计算脉冲在非线性耦合器中演化的Matlab 程序 FN^FvQ /*rhtrS) % This Matlab script file solves the coupled nonlinear Schrodinger equations of
k'3Wt*i % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
t ^ SzqB % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0
n
vSvk % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
(zcLx;N
|E)aT#$f' %fid=fopen('e21.dat','w');
{38bv. 3' N = 128; % Number of Fourier modes (Time domain sampling points)
s a&) #Z: M1 =3000; % Total number of space steps
. iwZ*b{ J =100; % Steps between output of space
j/!H$0PN T =10; % length of time windows:T*T0
/)L
0`:I# T0=0.1; % input pulse width
`T& jPA9eY MN1=0; % initial value for the space output location
y 1\'( 1 dt = T/N; % time step
oBQm05x" n = [-N/2:1:N/2-1]'; % Index
v]VWDT
` t = n.*dt;
jZ*WN|FK? u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
|j~lkzPnV u20=u10.*0.0; % input to waveguide 2
5&!c7$K0 u1=u10; u2=u20;
$XnPwOj U1 = u1;
s1j{x&OSq U2 = u2; % Compute initial condition; save it in U
#0Ds'pE- ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
+^|iZbZKx w=2*pi*n./T;
#UP~iHbt\ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
%; "@Ah L=4; % length of evoluation to compare with S. Trillo's paper
s Be7"^ dz=L/M1; % space step, make sure nonlinear<0.05
En VuD
9 for m1 = 1:1:M1 % Start space evolution
{KL5GowH u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
ci9R.U) u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
|CFRJN-J" ca1 = fftshift(fft(u1)); % Take Fourier transform
@.C{OSH E ca2 = fftshift(fft(u2));
c a<" c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
]/X(V|t c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
f58?5(Dc| u2 = ifft(fftshift(c2)); % Return to physical space
/0MDISQy9 u1 = ifft(fftshift(c1));
@ R|'X if rem(m1,J) == 0 % Save output every J steps.
0%`4px4J U1 = [U1 u1]; % put solutions in U array
/iaf ^
> U2=[U2 u2];
5e8AmY8; MN1=[MN1 m1];
q8P.,%
z1=dz*MN1'; % output location
}iB|sl2J end
[^Y A=K hu end
SkQswH hg=abs(U1').*abs(U1'); % for data write to excel
w f.T3 ha=[z1 hg]; % for data write to excel
BqK(DH^9 N t1=[0 t'];
^Q<mV*~ hh=[t1' ha']; % for data write to excel file
~nLN`H d %dlmwrite('aa',hh,'\t'); % save data in the excel format
!U%T&?E l figure(1)
KJn! Ap waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
O `1! figure(2)
),:c+~@@kT waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
V N{NA +I k44Q):ncY7 非线性超快脉冲耦合的数值方法的Matlab程序 bPK Ow< oPf)be| # 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。
OPJ: XbG
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
h B;VCg8 l\0w;:N3 Elj_,z x\e;+ubt} % This Matlab script file solves the nonlinear Schrodinger equations
uP $ Cj % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
g^ Yl TB % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`O?T.p) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
y m,H@~ 75T_Dx(H C=1;
-ezY= 0Q& M1=120, % integer for amplitude
g>0XxjP4 M3=5000; % integer for length of coupler
W1Lr_z6
N = 512; % Number of Fourier modes (Time domain sampling points)
YpAg dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
dC e4u<so\ T =40; % length of time:T*T0.
[H\:pP8t dt = T/N; % time step
<:FP4e
"( n = [-N/2:1:N/2-1]'; % Index
Jb)#fH$L t = n.*dt;
j:T/ iH!YF ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`O?TUQGR w=2*pi*n./T;
WO4=Mt e? g1=-i*ww./2;
G|w=ez g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
yH 9!GS# g3=-i*ww./2;
/v|"0 P1=0;
kd:$oS_*s P2=0;
W%2
80\h P3=1;
1% F?B-k P=0;
jCA C
` for m1=1:M1
>SN|?|2U/ p=0.032*m1; %input amplitude
HmfG$Z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
87%*+n:?* s1=s10;
v8gdU7Ll, s20=0.*s10; %input in waveguide 2
$8USyGi3J s30=0.*s10; %input in waveguide 3
OH^N" L s2=s20;
jN-vY< ?h] s3=s30;
{qW~"z*
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
:WI.LKlo ~ %energy in waveguide 1
> oA? 6x p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Om'+]BBN %energy in waveguide 2
[ xOzzp4 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
bPD`+: A_ %energy in waveguide 3
cfox7FmW for m3 = 1:1:M3 % Start space evolution
t kQH\5 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
KTvzOI8 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
J89Dul l
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
|4mpohX sca1 = fftshift(fft(s1)); % Take Fourier transform
9][(Iu]h7 sca2 = fftshift(fft(s2));
fP
tm0.r sca3 = fftshift(fft(s3));
i&njqK!wS sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
>&g}7d% sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)15Z#` x sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
7"7rmZ s3 = ifft(fftshift(sc3));
$@d9<83= s2 = ifft(fftshift(sc2)); % Return to physical space
; Sd\VR s1 = ifft(fftshift(sc1));
!3i Gz_y end
svelYe#9z p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
PiV7*F4qI. p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
}>^Q'BW;65 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
l$K,#P<) P1=[P1 p1/p10];
+$xeoxU>; P2=[P2 p2/p10];
2 o a#0`{ P3=[P3 p3/p10];
O20M[_S P=[P p*p];
Tmh(=
TB' end
_A<u#.yd figure(1)
a9n^WOJ6 plot(P,P1, P,P2, P,P3);
VL[R(a6c
< ; fw 1 转自：
http://blog.163.com/opto_wang/
