计算脉冲在非线性耦合器中演化的Matlab 程序 A1C@'9R*
R[V%59#{Z % This Matlab script file solves the coupled nonlinear Schrodinger equations of
4-m%[ D
|W % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
2{& " 3dq % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+ $-a:zx`l % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^K"`k43{ ZoUf Q!2* %fid=fopen('e21.dat','w');
#GF1MFkoS N = 128; % Number of Fourier modes (Time domain sampling points)
qg O)@B+ M1 =3000; % Total number of space steps
@dXf_2Tv= J =100; % Steps between output of space
Jx}5`{\ T =10; % length of time windows:T*T0
J +zqu T0=0.1; % input pulse width
}vi%pfrB MN1=0; % initial value for the space output location
~` BOz P dt = T/N; % time step
fZZ!kea[ n = [-N/2:1:N/2-1]'; % Index
aX|`G]PhdI t = n.*dt;
X;1q1X)K u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
xv2;h4{< u20=u10.*0.0; % input to waveguide 2
ReRRFkO"2 u1=u10; u2=u20;
L?P8/]DGp U1 = u1;
3EFk] X U2 = u2; % Compute initial condition; save it in U
1>2397 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
=nsY[ s< w=2*pi*n./T;
_CZ* z g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
:!/}*B L=4; % length of evoluation to compare with S. Trillo's paper
e nNn*.*| dz=L/M1; % space step, make sure nonlinear<0.05
c.~|)^OXXO for m1 = 1:1:M1 % Start space evolution
nu Q"\ G u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
8(A:XQN"h u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
V_~wWuZ - ca1 = fftshift(fft(u1)); % Take Fourier transform
l}wBthwCc ca2 = fftshift(fft(u2));
M}c_KFMV c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
O$$N{ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
4?&=H
*H: u2 = ifft(fftshift(c2)); % Return to physical space
vhg4E80Kr u1 = ifft(fftshift(c1));
lA1R$ if rem(m1,J) == 0 % Save output every J steps.
cmI8Xf]"P- U1 = [U1 u1]; % put solutions in U array
0I
k@d'7 U2=[U2 u2];
wO"Q{oi+ MN1=[MN1 m1];
Tx xc-$z z1=dz*MN1'; % output location
U` U/|@6 end
FYj3 !
H end
)SQ g hg=abs(U1').*abs(U1'); % for data write to excel
H!A^ MI ha=[z1 hg]; % for data write to excel
H(X~ =r t1=[0 t'];
V *] !N hh=[t1' ha']; % for data write to excel file
+]{X-R %dlmwrite('aa',hh,'\t'); % save data in the excel format
|joGrW v4 figure(1)
t_N
`e(V waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
4$J/e? i figure(2)
Q-0[l/A}a waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
@s/ q Oq? +VeLd+Q} 非线性超快脉冲耦合的数值方法的Matlab程序 <@yyx7 9GEcs(A* 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。
9O)>>1}*S 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
6nwO:?1o9 rfZA21y{? ( u _ sz 3o?Lz7L % This Matlab script file solves the nonlinear Schrodinger equations
F lZ]R % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
eyM3W}[S$/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
i|| YD-hkK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\uaJw\EZ p-}:7CXP C=1;
%`TLs ^ M1=120, % integer for amplitude
nGf@zJDb M3=5000; % integer for length of coupler
[brrziZ N = 512; % Number of Fourier modes (Time domain sampling points)
3ty){#: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
4 A<c@g2 T =40; % length of time:T*T0.
WZMsmhU@T dt = T/N; % time step
XC$~! n = [-N/2:1:N/2-1]'; % Index
NanU%# & t = n.*dt;
+!<`$+W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
pr?/rXw w=2*pi*n./T;
ooAZ,l=8 g1=-i*ww./2;
Pv'x|p* g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
gu/Yc`S[ g3=-i*ww./2;
J0K"WmW P1=0;
v+OVZDf P2=0;
oHYD6 qJX{ P3=1;
-K !-a'J P=0;
- "<f( for m1=1:M1
}8SHw|- p=0.032*m1; %input amplitude
bcYz ?o6 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
cBA[ D~s s1=s10;
~RJg.9V s20=0.*s10; %input in waveguide 2
}>w;
+XU s30=0.*s10; %input in waveguide 3
WIghP5% W s2=s20;
&-zI7@! s3=s30;
DkIkiw{L p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
u|ZO"t %energy in waveguide 1
7jPmI p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
9+:Trc\%N %energy in waveguide 2
phdN9<Z p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
/[s$A? %energy in waveguide 3
8 7Kx7CKF" for m3 = 1:1:M3 % Start space evolution
'3Ri/V, s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
jt3S A
[cy s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
tFwlx3 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
L:<'TXsRA sca1 = fftshift(fft(s1)); % Take Fourier transform
c>g%oE sca2 = fftshift(fft(s2));
".\(A f2 sca3 = fftshift(fft(s3));
SS`C0&I@p sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
j7d;1 zB+G sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
u v5@Alm sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
hq BRh+[ s3 = ifft(fftshift(sc3));
{
\ePJG# s2 = ifft(fftshift(sc2)); % Return to physical space
*/)gk=x8 s1 = ifft(fftshift(sc1));
h2>0#Vp3j end
:q=OW1^k^ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
5f5ZfK3<i p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
>W< 5$ .G p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
mm 8O P1=[P1 p1/p10];
-}J8|gwwp P2=[P2 p2/p10];
R32d(2%5K P3=[P3 p3/p10];
[OcD#~drO P=[P p*p];
DkIF vsLK end
93\,m+- figure(1)
2}b bdX x plot(P,P1, P,P2, P,P3);
sn( }5; BP6Shc|C 转自：
http://blog.163.com/opto_wang/
