计算脉冲在非线性耦合器中演化的Matlab 程序 |R9Lben', BmX'%5ho % This Matlab script file solves the coupled nonlinear Schrodinger equations of
uE's& H % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
h0PDFMM< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
g s'M^|e) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
NpH8=H9 D;Qx 9^. %fid=fopen('e21.dat','w');
2`f{D ~w N = 128; % Number of Fourier modes (Time domain sampling points)
EsGu#lD2 M1 =3000; % Total number of space steps
cZh0\Dy U J =100; % Steps between output of space
p1 KhI;^ T =10; % length of time windows:T*T0
L jy797{f T0=0.1; % input pulse width
aN0[6+KP; MN1=0; % initial value for the space output location
st RM *. dt = T/N; % time step
~71U s n = [-N/2:1:N/2-1]'; % Index
P=n_wE t = n.*dt;
[inlxJD u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
juHL$SGC u20=u10.*0.0; % input to waveguide 2
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u1=u10; u2=u20;
g"P%sA/E+ U1 = u1;
M|DMo i8x U2 = u2; % Compute initial condition; save it in U
Sb`[ +i' ` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
64/Zf XD w=2*pi*n./T;
M/<ypJ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
JH . XZM& L=4; % length of evoluation to compare with S. Trillo's paper
uuY^Q;^I* dz=L/M1; % space step, make sure nonlinear<0.05
kd'b_D[$H for m1 = 1:1:M1 % Start space evolution
W;OGdAa_ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
b9j}QK u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
]F y' M ca1 = fftshift(fft(u1)); % Take Fourier transform
(kxS0 ]= ca2 = fftshift(fft(u2));
;73S;IPR c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Q#p)?:o/ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
9<Pg2#*N0 u2 = ifft(fftshift(c2)); % Return to physical space
rRe5Q u1 = ifft(fftshift(c1));
0nw i5 if rem(m1,J) == 0 % Save output every J steps.
Xw4Eti._D U1 = [U1 u1]; % put solutions in U array
2w.FC U2=[U2 u2];
u n v:sV#b MN1=[MN1 m1];
R
(f:U C z1=dz*MN1'; % output location
}QI \K end
8:TX9`, end
bg zd($)u hg=abs(U1').*abs(U1'); % for data write to excel
AIHH@z ha=[z1 hg]; % for data write to excel
-N' (2' t1=[0 t'];
KTm^}')C8 hh=[t1' ha']; % for data write to excel file
b-& rMM L %dlmwrite('aa',hh,'\t'); % save data in the excel format
#z(:n5$F figure(1)
1TZ[i waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
m^ xTV-#l@ figure(2)
gNZwD6GMe? waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
kZ%
AGc E^-c,4'F 非线性超快脉冲耦合的数值方法的Matlab程序 !BoGSI fV"Y/9}( 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。
;?Pz 0,{h 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
9
/H~hEVK l+Wux$6U 8>C4w 5kF ,Q"'q0hM= % This Matlab script file solves the nonlinear Schrodinger equations
0f qcPi % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
=IL\T8y09 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+-!3ruwSn % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7UBDd1 3 /RwCtc C=1;
b~.$1oZ M1=120, % integer for amplitude
LDg9@esi M3=5000; % integer for length of coupler
s\d3u` G N = 512; % Number of Fourier modes (Time domain sampling points)
Gpu[<Z4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
n{ QyqI T =40; % length of time:T*T0.
mlByE,S2E dt = T/N; % time step
.F ?ww}2p] n = [-N/2:1:N/2-1]'; % Index
"Da 1BuX\ t = n.*dt;
?A@y4<8R| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
12^uu)6Xm, w=2*pi*n./T;
:-x?g2M Y g1=-i*ww./2;
0N1t.3U g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ranem0KQ)] g3=-i*ww./2;
hlVC+%8 P1=0;
f,O10`4s P2=0;
Xq1#rK( P3=1;
I[%IW4jJ P=0;
KGJSGvo+y for m1=1:M1
t]&.'n, p=0.032*m1; %input amplitude
n~lB } s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
`ulQ C s1=s10;
>)K3 s20=0.*s10; %input in waveguide 2
P"7` : a s30=0.*s10; %input in waveguide 3
s`x2Go s2=s20;
0Px Hf* s3=s30;
!hHe` p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
bm;iX*~ %energy in waveguide 1
7T[L5-g p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
T]0K4dp+ %energy in waveguide 2
4b}p[9k p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
L s2OnL9 %energy in waveguide 3
u/W{JPlL for m3 = 1:1:M3 % Start space evolution
\0|x<~#j' s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
C 9%bD s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
TD\TVK3P s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
i<S \x sca1 = fftshift(fft(s1)); % Take Fourier transform
pKLcg"{[F sca2 = fftshift(fft(s2));
ta&z lZt sca3 = fftshift(fft(s3));
UW":&`i sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
(B` NnL$ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
NL.3qx sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
_U}|Le@ e s3 = ifft(fftshift(sc3));
:/6:&7s s2 = ifft(fftshift(sc2)); % Return to physical space
U$D:gZ s1 = ifft(fftshift(sc1));
*e ffDNE! end
Gh_5$@ hF p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
]9 @4P$I p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
86%k2~L
p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
/;_$:`|/ P1=[P1 p1/p10];
<2* +Y|Lk2 P2=[P2 p2/p10];
kX V P3=[P3 p3/p10];
C=c&.-Nb9 P=[P p*p];
@{V`g8P> end
%w_MR C figure(1)
="T}mc plot(P,P1, P,P2, P,P3);
h(2{+Y+ p!DdX 转自：
http://blog.163.com/opto_wang/
