计算脉冲在非线性耦合器中演化的Matlab 程序 \GN5Sy]r 8Md KH7 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
w>e OERZa % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
;-F#a+2]! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
, /pE*Yk % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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#T`z %fid=fopen('e21.dat','w');
XN Y(@ N = 128; % Number of Fourier modes (Time domain sampling points)
ME(!xI//JZ M1 =3000; % Total number of space steps
TFhj]r^ { J =100; % Steps between output of space
H0S 7k`. T =10; % length of time windows:T*T0
cjL!$O E6 T0=0.1; % input pulse width
C o M8 MN1=0; % initial value for the space output location
h(fh |R< dt = T/N; % time step
JmK+#o n = [-N/2:1:N/2-1]'; % Index
ETIf x)B- t = n.*dt;
mMR[( u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
;Mc }I f* u20=u10.*0.0; % input to waveguide 2
0-FbV,:; u1=u10; u2=u20;
*VpQ(" U1 = u1;
tP UQ "S U2 = u2; % Compute initial condition; save it in U
L TF%b AQ, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
!(]|!F [m w=2*pi*n./T;
KN n E5f g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
j EX([J1 L=4; % length of evoluation to compare with S. Trillo's paper
{>:2Ff]O: dz=L/M1; % space step, make sure nonlinear<0.05
T F'ssD for m1 = 1:1:M1 % Start space evolution
REJ}T: u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
3+Q6<MS
q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
~ M"[FYw[ ca1 = fftshift(fft(u1)); % Take Fourier transform
;RrfE8mGj ca2 = fftshift(fft(u2));
5H79) n> c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Zqao4 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
E,;nx^`!l u2 = ifft(fftshift(c2)); % Return to physical space
1)%o:Xy o u1 = ifft(fftshift(c1));
%l,Xt"nS# if rem(m1,J) == 0 % Save output every J steps.
\ l:n U1 = [U1 u1]; % put solutions in U array
BdceINI U2=[U2 u2];
4]cOTXk9C MN1=[MN1 m1];
lfhB2^ ^ z1=dz*MN1'; % output location
cc>h=%s` end
k"; ;Snk end
5rc<ibGh hg=abs(U1').*abs(U1'); % for data write to excel
sU8D;ML7 ha=[z1 hg]; % for data write to excel
h1BdASn_ t1=[0 t'];
ev; &$Hc hh=[t1' ha']; % for data write to excel file
BKIt ,7j %dlmwrite('aa',hh,'\t'); % save data in the excel format
UkdQ#b1 figure(1)
P -Pt{: waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
~6OdPD figure(2)
U{ Y)\hR- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
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z+x X9P-fF?0 非线性超快脉冲耦合的数值方法的Matlab程序 (YR1ML3N !,\]> c 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。
0]Li "Wb 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
{ d/k0H <%!@cE+y V7& L+]! ]!f=b\-Av % This Matlab script file solves the nonlinear Schrodinger equations
#):F XB$a % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
67#;.}4a % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
rsP1?Hxq % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ut o4bs: #R)$nv:h?^ C=1;
2sXW eiJy; M1=120, % integer for amplitude
E Z$m4: {e M3=5000; % integer for length of coupler
SDot0`s> N = 512; % Number of Fourier modes (Time domain sampling points)
%9M_ * ] dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^@N @ gB T =40; % length of time:T*T0.
K(_nfE{ dt = T/N; % time step
{RzlmDStV n = [-N/2:1:N/2-1]'; % Index
b[/-lNrc t = n.*dt;
UCl,sn ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`=FfzL w=2*pi*n./T;
$FD0MrB_+ g1=-i*ww./2;
M[X& Q g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ua2SW(C@ g3=-i*ww./2;
x1TB
(^aX P1=0;
S3 &L P2=0;
E*CY/F I_ P3=1;
\s,ZE6dQ P=0;
wp} PQw: for m1=1:M1
Fd3V5h p=0.032*m1; %input amplitude
VPf=LSxJe s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
or0f%wAF s1=s10;
{|
Tl3 s20=0.*s10; %input in waveguide 2
R7vO,kZ6Q s30=0.*s10; %input in waveguide 3
O 7E0{8 s2=s20;
* c xYB s3=s30;
HogT#BMs p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
kMK-E<g %energy in waveguide 1
@c5TSHSL. p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
's JYt^ %energy in waveguide 2
Q q>M} p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
v\& Wb_;A %energy in waveguide 3
X+iUT for m3 = 1:1:M3 % Start space evolution
mI}1si=$ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
m&fm<?| s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
3^C s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
hv8V=Z'Q sca1 = fftshift(fft(s1)); % Take Fourier transform
@<;0 h| sca2 = fftshift(fft(s2));
w; )@2} sca3 = fftshift(fft(s3));
.h{`e>d sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
06L/i, sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
SxH b76 ; sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
rtC.!].;% s3 = ifft(fftshift(sc3));
.I<#i9Le s2 = ifft(fftshift(sc2)); % Return to physical space
LLCMp3q Bz s1 = ifft(fftshift(sc1));
[$f end
Eqnc("m) p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
<w<&,xM p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
kbiMqiPG p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
jgbE@IA@!' P1=[P1 p1/p10];
~:v" TuuK P2=[P2 p2/p10];
{e,S}:$g4 P3=[P3 p3/p10];
X)x$h{ OE P=[P p*p];
6Xbo:# end
(@[c;+x figure(1)
p%ek)tT plot(P,P1, P,P2, P,P3);
CB\E@u, Ar,B7-F! 转自：
http://blog.163.com/opto_wang/
