计算脉冲在非线性耦合器中演化的Matlab 程序 YuZxKuGy =vv4;az
X % This Matlab script file solves the coupled nonlinear Schrodinger equations of
j5,vSh~q;' % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
!XvQm*1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
.5',w"R % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
#N=!O/Y EMDsi2 %fid=fopen('e21.dat','w');
bk**% ] N = 128; % Number of Fourier modes (Time domain sampling points)
ctv =8SFv( M1 =3000; % Total number of space steps
b|cUKsL5 J =100; % Steps between output of space
f\ wP}c' T =10; % length of time windows:T*T0
p#~Dq(Q T0=0.1; % input pulse width
|g3 a1El MN1=0; % initial value for the space output location
RN0@Q~oTI dt = T/N; % time step
JO4rU-
n n = [-N/2:1:N/2-1]'; % Index
&gn^i!%Z) t = n.*dt;
VPB,8zb ] u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
8u,f<XHi"a u20=u10.*0.0; % input to waveguide 2
!18M!8Xea u1=u10; u2=u20;
<mm. b U1 = u1;
liW0v!jBo U2 = u2; % Compute initial condition; save it in U
p? mQ\O8F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
a)+;<GZ ~ w=2*pi*n./T;
/e^q>>z g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ltKUpRE\? L=4; % length of evoluation to compare with S. Trillo's paper
X
8 V^ dz=L/M1; % space step, make sure nonlinear<0.05
q
F \a]e for m1 = 1:1:M1 % Start space evolution
9Ytf7NpR u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
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u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
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`n ca1 = fftshift(fft(u1)); % Take Fourier transform
TwlrncK* ca2 = fftshift(fft(u2));
HQ8oOn c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
(RP "VEVR c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
O<&8 gk~ u2 = ifft(fftshift(c2)); % Return to physical space
$"d< F3k u1 = ifft(fftshift(c1));
OC$Y8Ofr if rem(m1,J) == 0 % Save output every J steps.
yw|O,V<4N U1 = [U1 u1]; % put solutions in U array
<<z YF.9L] U2=[U2 u2];
a&6e~E$K2 MN1=[MN1 m1];
#S57SD z1=dz*MN1'; % output location
_H:mBk,, end
"T`Q, end
]-Z="YPY hg=abs(U1').*abs(U1'); % for data write to excel
^:.=S`,^ ha=[z1 hg]; % for data write to excel
`u%`N j t1=[0 t'];
[
7W@/qqv hh=[t1' ha']; % for data write to excel file
,k*g `OTW %dlmwrite('aa',hh,'\t'); % save data in the excel format
*C~O[:6D figure(1)
,)u\G(N waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
mHqw,28} figure(2)
oUMY?[Wp waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
sx ;7 UN 7>c0B 非线性超快脉冲耦合的数值方法的Matlab程序 IXp (Aeb 1m*fkM# 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
:G/T{87H Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@`&kn;7T 'eN cQJh A4lh`n5% D YJ F6O % This Matlab script file solves the nonlinear Schrodinger equations
c$.h]&~dN % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
g$c\(isY; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
E2 M|b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|Co ?uv
i 0ZY.~b'eu C=1;
f%Y'7~9bA M1=120, % integer for amplitude
#&JhA2]q M3=5000; % integer for length of coupler
wb@TYvDt N = 512; % Number of Fourier modes (Time domain sampling points)
f; <qGM.#| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Q`nsL)J T =40; % length of time:T*T0.
n>d@}hyv dt = T/N; % time step
oe<9CK:?> n = [-N/2:1:N/2-1]'; % Index
7^}np^[HB t = n.*dt;
26yjQ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0{0|M8 w=2*pi*n./T;
?lg
g1=-i*ww./2;
b5kw*h+/'h g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3<ikMUq& g3=-i*ww./2;
ys+ AY^/ P1=0;
O?<R.W<QI P2=0;
gO kq>i_ P3=1;
N"X;aVFs_ P=0;
p IKQx5; for m1=1:M1
gxry?': p=0.032*m1; %input amplitude
D^+#RR'#, s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
~)';[Ha s1=s10;
V=)0{7-9 s20=0.*s10; %input in waveguide 2
%d<uOCf\Q s30=0.*s10; %input in waveguide 3
l+e L:C! s2=s20;
XH_XGzBQS s3=s30;
=|)W#x9= p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~NYy@ l %energy in waveguide 1
*#O8 ^3D_c p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
>'>onAIL %energy in waveguide 2
?&Zf b p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
RrM C[2=
%energy in waveguide 3
}!tJ3G for m3 = 1:1:M3 % Start space evolution
YzTmXwuA5 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
9G 7lPK s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Gw3H1:yo s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
V2< 4~J2:9 sca1 = fftshift(fft(s1)); % Take Fourier transform
mez )G| sca2 = fftshift(fft(s2));
RQzcsO sca3 = fftshift(fft(s3));
n9.` 5BH7/ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
K)m\xzT/ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
K!|%mI8gk sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
a <-'4D/ s3 = ifft(fftshift(sc3));
>Ux5UD s2 = ifft(fftshift(sc2)); % Return to physical space
}]0f -} s1 = ifft(fftshift(sc1));
yDwG,)m 4s end
_wa1R+`_ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
y/!h.[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
%O$4da"y p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
! } u '% P1=[P1 p1/p10];
Y9h~ hD P2=[P2 p2/p10];
NXQdy g, P3=[P3 p3/p10];
qT(
3M9! P=[P p*p];
{-2 8% end
1BQB8i-, figure(1)
i3T]<&+j5 plot(P,P1, P,P2, P,P3);
^4Ta0kDn _1D'9!+ 转自：
http://blog.163.com/opto_wang/
