计算脉冲在非线性耦合器中演化的Matlab 程序 - I~\ JE;!~= % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Qn@[{%),4 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
~;oa W<" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+,eF(VS ! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
O/oLQoH r$,Xv+} %fid=fopen('e21.dat','w');
Pe@*')o* N = 128; % Number of Fourier modes (Time domain sampling points)
^,Ft7 JAn M1 =3000; % Total number of space steps
&InFC5A J =100; % Steps between output of space
H$6;{IUz~ T =10; % length of time windows:T*T0
D#d/?\2 T0=0.1; % input pulse width
E/ ^N
MN1=0; % initial value for the space output location
,oJ$m$(Lj dt = T/N; % time step
!"
@<! n = [-N/2:1:N/2-1]'; % Index
*tl; 0<n t = n.*dt;
{7E pljH@ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Wyb+ K)Tg u20=u10.*0.0; % input to waveguide 2
D+Z 2y1 u1=u10; u2=u20;
@$;I% U1 = u1;
.Z@ i z5 U2 = u2; % Compute initial condition; save it in U
#eKH'fE ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|[$ TT$Fb w=2*pi*n./T;
R^ yh, g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ZU l-&P_X L=4; % length of evoluation to compare with S. Trillo's paper
n -xCaq dz=L/M1; % space step, make sure nonlinear<0.05
L!Gpk) }[i for m1 = 1:1:M1 % Start space evolution
<4-g2.\ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
`F_R J.g*p u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
5GURf G3{ ca1 = fftshift(fft(u1)); % Take Fourier transform
~b6c:db3 ca2 = fftshift(fft(u2));
W A#y& c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
w$jSlgUHy) c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
q( %)^C u2 = ifft(fftshift(c2)); % Return to physical space
4UMOC_ u1 = ifft(fftshift(c1));
$Q= S`z= if rem(m1,J) == 0 % Save output every J steps.
Y,-! QFS# U1 = [U1 u1]; % put solutions in U array
Xj<xen( U2=[U2 u2];
<ti,W n. MN1=[MN1 m1];
4G j z1=dz*MN1'; % output location
:,.HJ[Vg& end
FMT_X end
yL2 3 Nqe hg=abs(U1').*abs(U1'); % for data write to excel
Ys<z% ha=[z1 hg]; % for data write to excel
X#ud_+6x t1=[0 t'];
D@m3bsMwe hh=[t1' ha']; % for data write to excel file
UTO$L|K %dlmwrite('aa',hh,'\t'); % save data in the excel format
UW{C`^?=B figure(1)
5
axt\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
}wC=p>zA figure(2)
~NIqO4 D waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
af&P;#U D&D- E~b^ 非线性超快脉冲耦合的数值方法的Matlab程序 }5}#QHF U[hokwZ 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。
gj4ONmY 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
PVrNS7 Rk/ X*`b}^T 4XSq\.@G !y3XIbdS" % This Matlab script file solves the nonlinear Schrodinger equations
%U9f`qE % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
k>:\4uI|<\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%Ybr5 $_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
27Vx<W zG<>-?q~' C=1;
m[hHaX M1=120, % integer for amplitude
,8stEp9~h] M3=5000; % integer for length of coupler
Wli!s~c5Fo N = 512; % Number of Fourier modes (Time domain sampling points)
S fPtG dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
'_" S/X +v T =40; % length of time:T*T0.
.G >~xm0 dt = T/N; % time step
GYV%R D # n = [-N/2:1:N/2-1]'; % Index
xiF}{25 a t = n.*dt;
xo{z4W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G~/*! ?&z w=2*pi*n./T;
[>lQi X g1=-i*ww./2;
d,o|> e$ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
jV#1d8qm g3=-i*ww./2;
}S}%4c> P1=0;
?_.
SV g P2=0;
M[L@ej P3=1;
0SJ(Ln`0K P=0;
j+2-Xy' for m1=1:M1
2c3/iYCKP p=0.032*m1; %input amplitude
wIF)(t-): s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
n.1$p s1=s10;
Iv?1 XI= s20=0.*s10; %input in waveguide 2
hPt=j{aJ%< s30=0.*s10; %input in waveguide 3
w}
r mYQ s2=s20;
7Kt i& T s3=s30;
LftzW{>gI" p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~$YasFEz %energy in waveguide 1
9 $ zx<O p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Rj-4K@a8#N %energy in waveguide 2
y4Nam87;/? p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Ee=!bv(%70 %energy in waveguide 3
H:o=gP60] for m3 = 1:1:M3 % Start space evolution
\mw5
~Rf; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1(jx.W3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
`-5gsJ
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
~jJ e|zg> sca1 = fftshift(fft(s1)); % Take Fourier transform
KD'}9{F, sca2 = fftshift(fft(s2));
3H%bbFy sca3 = fftshift(fft(s3));
6`5DR~ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
;s5JYR sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
f_IsY+ @ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
h-\+# .YP s3 = ifft(fftshift(sc3));
Q>uJ: [x+ s2 = ifft(fftshift(sc2)); % Return to physical space
ge% tj O s1 = ifft(fftshift(sc1));
#YSFiy:+r_ end
S*H
@`Do%d p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
x'V:qv*O p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
E- #C#B p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
t y8E;[ ' P1=[P1 p1/p10];
J$,bsMIX P2=[P2 p2/p10];
8> (/:u_x P3=[P3 p3/p10];
&Vg)/t; P=[P p*p];
"f-HOd\= end
5B;; {GR figure(1)
VRUA <x plot(P,P1, P,P2, P,P3);
V|pO";%>, aQ0pYk~( 转自：
http://blog.163.com/opto_wang/
