计算脉冲在非线性耦合器中演化的Matlab 程序 nlebFDb 7 sK%Hx` % This Matlab script file solves the coupled nonlinear Schrodinger equations of
[x<6v}fRn % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
AMD?LjY~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
r%,H*DOu % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"c/s/$k// +e8>?dkq %fid=fopen('e21.dat','w');
d[]p_oIQq N = 128; % Number of Fourier modes (Time domain sampling points)
fE w=I7{Y M1 =3000; % Total number of space steps
H[7cA9FI J =100; % Steps between output of space
4iv]N 4 T =10; % length of time windows:T*T0
|^PLZ> T0=0.1; % input pulse width
<@e+-$ MN1=0; % initial value for the space output location
jfY{z=*]u dt = T/N; % time step
k<Tez{< n = [-N/2:1:N/2-1]'; % Index
J/x@$' t = n.*dt;
HD:%Yv u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+|?|8"Qg u20=u10.*0.0; % input to waveguide 2
r[v-?W' u1=u10; u2=u20;
%]<RRH.w U1 = u1;
5{ FM#@ U2 = u2; % Compute initial condition; save it in U
uPFHlT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
.b#9q6F-/ w=2*pi*n./T;
PNJe&q0* g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
&=-e`=qJ'6 L=4; % length of evoluation to compare with S. Trillo's paper
$,;S\JmWP dz=L/M1; % space step, make sure nonlinear<0.05
\|~?x#aA for m1 = 1:1:M1 % Start space evolution
T")i+v u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
< 4Q1 2: u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
lkg "'p{ ca1 = fftshift(fft(u1)); % Take Fourier transform
fi&uB9hc ca2 = fftshift(fft(u2));
TmYP_5g: c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
7V=MRf&xQ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Xn/ n|[ u2 = ifft(fftshift(c2)); % Return to physical space
\o B' u1 = ifft(fftshift(c1));
g %\$ !b if rem(m1,J) == 0 % Save output every J steps.
*"5N>F[L U1 = [U1 u1]; % put solutions in U array
f]ue#O U2=[U2 u2];
skI(]BDf MN1=[MN1 m1];
5c]}G.NV z1=dz*MN1'; % output location
3ximNQ} S end
Q54r?|'V end
?Q96,T-)
c hg=abs(U1').*abs(U1'); % for data write to excel
(LRM~ 5KVg ha=[z1 hg]; % for data write to excel
CZyz;Jtk t1=[0 t'];
^Ti_<<X hh=[t1' ha']; % for data write to excel file
P{S\pWZkk %dlmwrite('aa',hh,'\t'); % save data in the excel format
_~;&)cn,0 figure(1)
2$
|]Vj*Zs waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
j2 } figure(2)
zJ ;>.0 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
E.J 0fwyT !/ j,hO4Z4 非线性超快脉冲耦合的数值方法的Matlab程序 }!%JYG^!D bo@,4xw 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。
:K~rvv\L7 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
3`A>j" p^1zIC>F q^ a|wTC F$Im9T6 % This Matlab script file solves the nonlinear Schrodinger equations
qKdS7SoS % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
+VCo$o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
, 3X: ) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
M18qa,fK{ NunV8atn: C=1;
>Mvka;T] M1=120, % integer for amplitude
<4bz/^ M3=5000; % integer for length of coupler
qoj^ _s6 N = 512; % Number of Fourier modes (Time domain sampling points)
EntF@ln! dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
:dP~.ZY7 T =40; % length of time:T*T0.
e~{^oM dt = T/N; % time step
B%tIwUE2 n = [-N/2:1:N/2-1]'; % Index
{L @+(I t = n.*dt;
'>j<yaD' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7} b e>( w=2*pi*n./T;
Rj[ hhSx 2 g1=-i*ww./2;
2_;] g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
hv* >%p g3=-i*ww./2;
6HoqEku/Q P1=0;
EM=w?T P2=0;
~U6" ? P3=1;
CjZZm^O P=0;
n*Q`g@` for m1=1:M1
P|e`^Frxt p=0.032*m1; %input amplitude
OJAx:& ]3 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
CI`N8
f=v s1=s10;
5Go0}'*% s20=0.*s10; %input in waveguide 2
#HeM,;Xp s30=0.*s10; %input in waveguide 3
!;%y$$gxh s2=s20;
kG/X"6p Z s3=s30;
b'i'GJBQ+$ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
dUS ZNY %energy in waveguide 1
aG%kmS&fv p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
pb#mg^8 %energy in waveguide 2
7K&}C;+ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
LP:nba : %energy in waveguide 3
No)
m/17y for m3 = 1:1:M3 % Start space evolution
n H@(Y&S s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
>1 @Ltvm s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
C.~ j'5N s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
x?"#gK`3; sca1 = fftshift(fft(s1)); % Take Fourier transform
e}A&V + sca2 = fftshift(fft(s2));
mwh{ "FL( sca3 = fftshift(fft(s3));
f/} sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Wta] BX sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Cq>6rn sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
fXO_ g s3 = ifft(fftshift(sc3));
z 8HsYf(! s2 = ifft(fftshift(sc2)); % Return to physical space
V<8 K@/n@ s1 = ifft(fftshift(sc1));
Vtb1[cnna end
y4@gGC= p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
8eluO ?p p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
=m7H)z)i*J p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
B5ea(j P1=[P1 p1/p10];
$X \va?( P2=[P2 p2/p10];
]H ~Y7\N-v P3=[P3 p3/p10];
ju|]Qlek P=[P p*p];
W|MWXs5'1* end
m@jge)O&D figure(1)
whye)w plot(P,P1, P,P2, P,P3);
s)zJT vE%s, E, 转自：
http://blog.163.com/opto_wang/
