计算脉冲在非线性耦合器中演化的Matlab 程序 %z(nZ%,Z XCGJ~ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
i5>]$j1/ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
AC$:.KLI % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@@,l0/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]0VjVU- a/Cd;T 2 %fid=fopen('e21.dat','w');
l Jfn3 N = 128; % Number of Fourier modes (Time domain sampling points)
/ GK1}h M1 =3000; % Total number of space steps
5 ,0fL J =100; % Steps between output of space
Z>) (yi9+ T =10; % length of time windows:T*T0
Hvn{aLa. T0=0.1; % input pulse width
b`@aiXN)+ MN1=0; % initial value for the space output location
>&| C
E 2' dt = T/N; % time step
O; u&>BMk n = [-N/2:1:N/2-1]'; % Index
q& h&GZ t = n.*dt;
rI\G&OqpP u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
o2FQ/EIE u20=u10.*0.0; % input to waveguide 2
s /,wyxKd u1=u10; u2=u20;
R).?lnS 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
N {}XHA for m1 = 1:1:M1 % Start space evolution
`g2DN#q[0 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
#PzRhanX u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
e B`7C"Z ca1 = fftshift(fft(u1)); % Take Fourier transform
ohFUy}y ca2 = fftshift(fft(u2));
A8? uCkG c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
CH6^ ;. c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
pq 4/>WzE u2 = ifft(fftshift(c2)); % Return to physical space
Pa .D+ u1 = ifft(fftshift(c1));
vjy 5 9m if rem(m1,J) == 0 % Save output every J steps.
+ht -Bl U1 = [U1 u1]; % put solutions in U array
wzr3 y}fCe U2=[U2 u2];
jt?937{ MN1=[MN1 m1];
s3+ ^q z1=dz*MN1'; % output location
,4 bqjkX5q end
qRXb 9c end
6]=$c<. & hg=abs(U1').*abs(U1'); % for data write to excel
a=<l}`* ha=[z1 hg]; % for data write to excel
SjT8 eH # t1=[0 t'];
& {): x hh=[t1' ha']; % for data write to excel file
-lKk.Y.}r %dlmwrite('aa',hh,'\t'); % save data in the excel format
WUQlAsme figure(1)
9 sQ 4
$ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
- J 9K figure(2)
PVGvj c 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 vJ__jO"Sq R<}n?f\#JZ 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。
<P)vx 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
0B0Uay'd_ ]]
R*sd* 50 :gk*h y p`@7hf|hm % This Matlab script file solves the nonlinear Schrodinger equations
yF &"'L % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
A.a UWh % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K5O8G % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$"z|^ze :wn9bCom?M C=1;
:Ogt{t M1=120, % integer for amplitude
VKW9R n9Qg M3=5000; % integer for length of coupler
={[ s)G N = 512; % Number of Fourier modes (Time domain sampling points)
eyq8wQT dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
ou;E@`h;x T =40; % length of time:T*T0.
UADD 7d dt = T/N; % time step
%F'*0< n = [-N/2:1:N/2-1]'; % Index
D$W&6' t = n.*dt;
=-XI)JV# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#7!P3j w=2*pi*n./T;
}@
Nurs)%_ g1=-i*ww./2;
Tw|cg B g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
T %
g3=-i*ww./2;
{H
FF|Dx P1=0;
8lAs~c P2=0;
KkVFY+/) P3=1;
g4(vgW OW` P=0;
\ W3\P= for m1=1:M1
>s yQDB p=0.032*m1; %input amplitude
4l0ON>W( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
^oNk}:> s1=s10;
[42vO s20=0.*s10; %input in waveguide 2
@D<q=:k s30=0.*s10; %input in waveguide 3
R5i v]8X4W s2=s20;
's.%rre% s3=s30;
iNn]~L1 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
1&S34wJF %energy in waveguide 1
<ob+Ano$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
os| Y=a %energy in waveguide 2
6#egy|("nF p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
)<w`E{q %energy in waveguide 3
Nqih LUv for m3 = 1:1:M3 % Start space evolution
RP}.E i s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
$i s|B9 B s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
739J] M s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ig
Mm.1> sca1 = fftshift(fft(s1)); % Take Fourier transform
8V c g30_+ sca2 = fftshift(fft(s2));
rQ0V3x1"Qx sca3 = fftshift(fft(s3));
;J"b% ~Gn sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
*82f {t] sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
"c[ D 0{\{ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
i
*W9 4 s3 = ifft(fftshift(sc3));
m'|{AjH
z6 s2 = ifft(fftshift(sc2)); % Return to physical space
9mdp \A s1 = ifft(fftshift(sc1));
kHj|:,'sV end
Z)RoFD1]C p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
$ b Q4[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
.8[Db1W p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
{VWX?Mm P1=[P1 p1/p10];
qPJU}(9#B P2=[P2 p2/p10];
P<AN`un
P3=[P3 p3/p10];
gwvy$H P=[P p*p];
JGS4r+ end
J|k~e,C figure(1)
*], ]E; plot(P,P1, P,P2, P,P3);
Dps0$f c &|t*9 D 转自：
http://blog.163.com/opto_wang/
