计算脉冲在非线性耦合器中演化的Matlab 程序 j^"Z^TEBT b-@6w(j % This Matlab script file solves the coupled nonlinear Schrodinger equations of
;KWR/?ec % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
d /+s R@\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
w t? 8-_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
N9r02c 6K5KZZ G
%fid=fopen('e21.dat','w');
$oHlfV/! N = 128; % Number of Fourier modes (Time domain sampling points)
c_)vWU M1 =3000; % Total number of space steps
Y]0oF_ :7 J =100; % Steps between output of space
l&dHH_m3 T =10; % length of time windows:T*T0
Jb#*QJ= T0=0.1; % input pulse width
M P-A^QT MN1=0; % initial value for the space output location
M6jP>fbV* dt = T/N; % time step
cH.T6u_% n = [-N/2:1:N/2-1]'; % Index
_~d C >`K t = n.*dt;
P)XkqOGpT9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
G0^WQ Q4 u20=u10.*0.0; % input to waveguide 2
4~53% =+ u1=u10; u2=u20;
VTa?y U1 = u1;
@ `t )ly#N U2 = u2; % Compute initial condition; save it in U
\_#0Z+pX ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
K M*sLC # w=2*pi*n./T;
U#gHc:$ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
_Z~w pO}/ L=4; % length of evoluation to compare with S. Trillo's paper
&kB[jz_[A dz=L/M1; % space step, make sure nonlinear<0.05
T?I&n[Y| for m1 = 1:1:M1 % Start space evolution
U59uP
7n u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
p4\ %*ovQt u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
mR,p?[P ca1 = fftshift(fft(u1)); % Take Fourier transform
/t ikLJ ca2 = fftshift(fft(u2));
if9I7@ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
dJ"3F(X c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
X4>c(1 e u2 = ifft(fftshift(c2)); % Return to physical space
|{k;p fPV u1 = ifft(fftshift(c1));
l!ltgj if rem(m1,J) == 0 % Save output every J steps.
LDN'o1$qo U1 = [U1 u1]; % put solutions in U array
7 6~x|6) U2=[U2 u2];
L}ud+Wfox MN1=[MN1 m1];
z%Ywjfn' z1=dz*MN1'; % output location
.L0pS.=LT end
T
{a%:=` end
B08q/ qi hg=abs(U1').*abs(U1'); % for data write to excel
[CGvM { ha=[z1 hg]; % for data write to excel
LyhLPU0^q t1=[0 t'];
%L+/GtxK hh=[t1' ha']; % for data write to excel file
8RbtI4 %dlmwrite('aa',hh,'\t'); % save data in the excel format
! s/ij' T figure(1)
wb 2N$Ew= waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
L`cc2.F figure(2)
WZ&/l 65J waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
yL^1s\<ddW BP6;dF5 E 非线性超快脉冲耦合的数值方法的Matlab程序 E B)j&y_ -N(y+~wN 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 ?4"8_ 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
`W
e M F'lG=c3N G'q7@d {' ?d%+ 85 % This Matlab script file solves the nonlinear Schrodinger equations
Mc oHV]x % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
i)Vqvb0Q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
m1a0uEA
G % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
EMU~gwPR m{`O.6# O C=1;
d i]z M1=120, % integer for amplitude
q]=. Aik M3=5000; % integer for length of coupler
UTc$zc7 N = 512; % Number of Fourier modes (Time domain sampling points)
X0^gj>GI| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
I! {AWfp0 T =40; % length of time:T*T0.
MI0'ou8l dt = T/N; % time step
$]:I1I n = [-N/2:1:N/2-1]'; % Index
T/p}Us t = n.*dt;
N*$<K jw ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
aCcBm c w=2*pi*n./T;
g2^7PtJg g1=-i*ww./2;
{6^c3R[
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
FSoL |lH g3=-i*ww./2;
@y[Zr6\z P1=0;
l %=yT6 P2=0;
9~I\WjB
" P3=1;
Ij( S"P@ P=0;
-20 o%t for m1=1:M1
I7r{&X) D p=0.032*m1; %input amplitude
"B*a|
'n! s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
n9 ]^v-]K s1=s10;
AT}}RE@vq s20=0.*s10; %input in waveguide 2
TDBWYppM s30=0.*s10; %input in waveguide 3
k:4 Z c3 s2=s20;
MB" uJUk s3=s30;
fs&J%ku\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)|@b
GEk %energy in waveguide 1
%/>\`d? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
LO[1xE9 %energy in waveguide 2
yc|C}oQF p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
l
" pCxA %energy in waveguide 3
^ 'FC. for m3 = 1:1:M3 % Start space evolution
%E?:9. :NJ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
7s; <5xc s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
m(q6Xe:Vc s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
hhlQ!WV2 sca1 = fftshift(fft(s1)); % Take Fourier transform
q -M&f@Il sca2 = fftshift(fft(s2));
OOQf a#~k sca3 = fftshift(fft(s3));
{S%)GvrT sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Ziu f<X{ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
/ _@S*=T5 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
q~p,A>K s3 = ifft(fftshift(sc3));
sS d s2 = ifft(fftshift(sc2)); % Return to physical space
!H{ )L@f s1 = ifft(fftshift(sc1));
2`+ ?s end
>9a%"<(2# p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
N#@xo) -H p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
\ 3n{ %\_ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Kv:U QdnU[ P1=[P1 p1/p10];
z{d] ,M P2=[P2 p2/p10];
O HssUt P3=[P3 p3/p10];
6#T?g7\pyR P=[P p*p];
kuu9'Sqc'b end
(aVs p *E figure(1)
kMKI=>s+ plot(P,P1, P,P2, P,P3);
)wP0U{7?v Odxq ]HlbO 转自：
http://blog.163.com/opto_wang/
