计算脉冲在非线性耦合器中演化的Matlab 程序 XhjH68S( 7<DlA>(oUX % This Matlab script file solves the coupled nonlinear Schrodinger equations of
h-<2N)>! % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
M \rW % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
'Y{ fah % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
HM ;9%rtO ).e_iE[& %fid=fopen('e21.dat','w');
'H- : >'k N = 128; % Number of Fourier modes (Time domain sampling points)
6tBL?'pG M1 =3000; % Total number of space steps
5SKj% %B2, J =100; % Steps between output of space
)e`$' y@L$ T =10; % length of time windows:T*T0
(<!Yw|~ T0=0.1; % input pulse width
:G\f(2@ MN1=0; % initial value for the space output location
[" VUSa dt = T/N; % time step
B* #lkMr
n = [-N/2:1:N/2-1]'; % Index
uc4#giCD t = n.*dt;
WVl yR\. u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
zX{K\yp u20=u10.*0.0; % input to waveguide 2
dq[X:3i u1=u10; u2=u20;
ousvsP%' U1 = u1;
,;9byb U2 = u2; % Compute initial condition; save it in U
~ {OBRC ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
FY h+G-Y# w=2*pi*n./T;
mb_*FJB-_ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
QyN<o{\FD! L=4; % length of evoluation to compare with S. Trillo's paper
9M{z@H/ dz=L/M1; % space step, make sure nonlinear<0.05
]G m"U!h* for m1 = 1:1:M1 % Start space evolution
H.#<&5f u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
eCHT) 35u u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
g9~>m JR ca1 = fftshift(fft(u1)); % Take Fourier transform
(F9U`1~4 ca2 = fftshift(fft(u2));
w3oh8NRs_ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&'
E( c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
YJi C}.4 Q u2 = ifft(fftshift(c2)); % Return to physical space
<RQ\nU u1 = ifft(fftshift(c1));
Fy_D[g if rem(m1,J) == 0 % Save output every J steps.
J_) .H d U1 = [U1 u1]; % put solutions in U array
CYD&#+o U2=[U2 u2];
ha_ &U@w MN1=[MN1 m1];
ZdQt! z1=dz*MN1'; % output location
CtiTXDc_ end
. AJ(nJ) end
6S*L[zBnA\ hg=abs(U1').*abs(U1'); % for data write to excel
;#a^M*e ha=[z1 hg]; % for data write to excel
zi M~V' t1=[0 t'];
Hxe!68{aR hh=[t1' ha']; % for data write to excel file
Bg.~#H %dlmwrite('aa',hh,'\t'); % save data in the excel format
{akS K figure(1)
>S\D+1PV waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
_Ec9g^I10 figure(2)
V?x&.C2Z waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ft$@':F CHxu%- g 非线性超快脉冲耦合的数值方法的Matlab程序 mOm_a9M L AG ?cI@', 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
7mG/f Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
x,)|;HXm 3^ NHV g 53> y< P_Rh& gkuK % This Matlab script file solves the nonlinear Schrodinger equations
yb{ud % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
k0[b4cr` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
y>4r<Y ZQ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`r?xo7 NrQGoAOw C=1;
E8$k}I M1=120, % integer for amplitude
"N'|N., M3=5000; % integer for length of coupler
O"%b@$p\L N = 512; % Number of Fourier modes (Time domain sampling points)
. ;),e# dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2/[J<c\G T =40; % length of time:T*T0.
hsYS<] dt = T/N; % time step
/K!&4mK n = [-N/2:1:N/2-1]'; % Index
of? hP1kl[ t = n.*dt;
s#phs `v ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
6k569c{7 w=2*pi*n./T;
-B+ Pl* g1=-i*ww./2;
\53(D7 + g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
=v-qao7xCV g3=-i*ww./2;
^g^R[8 P1=0;
&~9'7 n! P2=0;
zn!H&!8& P3=1;
.K
I6<k/ P=0;
'E_M , Y for m1=1:M1
dXwfOC\\ p=0.032*m1; %input amplitude
VTM*=5|c s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
gXrXVv<)yw s1=s10;
kBF.TGT[l s20=0.*s10; %input in waveguide 2
"$@>n(w s30=0.*s10; %input in waveguide 3
e u{ s2=s20;
V]4g-
CS[ s3=s30;
{0~ Sj% Ze p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
j.}@ 9 %energy in waveguide 1
p]z< 43O$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
)(^L * %energy in waveguide 2
m I$< +S1! p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
b-'T>1V %energy in waveguide 3
c)L1@ qdZ for m3 = 1:1:M3 % Start space evolution
nw.,` M,N s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
yf
7Sz$Eq s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
45?aV@ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
hU:
9zLe sca1 = fftshift(fft(s1)); % Take Fourier transform
h\]D:S sca2 = fftshift(fft(s2));
$ 9~6M* sca3 = fftshift(fft(s3));
"`va_Mk sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
l*l?aI sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
F},#%_4 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
*!mT#Vm^ s3 = ifft(fftshift(sc3));
n:TW Z.9 s2 = ifft(fftshift(sc2)); % Return to physical space
A(j9T, ! s1 = ifft(fftshift(sc1));
*F4"mr|\ end
O1C| {
M p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Y! 8 I p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Npr<{}ZE p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
s2IjZF { P1=[P1 p1/p10];
seNJ 6p=` P2=[P2 p2/p10];
ET2 ^1X#j P3=[P3 p3/p10];
LtJl \m.th P=[P p*p];
`<cn b!] end
Un~
}M/ figure(1)
!@.9> "FU plot(P,P1, P,P2, P,P3);
cPx] :sC G8sxg&bf{ 转自：
http://blog.163.com/opto_wang/
