计算脉冲在非线性耦合器中演化的Matlab 程序 XL}<1- } zG
c[Z3N % This Matlab script file solves the coupled nonlinear Schrodinger equations of
3|Y!2b(:? % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
7=*VpX1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
]wuy_+$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;S/7 h6 Jll-X\O`- %fid=fopen('e21.dat','w');
n D,{3B#
N = 128; % Number of Fourier modes (Time domain sampling points)
*,\` o~ M1 =3000; % Total number of space steps
.%0ne:5 J =100; % Steps between output of space
$rG< uO T =10; % length of time windows:T*T0
YJ2ro-X T0=0.1; % input pulse width
u:` y] MN1=0; % initial value for the space output location
\T-~JQVj dt = T/N; % time step
hGP1(pH. n = [-N/2:1:N/2-1]'; % Index
I&1!v8 t = n.*dt;
px9>:t[P u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
j:1uP^. u20=u10.*0.0; % input to waveguide 2
| D.C!/69 u1=u10; u2=u20;
n!N\zx8 U1 = u1;
Dr"/ 3xm U2 = u2; % Compute initial condition; save it in U
hPufzhT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8 HoP( +? w=2*pi*n./T;
X$wehMBX g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
MPRO
!45Z L=4; % length of evoluation to compare with S. Trillo's paper
@5}gsC dz=L/M1; % space step, make sure nonlinear<0.05
Z-|li}lDr for m1 = 1:1:M1 % Start space evolution
d A#{Cn; u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Ls: =A6AGM u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
wTpD1"_R ca1 = fftshift(fft(u1)); % Take Fourier transform
N5 q725zJ ca2 = fftshift(fft(u2));
X _70]^XL c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
,{j4 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
-W T3)On u2 = ifft(fftshift(c2)); % Return to physical space
u+% tPe u1 = ifft(fftshift(c1));
jFj~]]j if rem(m1,J) == 0 % Save output every J steps.
f:%SW U1 = [U1 u1]; % put solutions in U array
[a8+( U2=[U2 u2];
H(\V+@~>AD MN1=[MN1 m1];
]R Mb,hJ z1=dz*MN1'; % output location
wR7aQg end
;1LG&h,K end
"r-l8 r, hg=abs(U1').*abs(U1'); % for data write to excel
o?!uX|Fy ha=[z1 hg]; % for data write to excel
=FBIrw{w t1=[0 t'];
bc}dYK3$q hh=[t1' ha']; % for data write to excel file
0:dB
9 %dlmwrite('aa',hh,'\t'); % save data in the excel format
Tj,2r]g`< figure(1)
dokuyiN\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
jpO3 8H0) figure(2)
z`'P>.x
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
yzc pG6 , I>((o` 非线性超快脉冲耦合的数值方法的Matlab程序 {Nq?#%vdT 8!j=vCv 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。
&N{zkMf 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
M1uP\Sa !P" ? ~.Q4c*_b ~N[|bPRmhE % This Matlab script file solves the nonlinear Schrodinger equations
mG}k 3e - % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
z^~U]S3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
zH+<bEo=1= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]7F)bIG[ WTu{,Q C=1;
EVS K8T, M1=120, % integer for amplitude
fNEz M3=5000; % integer for length of coupler
fm6]CU1^ N = 512; % Number of Fourier modes (Time domain sampling points)
:bw 6 k dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
M,L@k T =40; % length of time:T*T0.
hgj0tIi/ dt = T/N; % time step
8D T@h8tA n = [-N/2:1:N/2-1]'; % Index
kGj]i@(PA4 t = n.*dt;
L{K*~B -p ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Y\>\[*.v w=2*pi*n./T;
5 V rcR=?O g1=-i*ww./2;
di<B ~:l58 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
) ]]|d g3=-i*ww./2;
^8\Y`Z0% P1=0;
g _x\T+= P2=0;
z9fNk% P3=1;
0hZxN2r P=0;
ws().IZ for m1=1:M1
6)+9G_ p=0.032*m1; %input amplitude
KF4see;; s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
'Ix5,^M}B s1=s10;
+cw{aI`a8 s20=0.*s10; %input in waveguide 2
;;6\q!7` s30=0.*s10; %input in waveguide 3
{"\q(R0 s2=s20;
YRu%j4Tx s3=s30;
Qasr:p+ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
aZC*7AK
%energy in waveguide 1
}9 FD/ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
aKD;1| ) %energy in waveguide 2
%g5jY%dg.r p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
%)dI2 J^Xf %energy in waveguide 3
%8g$T6E[<2 for m3 = 1:1:M3 % Start space evolution
V!}L <cN s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
_jk|}IB;X s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
)PHl>0i! s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
!~tnt i6 sca1 = fftshift(fft(s1)); % Take Fourier transform
] :GfO go sca2 = fftshift(fft(s2));
{z-Nl H
sca3 = fftshift(fft(s3));
TVj1C sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
hX %s]" sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
78^Y;2 P]W sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
3lyQn " s3 = ifft(fftshift(sc3));
w4`!Te s2 = ifft(fftshift(sc2)); % Return to physical space
Fv;u1Atiw s1 = ifft(fftshift(sc1));
_4~k3%w\`l end
H.)fO ctbO p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
a'm!M:w p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2;O c^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[gTQ- P1=[P1 p1/p10];
\v.HG]
/u P2=[P2 p2/p10];
my=*zziN P3=[P3 p3/p10];
IZ|c <#r6 P=[P p*p];
a{5H33JA end
57'q;I figure(1)
V5cb}xx plot(P,P1, P,P2, P,P3);
xqU^I5Z ?UU5hek+m 转自：
http://blog.163.com/opto_wang/
