计算脉冲在非线性耦合器中演化的Matlab 程序 (%"M% Qko iU{bPyz , % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Yv E$fX= % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
/8@JWK^I{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
FOgF '!K % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
h<\o[n7j 4 %~$A`7 %fid=fopen('e21.dat','w');
<splLZW3k N = 128; % Number of Fourier modes (Time domain sampling points)
NqvL,~1G M1 =3000; % Total number of space steps
ChF:N0w?
p J =100; % Steps between output of space
1@RctI_} T =10; % length of time windows:T*T0
+Sv`23G@ T0=0.1; % input pulse width
qlD+[`=b MN1=0; % initial value for the space output location
XWZ
*{/u dt = T/N; % time step
} WY7!Y n = [-N/2:1:N/2-1]'; % Index
*O,\/aQ+ t = n.*dt;
KB <n- ' u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
F h9`8 u20=u10.*0.0; % input to waveguide 2
6tB- u1=u10; u2=u20;
dQ@ e+u5 U1 = u1;
&e@2zfl7 U2 = u2; % Compute initial condition; save it in U
bVSa}&*k M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1u7 5 w=2*pi*n./T;
A;m)/@ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
OsPx-|f
S~ L=4; % length of evoluation to compare with S. Trillo's paper
/lkIbmV dz=L/M1; % space step, make sure nonlinear<0.05
)VQ:L:1t( for m1 = 1:1:M1 % Start space evolution
&N GYV u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
YFOSv]w u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
+b1(sk=4z ca1 = fftshift(fft(u1)); % Take Fourier transform
~{iBm"4 ca2 = fftshift(fft(u2));
&10vdAnBRC c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
1U.se` L c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
9 "1 0:\U u2 = ifft(fftshift(c2)); % Return to physical space
/
*xP`'T u1 = ifft(fftshift(c1));
S9J<3
= if rem(m1,J) == 0 % Save output every J steps.
db`xlvrCY U1 = [U1 u1]; % put solutions in U array
aAiSP+# U2=[U2 u2];
'x{g P?. MN1=[MN1 m1];
-q|K\>tgU z1=dz*MN1'; % output location
+'Pl? QyH end
f!a[+^RB: end
:,%~rR hg=abs(U1').*abs(U1'); % for data write to excel
FFb`4. ha=[z1 hg]; % for data write to excel
Ypo O: t1=[0 t'];
6 /gh_'& hh=[t1' ha']; % for data write to excel file
eWS[|' dl %dlmwrite('aa',hh,'\t'); % save data in the excel format
c-3AzB#[ figure(1)
m619bzFlB waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
^;@q^b)ZP figure(2)
t%ye : waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Ac'[( UhYeyT 非线性超快脉冲耦合的数值方法的Matlab程序 D Z5%- 1%Xwk2l,8b 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。
d a we!w! 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
o0^..f =` [ 08 8o#*0d| sufidi % This Matlab script file solves the nonlinear Schrodinger equations
e p~3e5 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
-v .\CtpHv % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
w'z ?1M(* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$'*@g1v Y Gf\Dc C=1;
cP%mkh_ri M1=120, % integer for amplitude
A9\m .3jo M3=5000; % integer for length of coupler
vJVL%,7 N = 512; % Number of Fourier modes (Time domain sampling points)
Da*=uW9 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
" - S2${ T =40; % length of time:T*T0.
8-5MGh0L dt = T/N; % time step
exrsYo!% n = [-N/2:1:N/2-1]'; % Index
w~+5F SdH t = n.*dt;
_+YCwg ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
jm0J)Z_"nr w=2*pi*n./T;
i71 , g1=-i*ww./2;
uN20sD} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
l_Gv dD g3=-i*ww./2;
RB.& ,1 P1=0;
l|z
'Lwwm5 P2=0;
7yo/ sb9h P3=1;
S/G6NBnbS P=0;
N|K,{
p^li for m1=1:M1
L9nv05B p=0.032*m1; %input amplitude
OY7\*wc: s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
6*cG>I . Z s1=s10;
l{F^ "_U s20=0.*s10; %input in waveguide 2
R}njFQvS) s30=0.*s10; %input in waveguide 3
}VxbO8\b( s2=s20;
J/S 47J~ s3=s30;
xO)vn\uJ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
j jbBv~vs %energy in waveguide 1
/Y@^B,6 \ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
u}Vc2a,WV %energy in waveguide 2
^N}zePy0 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
g3Q]W(F%$ %energy in waveguide 3
qa wb9Iud0 for m3 = 1:1:M3 % Start space evolution
D,%R[F? 5O s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
"@U9'rKx s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
=KqcWN3k s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
x'kwk sca1 = fftshift(fft(s1)); % Take Fourier transform
@r 4ZN6Wn sca2 = fftshift(fft(s2));
7 sKN ` sca3 = fftshift(fft(s3));
Kk+IUs sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
q(<#7 spz sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
>(5*y=\i sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Q<W9<&VZe s3 = ifft(fftshift(sc3));
)w];eF0c s2 = ifft(fftshift(sc2)); % Return to physical space
Z&FC:4!! s1 = ifft(fftshift(sc1));
% Z~, F? end
k%-_z}:3V p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Au jvKQ( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
%"^$$$6% p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
sW!pMkd_ P1=[P1 p1/p10];
\hN\ px P2=[P2 p2/p10];
wLwAtjW) P3=[P3 p3/p10];
Li~(kw3 P=[P p*p];
cAq>|^f0a end
"+3p??h%Rq figure(1)
'U
', 9 plot(P,P1, P,P2, P,P3);
nM:e<`r YSwAu,$jf 转自：
http://blog.163.com/opto_wang/
