计算脉冲在非线性耦合器中演化的Matlab 程序 }U7 ><I 1rhQ{6 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
GvT'v0&+ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
c- ^\YSDMN % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
uCpk1d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Z(- @8=0 m/W)IG> %fid=fopen('e21.dat','w');
4*9: N = 128; % Number of Fourier modes (Time domain sampling points)
u-E* _% y M1 =3000; % Total number of space steps
b 7bbrR8 J =100; % Steps between output of space
ws$!-t4<( T =10; % length of time windows:T*T0
v Zpt}u T0=0.1; % input pulse width
4]]1J L(Ka MN1=0; % initial value for the space output location
"5R8Zl+ dt = T/N; % time step
O
WVa&8O n = [-N/2:1:N/2-1]'; % Index
/8w
_jjW t = n.*dt;
U GJ#
"9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
.pQ4# AJ u20=u10.*0.0; % input to waveguide 2
& U8W(NxN u1=u10; u2=u20;
-kd_gbnr3 U1 = u1;
`$D2 w| U2 = u2; % Compute initial condition; save it in U
p V^hZ. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
S_B;m1 w=2*pi*n./T;
C vtG g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Yj^ n4G(h L=4; % length of evoluation to compare with S. Trillo's paper
n.$wW
= dz=L/M1; % space step, make sure nonlinear<0.05
9L'R;H?L for m1 = 1:1:M1 % Start space evolution
wA<#E6^ vG u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
kiFTx
&gf u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
0UvN ws ca1 = fftshift(fft(u1)); % Take Fourier transform
64OgE! ca2 = fftshift(fft(u2));
v='h c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
e&(Di,%: c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
[/ E_v gZ u2 = ifft(fftshift(c2)); % Return to physical space
)5U&^tJ u1 = ifft(fftshift(c1));
- \!"Kz/ if rem(m1,J) == 0 % Save output every J steps.
TY3WP$u U1 = [U1 u1]; % put solutions in U array
Td5;bg6Qy U2=[U2 u2];
&dkj T8L$ MN1=[MN1 m1];
~cSOni` z1=dz*MN1'; % output location
5M2G ;o end
r}y]B\/ end
u;Q'xuo3 hg=abs(U1').*abs(U1'); % for data write to excel
Py[Z9KLX ha=[z1 hg]; % for data write to excel
wV;qc3 t1=[0 t'];
Y|=/*?o} hh=[t1' ha']; % for data write to excel file
5/v@VUzH %dlmwrite('aa',hh,'\t'); % save data in the excel format
`\: 9 2+ figure(1)
h @"dpmpe waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
MKYXYR figure(2)
p`3pRrER waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Fss7xP' r~uWr'}a} 非线性超快脉冲耦合的数值方法的Matlab程序 Q2)z1'Wv d aIt `} s 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。
joh=0 nk;D 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
nJ `JF5tI sSC yjS'T H|H!VPof] eM*@zo<- % This Matlab script file solves the nonlinear Schrodinger equations
PYl(~Vac % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
[e+"G <> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
VGY#ph% % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Y
zXL8 N6Fj} m&E C=1;
2!/_Xh M1=120, % integer for amplitude
J}qk:xGL M3=5000; % integer for length of coupler
+1 H.5| N = 512; % Number of Fourier modes (Time domain sampling points)
\ qc 8;"@ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2bS)|#v<_t T =40; % length of time:T*T0.
\$2E dt = T/N; % time step
n_%JXm#\ n = [-N/2:1:N/2-1]'; % Index
L\8 tqy. t = n.*dt;
iXc-_V6 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
vIrLG1E K w=2*pi*n./T;
1\q2;5 g1=-i*ww./2;
\Clz#k8l1 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Lnnl++8Y g3=-i*ww./2;
Cyxt EzPp P1=0;
O&=?,zLO[ P2=0;
t+k"$zR P3=1;
+.Kmpw4 P=0;
+pJ;}+ for m1=1:M1
g83!il\ p=0.032*m1; %input amplitude
(u-i{< s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
e*e}X&|(g s1=s10;
MPMJkL$F^ s20=0.*s10; %input in waveguide 2
<L@0w8i` s30=0.*s10; %input in waveguide 3
>A|6 kzC s2=s20;
8@|_];9#. s3=s30;
. \ *Z: p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
4`G":nE?We %energy in waveguide 1
lcij}-z:%e p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
'+NmHu:q %energy in waveguide 2
+I#5? p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
e
=Vu; %energy in waveguide 3
G6xdGUM for m3 = 1:1:M3 % Start space evolution
J4h 7]
qt s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
ho2o/>Ef3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
8w~I(2S:# s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
!}^c.<38Q sca1 = fftshift(fft(s1)); % Take Fourier transform
} `4o + sca2 = fftshift(fft(s2));
%-|Po:6 sca3 = fftshift(fft(s3));
0 ]U
;5 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
_d&zH lc_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Gd`qZqx# sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
A5tY4?| s3 = ifft(fftshift(sc3));
Deq~" s2 = ifft(fftshift(sc2)); % Return to physical space
{j[[E/8N!y s1 = ifft(fftshift(sc1));
gk~.u end
vV-ATIf
^ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
& F[/@ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Y4}!9x p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
I@a7AuOw P1=[P1 p1/p10];
f3s0.G#l P2=[P2 p2/p10];
|cJyP9}n P3=[P3 p3/p10];
C<2vuZD P=[P p*p];
cu]2`DF end
g1 L$+xD^ figure(1)
%xf6 U>T plot(P,P1, P,P2, P,P3);
XRKL;|cd s2iR }< 转自：
http://blog.163.com/opto_wang/
