计算脉冲在非线性耦合器中演化的Matlab 程序 0.0!5D[ = lD]sk % This Matlab script file solves the coupled nonlinear Schrodinger equations of
+N@F,3yNa % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&/?j MyD@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0 Wm-` ZA % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
tY=TY{ RY 2f4 c;YS %fid=fopen('e21.dat','w');
RZ%X1$ N = 128; % Number of Fourier modes (Time domain sampling points)
0z#kV}wE M1 =3000; % Total number of space steps
=7,U qMl_ J =100; % Steps between output of space
)&<ExJQ& T =10; % length of time windows:T*T0
eR`<9 KBH T0=0.1; % input pulse width
@E;pT3; ) MN1=0; % initial value for the space output location
#B9[U}
8 dt = T/N; % time step
8m<<tv. n = [-N/2:1:N/2-1]'; % Index
3Q)>gh* t = n.*dt;
-P&e4sV{ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
IBh~(6 u20=u10.*0.0; % input to waveguide 2
Fo~v.+^? u1=u10; u2=u20;
18`%WUPnT U1 = u1;
N2e<Y_T U2 = u2; % Compute initial condition; save it in U
V+z)B+ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
x v l w=2*pi*n./T;
X+8p2xSO| g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
,ua1xsZl& L=4; % length of evoluation to compare with S. Trillo's paper
f tDV 3If dz=L/M1; % space step, make sure nonlinear<0.05
-~fI|A ^ for m1 = 1:1:M1 % Start space evolution
,[ L$ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
q04Dj-2< u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-+_&#twU ca1 = fftshift(fft(u1)); % Take Fourier transform
3PffQ,c[~ ca2 = fftshift(fft(u2));
@D=`iG% c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&J:)*EjVl5 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
$uh DBmb u2 = ifft(fftshift(c2)); % Return to physical space
Bx4GFCdifC u1 = ifft(fftshift(c1));
A o$z )<d' if rem(m1,J) == 0 % Save output every J steps.
G -
WJlu U1 = [U1 u1]; % put solutions in U array
/vu!5?S U2=[U2 u2];
qV,j) b3M MN1=[MN1 m1];
fM.|#eLi z1=dz*MN1'; % output location
Sw'?$j^3 end
9YhsJ~"Q end
zX `RN )C hg=abs(U1').*abs(U1'); % for data write to excel
0 +LloB ha=[z1 hg]; % for data write to excel
M k?I} t1=[0 t'];
0B/a$NC hh=[t1' ha']; % for data write to excel file
G9Tix\SpF %dlmwrite('aa',hh,'\t'); % save data in the excel format
|'_<(z figure(1)
|"v{RC0 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
':4pH#E figure(2)
*'-^R9dN.S waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
&Sa~Wtm |* 7+4"+CA 非线性超快脉冲耦合的数值方法的Matlab程序 c\MDOD%9 D7/Bp4I#o 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。
|>GIPfVT 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
I xBO$ 2 8 f5^@K\c DjvgKy=Jr_ I=a$1%BzEX % This Matlab script file solves the nonlinear Schrodinger equations
# HYkzjb % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
:j4
[_9\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
HYmXPpse % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
);H[lKy
k Z%W?# C=1;
\;gt&*$- M1=120, % integer for amplitude
*PU,Rc()6 M3=5000; % integer for length of coupler
Z]\^.x9S N = 512; % Number of Fourier modes (Time domain sampling points)
NI:N
W-! dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
4LJ}>e T =40; % length of time:T*T0.
U-<"i6mg ? dt = T/N; % time step
g>P9hIl n = [-N/2:1:N/2-1]'; % Index
]
Nipo'N; t = n.*dt;
KB A% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
' PYqp&gJ w=2*pi*n./T;
N\p]+[6 g1=-i*ww./2;
v=-3 ,C g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
,s&~U<Z g3=-i*ww./2;
Uy|=A7Ad
c P1=0;
-wMW@:M_ P2=0;
[ {LnE: P3=1;
j)6B^! P=0;
PGl -2 Cr for m1=1:M1
N2s%p6RMPD p=0.032*m1; %input amplitude
bKZ#>%|:o s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Q9tE ^d+% s1=s10;
u@u.N2H.% s20=0.*s10; %input in waveguide 2
W+C_=7_ s30=0.*s10; %input in waveguide 3
Vp"Ug,1 s2=s20;
Go7hDmu s3=s30;
+J8/,d p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
$!C+i"q$ %energy in waveguide 1
_k.bGYldk p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
r ;8z"* %energy in waveguide 2
h!CX`pBM p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
)Hm[j)YI %energy in waveguide 3
: ";D.{|| for m3 = 1:1:M3 % Start space evolution
b7sE s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
rGGepd s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
e4%*I8
^e s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ey\{C`(__y sca1 = fftshift(fft(s1)); % Take Fourier transform
4@iJ |l sca2 = fftshift(fft(s2));
G2 { M#H sca3 = fftshift(fft(s3));
AeCG2!8^0 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
H-KwkH`L4 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
(jMAa% sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
}Rxg E~ F s3 = ifft(fftshift(sc3));
$_zkq@ s2 = ifft(fftshift(sc2)); % Return to physical space
(,c?}TP s1 = ifft(fftshift(sc1));
;s. 5\YZ"k end
"u8o?8+q~ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
ww t()
p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
1( 7.V-(G p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
'Mx K}9 P1=[P1 p1/p10];
R:B BNzY}f P2=[P2 p2/p10];
3H}~eEg, P3=[P3 p3/p10];
S*m`' P=[P p*p];
JBEgiQ/ end
AKC foJ figure(1)
Etc?; Z[F# plot(P,P1, P,P2, P,P3);
bZay/ Zkj 6`baQ! xc. 转自：
http://blog.163.com/opto_wang/
