计算脉冲在非线性耦合器中演化的Matlab 程序 Jb4A!g5C j*05!j<' % This Matlab script file solves the coupled nonlinear Schrodinger equations of
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/}HND % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
RIQw+RG > % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
6
SosVE>Z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
70&]nb6f *zR %fid=fopen('e21.dat','w');
L_4Z x sIv N = 128; % Number of Fourier modes (Time domain sampling points)
N>J"^ GX M1 =3000; % Total number of space steps
QC\][I> J =100; % Steps between output of space
(xhwl=MX) T =10; % length of time windows:T*T0
dfoFs&CSKh T0=0.1; % input pulse width
sX aIQhZ MN1=0; % initial value for the space output location
|vY0[#E8& dt = T/N; % time step
U|HF;L n = [-N/2:1:N/2-1]'; % Index
Qy+&N*k> t = n.*dt;
l[J'FR: u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
4z##4^9g u20=u10.*0.0; % input to waveguide 2
h&4f9HhS= u1=u10; u2=u20;
)|@ H#kv? U1 = u1;
*1 [v08?! U2 = u2; % Compute initial condition; save it in U
P5*~ Wi` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T]fu[yRVvg w=2*pi*n./T;
CrIt h/Z g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
~yvOR`2Gg L=4; % length of evoluation to compare with S. Trillo's paper
Uc3-n`C dz=L/M1; % space step, make sure nonlinear<0.05
79 svlq= for m1 = 1:1:M1 % Start space evolution
lV0\UySH u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
h^ D]@H u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
m% {4 ca1 = fftshift(fft(u1)); % Take Fourier transform
LJ|2=lI+jb ca2 = fftshift(fft(u2));
JM@}+pX c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
AGN5 =K*D c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
9w=GB?/ u2 = ifft(fftshift(c2)); % Return to physical space
x1}7c9n K u1 = ifft(fftshift(c1));
DP D%8a)? if rem(m1,J) == 0 % Save output every J steps.
t
TAql n| U1 = [U1 u1]; % put solutions in U array
lc71Pp> U2=[U2 u2];
=k1 ,jn+ MN1=[MN1 m1];
#i Ooi9( z1=dz*MN1'; % output location
xj Oj1Hv end
AIvIQ$6} end
K;u<-?En hg=abs(U1').*abs(U1'); % for data write to excel
%Hk9.1hn5 ha=[z1 hg]; % for data write to excel
HCI|6{k t1=[0 t'];
ZgcJxWC< hh=[t1' ha']; % for data write to excel file
0
7Cufo I %dlmwrite('aa',hh,'\t'); % save data in the excel format
D9;2w7v figure(1)
LH4!QDK- waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
wW~y?A"{2 figure(2)
]Fc<% wzp waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
cGhnI& o
2 6R] 非线性超快脉冲耦合的数值方法的Matlab程序 ) /kf W -Yv0n3 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
(hB&OP5Fne Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8X@ p?43 | =^p`CT UvSvgDMl fAu^eS%>7 % This Matlab script file solves the nonlinear Schrodinger equations
Lbka*@ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
B>3 joe} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
tSVN}~1\ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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k.; j9@7\N< C=1;
k !S0-/ h M1=120, % integer for amplitude
0UEEvD5 M3=5000; % integer for length of coupler
+rw?k/ N = 512; % Number of Fourier modes (Time domain sampling points)
S <C'#vj dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
.{ ` : T =40; % length of time:T*T0.
sw.c w}1 dt = T/N; % time step
,9I %t%sb n = [-N/2:1:N/2-1]'; % Index
+*2 ]R~"M t = n.*dt;
GJ:65)KU ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T 5; zgr w=2*pi*n./T;
QxRT%;'Zh] g1=-i*ww./2;
@l)HX'z0d g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3BuG_ild g3=-i*ww./2;
~s@PP'! P1=0;
^ lrq`1k P2=0;
/;7\HZ$ @/ P3=1;
zW^_w&fd^j P=0;
|H`}w2U[j for m1=1:M1
sb Wn1 T
U p=0.032*m1; %input amplitude
%#xdD2oN s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:Ve>tZeW s1=s10;
"~R,%sY b( s20=0.*s10; %input in waveguide 2
EZy:_xjZ s30=0.*s10; %input in waveguide 3
sN`2"t/s s2=s20;
A>@ i
TI s3=s30;
n[~kcF p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Zd~'%(q %energy in waveguide 1
8$k `bZ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
woCmpCN*I %energy in waveguide 2
<L4.* p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
WmO.&zp %energy in waveguide 3
k3F* D for m3 = 1:1:M3 % Start space evolution
< Y5pAStg s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
DQC=f 8 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|'$E -[ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
.lclW0* sca1 = fftshift(fft(s1)); % Take Fourier transform
?b?6/_W~R sca2 = fftshift(fft(s2));
Gwyjie 9t sca3 = fftshift(fft(s3));
x=1Iuc;&3 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
rI/;L<c sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
,$"*X-1 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
t Pv3nh s3 = ifft(fftshift(sc3));
=L,s6J8_' s2 = ifft(fftshift(sc2)); % Return to physical space
-&N^S? s1 = ifft(fftshift(sc1));
`/ W6, ] end
{y5v"GR{YM p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
nitKX.t8 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
&J>XKO nl p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
D hN{Y8'~ P1=[P1 p1/p10];
j#}wg`P"A P2=[P2 p2/p10];
I4[sf P3=[P3 p3/p10];
rG#o*oA P=[P p*p];
$1aJd ZC7 end
%2H0JXKa, figure(1)
Hz?C9q3BX plot(P,P1, P,P2, P,P3);
<ttrd%VW 0\qLuF[) 转自：
http://blog.163.com/opto_wang/
