计算脉冲在非线性耦合器中演化的Matlab 程序 ;>u B$8<_7 wPEK5=\4Ob % This Matlab script file solves the coupled nonlinear Schrodinger equations of
? q7MbQw % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
xax[# Vl4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
c2t`i % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~s-bA#0S ^&D5J\][ %fid=fopen('e21.dat','w');
A!,c@Kv
3 N = 128; % Number of Fourier modes (Time domain sampling points)
0BNH~,0u M1 =3000; % Total number of space steps
x <a}*8" J =100; % Steps between output of space
Td ade+ T =10; % length of time windows:T*T0
w$IUm_~waa T0=0.1; % input pulse width
0cSm^a MN1=0; % initial value for the space output location
XD?Lu
_. dt = T/N; % time step
V~VUl) n = [-N/2:1:N/2-1]'; % Index
]
)iP?2{ t = n.*dt;
gg.]\#3g u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@ <3E `j'p u20=u10.*0.0; % input to waveguide 2
tA^+RO4 u1=u10; u2=u20;
@ R[K8 U1 = u1;
O&MH5^I U2 = u2; % Compute initial condition; save it in U
1d~d1Rd ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
A@Q6}ESD w=2*pi*n./T;
BYu(a
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
r95 ,X! L=4; % length of evoluation to compare with S. Trillo's paper
JNY ?] |= dz=L/M1; % space step, make sure nonlinear<0.05
*v%gNq for m1 = 1:1:M1 % Start space evolution
HU'w[r 6a u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
gyq6LRb
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
~r?tFE* + ca1 = fftshift(fft(u1)); % Take Fourier transform
bfpeK>T ca2 = fftshift(fft(u2));
Oe
x
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
r&Nh>6<&/ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
(V&8
WN u2 = ifft(fftshift(c2)); % Return to physical space
H#7=s{ u u1 = ifft(fftshift(c1));
'$Z@oCY# if rem(m1,J) == 0 % Save output every J steps.
YzQ(\._s U1 = [U1 u1]; % put solutions in U array
*+zFsu 4l U2=[U2 u2];
_YG@P1 MN1=[MN1 m1];
7TEpjSuF z1=dz*MN1'; % output location
XlD=<$Nk7 end
,}\LC;31, end
jI'?7@32` hg=abs(U1').*abs(U1'); % for data write to excel
q6N{N>-D ha=[z1 hg]; % for data write to excel
yZ 7)|j t1=[0 t'];
CVvl &on hh=[t1' ha']; % for data write to excel file
B8eZ}9X %dlmwrite('aa',hh,'\t'); % save data in the excel format
b l&9 O figure(1)
@54$IhhT~ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
oQrfrA&=M figure(2)
\9@}0}%` waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Y[vP] 7- x${C[gxq9F 非线性超快脉冲耦合的数值方法的Matlab程序 0C.5Qx xOPQ~J|z 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
T 59FRX Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ppRA%mhZ n-SO201[* #'O9Hn({ ob8}v*s % This Matlab script file solves the nonlinear Schrodinger equations
WY QVe_<z: % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
VRgckh
m % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
q+4dHS)x % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7X T(n v
E.;Hm ; C=1;
/s%-c!o^ M1=120, % integer for amplitude
S" @6, M3=5000; % integer for length of coupler
@{{L1[~:0 N = 512; % Number of Fourier modes (Time domain sampling points)
I$S*elv eG dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
={v(me0ZPb T =40; % length of time:T*T0.
}5 n\us dt = T/N; % time step
?$ov9U_ n = [-N/2:1:N/2-1]'; % Index
m >4 8?% t = n.*dt;
,aD~7QX1: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<$hv{a w=2*pi*n./T;
_.R]K$U g1=-i*ww./2;
s o1 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
\1&4wzT g3=-i*ww./2;
! ( +M P1=0;
/2E
Q:P P2=0;
7Y-Q, ?1 P3=1;
RhmkpboucC P=0;
l"
~
CAw; for m1=1:M1
a!4 p$pR p=0.032*m1; %input amplitude
wSCI? s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
`KLr!<i() s1=s10;
.b ` 8
+ s20=0.*s10; %input in waveguide 2
TD*AFR3Oz s30=0.*s10; %input in waveguide 3
\2[tM/+Bs s2=s20;
1c @S[y s3=s30;
RT vOaZ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
b C"h7$3 %energy in waveguide 1
pg!oi?Jn p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
}eA ) m %energy in waveguide 2
z>0$SBQ- p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
tS\Db'C7 %energy in waveguide 3
pYm# iz for m3 = 1:1:M3 % Start space evolution
ReD]M@; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
K:qc
"Q=C s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
nv+miyvvm s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
jj ;TS% sca1 = fftshift(fft(s1)); % Take Fourier transform
Ake l .& sca2 = fftshift(fft(s2));
OAF xf,b sca3 = fftshift(fft(s3));
ZwY mR = sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Il>o60u1 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Y1>OhHuN sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
c;]^aaQ+> s3 = ifft(fftshift(sc3));
b;*' j9ly s2 = ifft(fftshift(sc2)); % Return to physical space
_<2{8>EVf s1 = ifft(fftshift(sc1));
/*e<r6 end
G\5Bd o1g p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
w(Tr ,BFF p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
e HKb`K7C. p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
/E{tNd^S P1=[P1 p1/p10];
)m I>2<Z! P2=[P2 p2/p10];
IY[qW s P3=[P3 p3/p10];
v8'XchJ P=[P p*p];
hyJ&~i0P{J end
(Rr C<5" figure(1)
K0o${%'@7 plot(P,P1, P,P2, P,P3);
m+7% ]$ )+Z.J]$O- 转自：
http://blog.163.com/opto_wang/
