计算脉冲在非线性耦合器中演化的Matlab 程序 =)YYx8gR ;8T=uCi % This Matlab script file solves the coupled nonlinear Schrodinger equations of
I0vn d7 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
X@&uu0JJ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
)JQQ4D % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
FBAC9}V" ebe@.ZVSi %fid=fopen('e21.dat','w');
*F*fH>?C# N = 128; % Number of Fourier modes (Time domain sampling points)
$tHwJ!<$& M1 =3000; % Total number of space steps
.K1E1Z_ J =100; % Steps between output of space
{\/nUbo[ T =10; % length of time windows:T*T0
1!wEXH( T0=0.1; % input pulse width
Y^Q|l%Qrb MN1=0; % initial value for the space output location
cu^* x/0 , dt = T/N; % time step
Sc$wR{W<: n = [-N/2:1:N/2-1]'; % Index
YiuO u(X t = n.*dt;
_0q~s@- u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
w%dIe!sV u20=u10.*0.0; % input to waveguide 2
|Du13i4].& u1=u10; u2=u20;
Ju7C?)x U1 = u1;
X&?lDL7? U2 = u2; % Compute initial condition; save it in U
J<#`Ia V ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%OW9cqL>l w=2*pi*n./T;
%D ls36 F g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
z~e~K`S L=4; % length of evoluation to compare with S. Trillo's paper
@n X2*j*u dz=L/M1; % space step, make sure nonlinear<0.05
w LN2`ucC for m1 = 1:1:M1 % Start space evolution
niEEm`" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
tW :/R@@ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
wv.Ul rpx. ca1 = fftshift(fft(u1)); % Take Fourier transform
K}<!{/fi) ca2 = fftshift(fft(u2));
#K1BJ#KUt c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Y0yO ` W4 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
x<j"DS}S)D u2 = ifft(fftshift(c2)); % Return to physical space
AV 5\W } u1 = ifft(fftshift(c1));
W}2 &Pax if rem(m1,J) == 0 % Save output every J steps.
Owpg]p yVD U1 = [U1 u1]; % put solutions in U array
LL[#b2CKa U2=[U2 u2];
.hlQ?\ MN1=[MN1 m1];
n~ >h4=h z1=dz*MN1'; % output location
# G + end
Ipz
1+
#s' end
\*% i#]wO@ hg=abs(U1').*abs(U1'); % for data write to excel
BZ;}ROmqk ha=[z1 hg]; % for data write to excel
EcU'* t1=[0 t'];
/1W7<']>xV hh=[t1' ha']; % for data write to excel file
,J (5@8(>a %dlmwrite('aa',hh,'\t'); % save data in the excel format
mOgOHb2 figure(1)
A]iv)C;] waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
r d 6F"W figure(2)
g{W6a 2 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
$JhZ'Z TjUZv 1(L 非线性超快脉冲耦合的数值方法的Matlab程序 B>|U-[A !P~ PF:W~| 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
45 )ogg2 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
RCh$j&Tn v*H & F s"=F^# hX8gV~E=y % This Matlab script file solves the nonlinear Schrodinger equations
sUbz)BS#. % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Z6R:
rq % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
{yHB2=nI % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
P~\a)Szy V%BJNJ C=1;
Sj0 ucnuHi M1=120, % integer for amplitude
! 2Xr~u7a M3=5000; % integer for length of coupler
(~G5t(+ N = 512; % Number of Fourier modes (Time domain sampling points)
2E 3?0DL", dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
[W9e>Nsp0 T =40; % length of time:T*T0.
K$<`4#i dt = T/N; % time step
Ld\L Kwo n = [-N/2:1:N/2-1]'; % Index
qIDWl{b< t = n.*dt;
s!@ =rq ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1 ;\]D9i w=2*pi*n./T;
E/~"j g1=-i*ww./2;
(:?5 i` g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
+~w?Xw, g3=-i*ww./2;
H~?*KcZ 0\ P1=0;
;]gsJ9FK< P2=0;
"%oH@
= P3=1;
YN%=Oq P=0;
"e p ` for m1=1:M1
abROFI5.L p=0.032*m1; %input amplitude
!F+|Y "c s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
M<{5pH(K s1=s10;
h v$uH7Fz s20=0.*s10; %input in waveguide 2
; |>q zx s30=0.*s10; %input in waveguide 3
?w ]"~ s2=s20;
{PODisl>\D s3=s30;
[$( sUc(% p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
&/ >;LgN %energy in waveguide 1
r,2Xu p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Wl&
>6./{ %energy in waveguide 2
(s}Rj)V[^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
yhcNE8mkQ/ %energy in waveguide 3
{{V ;:+62 for m3 = 1:1:M3 % Start space evolution
cBz!U 8( s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
g08*}0- k s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
pqyWv; s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
z5XYpi_;[ sca1 = fftshift(fft(s1)); % Take Fourier transform
Ku<b0<` sca2 = fftshift(fft(s2));
MV"E?}0 sca3 = fftshift(fft(s3));
5^/, aI sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
`zdH1 p^w sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
42rj6m\ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
%`xV'2H s3 = ifft(fftshift(sc3));
Qg'c?[~W@ s2 = ifft(fftshift(sc2)); % Return to physical space
ZY E' C s1 = ifft(fftshift(sc1));
o Lg g end
b#D9 eJhS p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
J[ e} p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
![* :.CW p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
iYk' :iv}S P1=[P1 p1/p10];
Uc_jQ4e_ P2=[P2 p2/p10];
[J a)<!]< P3=[P3 p3/p10];
/xl4ohL$a P=[P p*p];
\hs/D+MCk end
r_b8,I6{] figure(1)
nd.57@*M plot(P,P1, P,P2, P,P3);
w Y8@1>ah <+V -k| 转自：
http://blog.163.com/opto_wang/
