计算脉冲在非线性耦合器中演化的Matlab 程序 S($Su7g%_ ZnW@YC#9 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
2;2}wM[ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Ki br ]w % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
d0'H DVd % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
LP];x3 ?K_
'@ %fid=fopen('e21.dat','w');
*\G)z|^yx N = 128; % Number of Fourier modes (Time domain sampling points)
p{D4"Qn+P9 M1 =3000; % Total number of space steps
!b nyJA J =100; % Steps between output of space
1} %B%*N T =10; % length of time windows:T*T0
aUU7{o_Z T0=0.1; % input pulse width
lIRlMLuG MN1=0; % initial value for the space output location
0Ua%DyJ dt = T/N; % time step
, %9df+5k n = [-N/2:1:N/2-1]'; % Index
K/=|8+IDL t = n.*dt;
a<~77~"4wn u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
oc z G|_ u20=u10.*0.0; % input to waveguide 2
"N?+VkZEv u1=u10; u2=u20;
%McE` 155 U1 = u1;
O @V%Cu U2 = u2; % Compute initial condition; save it in U
ml`8HXK0 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
dG7OqA:9 w=2*pi*n./T;
457\& g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
0Hxmm@ X2 L=4; % length of evoluation to compare with S. Trillo's paper
-G7TEq) dz=L/M1; % space step, make sure nonlinear<0.05
vw,rF`L jZ for m1 = 1:1:M1 % Start space evolution
|yEa5rd?W u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
T~0k"uTE u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
}7E^ZZ]f ca1 = fftshift(fft(u1)); % Take Fourier transform
V w|| !d ca2 = fftshift(fft(u2));
@a:>$t c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
VHJM*&5 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
f y :,_# u2 = ifft(fftshift(c2)); % Return to physical space
j)C,%Ol u1 = ifft(fftshift(c1));
,'xYlH 3s if rem(m1,J) == 0 % Save output every J steps.
y*pUlts< U1 = [U1 u1]; % put solutions in U array
{!t7[Ctb U2=[U2 u2];
x^4xq#Bb7 MN1=[MN1 m1];
*t[. =_v z1=dz*MN1'; % output location
D=m 'pL/pl end
FC i U end
J_ x13EaV0 hg=abs(U1').*abs(U1'); % for data write to excel
9l,a^@Y: ha=[z1 hg]; % for data write to excel
3b' QLfU&# t1=[0 t'];
1cS}J:0P hh=[t1' ha']; % for data write to excel file
NS%WeAf %dlmwrite('aa',hh,'\t'); % save data in the excel format
}by;F9&B figure(1)
5[0
O'%$ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
h3LE>}6D figure(2)
$,+O9 Et waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
r\qj! V-<GT ? 非线性超快脉冲耦合的数值方法的Matlab程序 h$4Hw+Yxs] Zjbc3 M5 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。
[<DZ*|+ 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
R"
;x vo* P"B0_EuR<T Ag{i q (X 3|.um_ % This Matlab script file solves the nonlinear Schrodinger equations
B2-V@ 06 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
yKYTi3 _( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/ "eey(X % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
JSW^dw& G:~k.1y[ C=1;
=c/wplv* M1=120, % integer for amplitude
N[<\>Ps|u M3=5000; % integer for length of coupler
bGc~W r| N = 512; % Number of Fourier modes (Time domain sampling points)
ma"3qGy dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
{
^cV lC_ T =40; % length of time:T*T0.
>-H {Z{VDd dt = T/N; % time step
S H! n = [-N/2:1:N/2-1]'; % Index
0NS<?p~_S t = n.*dt;
G 6T_O ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l
c+g &f w=2*pi*n./T;
b )B?
F g1=-i*ww./2;
ee yHy"@ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
!o:f$6EA~C g3=-i*ww./2;
{phNds% P1=0;
1v71rf&w P2=0;
vQ;Ex P3=1;
9WyAb3d' P=0;
:]\([Q+a for m1=1:M1
|Y ?H A& p=0.032*m1; %input amplitude
d3D] k, s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
9I}-[|`u s1=s10;
M7pOLP_1jB s20=0.*s10; %input in waveguide 2
u 6AA 4( s30=0.*s10; %input in waveguide 3
$<}$DH_Y s2=s20;
\Wxuk YH s3=s30;
vEJWFoeEFm p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ZrsBm_Rx %energy in waveguide 1
a{ L
d p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
I}1NB3>^ %energy in waveguide 2
#qK:J;Sn3 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
G3Z)Z) N %energy in waveguide 3
&5yV xL: for m3 = 1:1:M3 % Start space evolution
KV(Q;~8"X s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
SLa >7`<Q s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
y*qVc E s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
17%Mw@+ sca1 = fftshift(fft(s1)); % Take Fourier transform
nAv#?1cjz sca2 = fftshift(fft(s2));
\W~ N sca3 = fftshift(fft(s3));
Z&1\{PG3* sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
f4fvrL sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
h2G$@8t}I sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
3 2&;`]C s3 = ifft(fftshift(sc3));
]n6# VTz* s2 = ifft(fftshift(sc2)); % Return to physical space
Fld=5B^} s1 = ifft(fftshift(sc1));
e"|efE end
hgPa6Kd p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
+S o4r A*9 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
h`^jyoF"( p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
b,7k)ND1F P1=[P1 p1/p10];
b3=rG(0f P2=[P2 p2/p10];
F3On?x) P3=[P3 p3/p10];
l9{hq/V P=[P p*p];
-|$@-fY; end
v[1aW v: figure(1)
H\ F :95 plot(P,P1, P,P2, P,P3);
Cd#(X@n wW>A_{Y 转自：
http://blog.163.com/opto_wang/
