."eKh t1=[0 t'];
O a[ hh=[t1' ha']; % for data write to excel file
",#.?vT` %dlmwrite('aa',hh,'\t'); % save data in the excel format
-]N2V'QB figure(1)
h<.5:a waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ptCF))Zm' figure(2)
"{0G,tdA waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
#C S>_qe.{ M 8},RR@{ 非线性超快脉冲耦合的数值方法的Matlab程序 k8gH#ENNK O
NabL.CV 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。
qGinlE&\ 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
&Vl no* EC+t-:a] OSu&vFKz z/7q#~J, % This Matlab script file solves the nonlinear Schrodinger equations
bt}8ymcG % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
so-5% S % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+=tdgw/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
DUOoTl p sW>%mnx C=1;
-&/?&{Q0 M1=120, % integer for amplitude
C ,| & M3=5000; % integer for length of coupler
+){^HC\7h N = 512; % Number of Fourier modes (Time domain sampling points)
JE.$]){ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
P {Nvt/% T =40; % length of time:T*T0.
K?.~}82c dt = T/N; % time step
vs@d) $N n = [-N/2:1:N/2-1]'; % Index
bZowc {!\ t = n.*dt;
!I7$e& Uz@ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
wE
.H:q4& w=2*pi*n./T;
h:Pfiw] g1=-i*ww./2;
F^d J{<yX g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
+t!] nE # g3=-i*ww./2;
y0%@^^-Ru P1=0;
d4y#n=HnnV P2=0;
:H}iL* P3=1;
j0l,1=^>l P=0;
xm m,- u for m1=1:M1
/~LE1^1&U p=0.032*m1; %input amplitude
ing'' _ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2Kxb(q" s1=s10;
91R# /i s20=0.*s10; %input in waveguide 2
a %#UF@ I s30=0.*s10; %input in waveguide 3
is;g`m s2=s20;
*byUqY3( s3=s30;
<\229 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
J( 1Tl %energy in waveguide 1
i eyK$q p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
N&8$tJ(hhx %energy in waveguide 2
196a YL E p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
9< mM U: %energy in waveguide 3
Ym'h
vK for m3 = 1:1:M3 % Start space evolution
>.<VD7p s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
_c>iux; s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
1W|jC s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Zkp~qx sca1 = fftshift(fft(s1)); % Take Fourier transform
E '6>3n sca2 = fftshift(fft(s2));
Nl\`xl6y] sca3 = fftshift(fft(s3));
{B$CqsvJ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
OVLVsNg sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4"&-a 1N sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
'm<Lx _i s3 = ifft(fftshift(sc3));
7?dWAUF s2 = ifft(fftshift(sc2)); % Return to physical space
k*1Lr\1 s1 = ifft(fftshift(sc1));
#|9W9\f, end
BJ
UG<k p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
lZk
z \ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3kxo1eb
p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Ip8ml0oG P1=[P1 p1/p10];
LO U P P2=[P2 p2/p10];
l7QxngWw P3=[P3 p3/p10];
juEPUsE P=[P p*p];
4 \z@Evm end
':.Hz]]/A figure(1)
J v} plot(P,P1, P,P2, P,P3);
[8QK @5[ hjL;B 'IL 转自：
http://blog.163.com/opto_wang/
