计算脉冲在非线性耦合器中演化的Matlab 程序 *s/F4?* ClEtw % This Matlab script file solves the coupled nonlinear Schrodinger equations of
HH]LvK % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
1, /oS&?E % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@U9ov >E % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[[)HPHSQ % @IR7v~ %fid=fopen('e21.dat','w');
+yYz ;, \ N = 128; % Number of Fourier modes (Time domain sampling points)
l^SKd M1 =3000; % Total number of space steps
cL}g7D J =100; % Steps between output of space
s*Fmu7o43 T =10; % length of time windows:T*T0
rj6wKf z T0=0.1; % input pulse width
"{&!fD~w MN1=0; % initial value for the space output location
dtnAMa5$T dt = T/N; % time step
APF-*/K? n = [-N/2:1:N/2-1]'; % Index
-PX {W)Aw t = n.*dt;
ruA!+@or u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
!W6] + u20=u10.*0.0; % input to waveguide 2
>Rr]e`3wG u1=u10; u2=u20;
NTn-4 iJy U1 = u1;
a~{mRh U2 = u2; % Compute initial condition; save it in U
e06r5%|.% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8
/\rmf\ w=2*pi*n./T;
rSa 3u*xB g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
JU~l L=4; % length of evoluation to compare with S. Trillo's paper
:_vf1>[ dz=L/M1; % space step, make sure nonlinear<0.05
z7GLpTa for m1 = 1:1:M1 % Start space evolution
7wZKK0;T u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
z,^baU u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
a|OX 4 ca1 = fftshift(fft(u1)); % Take Fourier transform
YUc&X ^O ca2 = fftshift(fft(u2));
x&kF ;UC c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
p(
z.[ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
0uj3kr? cv u2 = ifft(fftshift(c2)); % Return to physical space
b>o38( u1 = ifft(fftshift(c1));
yJ?4B?p( if rem(m1,J) == 0 % Save output every J steps.
v_b%2;<1 U1 = [U1 u1]; % put solutions in U array
R@ihN?k U2=[U2 u2];
RCsd MN1=[MN1 m1];
a*o =,! z1=dz*MN1'; % output location
QupCr/Hs end
$L3UDX+F end
G"C'/ hg=abs(U1').*abs(U1'); % for data write to excel
&L;0% ha=[z1 hg]; % for data write to excel
-l^ u1z t1=[0 t'];
k3u3X~u hh=[t1' ha']; % for data write to excel file
qi$6y? %dlmwrite('aa',hh,'\t'); % save data in the excel format
Qxt ,@<IK figure(1)
N 0`)WLW waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
U t0oh figure(2)
pWe KN` waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
[ibnI2I]` g
}5lGz4 非线性超快脉冲耦合的数值方法的Matlab程序 2 x t
8F {&m^*YN/ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
`vUilh ^c Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Z?dz@d%C JH5ckgdZ r IY_1 )88z=5. % This Matlab script file solves the nonlinear Schrodinger equations
eR =P % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
}ob#LC, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
<Kn l6$B % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=M>pL+# l(*`,-pv: C=1;
6"z:s-V M1=120, % integer for amplitude
[>v.#:YM^ M3=5000; % integer for length of coupler
vDqmD{%4N N = 512; % Number of Fourier modes (Time domain sampling points)
l7n c8K dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0]fzjiaGt T =40; % length of time:T*T0.
oBpHmMzA dt = T/N; % time step
pFx7U RZA n = [-N/2:1:N/2-1]'; % Index
G
D$o |l]\ t = n.*dt;
3O y?_a$ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
x} {/) ?vC w=2*pi*n./T;
Jzo|$ W g1=-i*ww./2;
X6kCYTJYF g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
VMZ\9IwI g3=-i*ww./2;
( hp 52Vse P1=0;
JN,4#, P2=0;
2h%/exeS; P3=1;
"@#^/m) P=0;
7'LKyy
!"3 for m1=1:M1
">@]{e* p=0.032*m1; %input amplitude
i^f*Em1 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
k+t?EZ6L s1=s10;
W9+H /T7! s20=0.*s10; %input in waveguide 2
p
D-k<8| s30=0.*s10; %input in waveguide 3
j
Jt"= s2=s20;
3MH9%*w'0 s3=s30;
EyO=M~nsS p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
b bCH(fYbu %energy in waveguide 1
*eK\W00 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
>k }ea5+ %energy in waveguide 2
%-1-y]R| p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
^ ~' &K e %energy in waveguide 3
P{-j ^'y for m3 = 1:1:M3 % Start space evolution
Tr* 3:J } s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
C-u'Me)H s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6V-u<FJ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
mSdByT+dG sca1 = fftshift(fft(s1)); % Take Fourier transform
>"5 f B sca2 = fftshift(fft(s2));
)31{.c/ sca3 = fftshift(fft(s3));
nvY%{Zf$} sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
;UUpkOQO( sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
lY
- 2 e> sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Td(eNe_4 T s3 = ifft(fftshift(sc3));
Vq-W|<7C= s2 = ifft(fftshift(sc2)); % Return to physical space
Di) % vU s1 = ifft(fftshift(sc1));
1 etl:gcEC end
u a%@Ay1| p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
[J{\Ke0<e1 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
&YpViC4K. p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
!>RDHu2n P1=[P1 p1/p10];
Is&0h| P2=[P2 p2/p10];
QiKci%=SX P3=[P3 p3/p10];
pW5ch"HE P=[P p*p];
A S5' j end
n#$sLXVy figure(1)
h @AKfE!\~ plot(P,P1, P,P2, P,P3);
; YN`E zbY2gq@? 转自：
http://blog.163.com/opto_wang/
