计算脉冲在非线性耦合器中演化的Matlab 程序 *MQ`&;Qa, G &08Qb ,N % This Matlab script file solves the coupled nonlinear Schrodinger equations of
IyAD>Q^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
""*g\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
BZ(I]:oDL % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
k 7:Z\RGy N_/+B]r }T %fid=fopen('e21.dat','w');
tG~[E,/` N = 128; % Number of Fourier modes (Time domain sampling points)
%M:$ML6b< M1 =3000; % Total number of space steps
w F3 MzN=% J =100; % Steps between output of space
-A zOujSS T =10; % length of time windows:T*T0
x"r,l/gzy T0=0.1; % input pulse width
3-'3w , MN1=0; % initial value for the space output location
MjWxfW/ dt = T/N; % time step
M3r;Pdj2r n = [-N/2:1:N/2-1]'; % Index
f Xh{ _> t = n.*dt;
txE+A/>i9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
dsH*9t:z u20=u10.*0.0; % input to waveguide 2
vM50H u1=u10; u2=u20;
g>l+oH[Tv| U1 = u1;
-hc8IS U2 = u2; % Compute initial condition; save it in U
i[ :c G ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
}F"98s W w=2*pi*n./T;
SM8_C!h: g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
9E NI %Jz L=4; % length of evoluation to compare with S. Trillo's paper
.R
l7,1\ dz=L/M1; % space step, make sure nonlinear<0.05
`F3wO! for m1 = 1:1:M1 % Start space evolution
~+ 9v z u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
pC #LQ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
`?b'.Z_J ca1 = fftshift(fft(u1)); % Take Fourier transform
V7.g , ca2 = fftshift(fft(u2));
.(3ec/i4CF c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
X?XB!D7[ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
v\_ \bT1 u2 = ifft(fftshift(c2)); % Return to physical space
IUNr<w< u1 = ifft(fftshift(c1));
q^?a|l if rem(m1,J) == 0 % Save output every J steps.
# sxv?r U1 = [U1 u1]; % put solutions in U array
dMCoN8W U2=[U2 u2];
jw`05rw: MN1=[MN1 m1];
a=`]
L`|N z1=dz*MN1'; % output location
jsx&h
Y%( end
zWH)\>X59 end
-m@PqJF^ hg=abs(U1').*abs(U1'); % for data write to excel
WIuYSt)h ha=[z1 hg]; % for data write to excel
r-yUWIr
S t1=[0 t'];
*,IK4F6>: hh=[t1' ha']; % for data write to excel file
v5@M 34 %dlmwrite('aa',hh,'\t'); % save data in the excel format
;FW <% figure(1)
-/V(Z+dj waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
(m6 V)y figure(2)
o8|qT)O@U waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ifu!6_b. dfKGO$}V 非线性超快脉冲耦合的数值方法的Matlab程序 vbd)L$$20+ W)J MV 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。
IvlfX`(" 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
V1pBKr)v Dh}(B$~Oz+ VBw 5[ S[zGA<} % This Matlab script file solves the nonlinear Schrodinger equations
AI Kz]J0; % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
([}08OW@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
nO! &;E& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
z;F HZb9t, OM{ ^F=Ap C=1;
m C`*#[ M1=120, % integer for amplitude
bX,#z, M3=5000; % integer for length of coupler
j7lJ7BIr N = 512; % Number of Fourier modes (Time domain sampling points)
t$wb wP dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
`-Ozjb M T =40; % length of time:T*T0.
1dw{:X=j dt = T/N; % time step
@!u{>!~0 n = [-N/2:1:N/2-1]'; % Index
+ima$a0Zyt t = n.*dt;
3T0~ k-- ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
yNow hh w=2*pi*n./T;
{\CWoFht> g1=-i*ww./2;
4(LLRzzW g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
GK!@|Kk8q7 g3=-i*ww./2;
xr7}@rq"U< P1=0;
BxjSo ^n P2=0;
p:5NMo P3=1;
Y0T :% P=0;
`[g$EXX for m1=1:M1
kfZ `|w@q p=0.032*m1; %input amplitude
Qrg- xu= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-Dx3*Zh P s1=s10;
X:$vP'B> s20=0.*s10; %input in waveguide 2
}7(+#ISK6 s30=0.*s10; %input in waveguide 3
] % HxzJ s2=s20;
I;%1xdPt s3=s30;
e15yDwvB p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
-0#"<!N %energy in waveguide 1
PA
?2K4 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
6?~9{0 %energy in waveguide 2
0NGth(2 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
$q z{L~ < %energy in waveguide 3
] xHiy+ for m3 = 1:1:M3 % Start space evolution
6j XDLI s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
n:OXv}pv s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|1(x2x%}D^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
'ia-h7QWS sca1 = fftshift(fft(s1)); % Take Fourier transform
C@eL9R;N1 sca2 = fftshift(fft(s2));
t;6 < k7h sca3 = fftshift(fft(s3));
b4-gNF]Yt sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#e-K It sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
O-
QT+] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
?'+]d;U O& s3 = ifft(fftshift(sc3));
O>qlWPht s2 = ifft(fftshift(sc2)); % Return to physical space
m~AAO{\:b s1 = ifft(fftshift(sc1));
) 'T].kWW end
2Ax"X12{6 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
8sG?|u p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
?Y3i-jY p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
$q:l \ P1=[P1 p1/p10];
hmo4H3g!N P2=[P2 p2/p10];
L?+N:G
P3=[P3 p3/p10];
:?\29j#*V P=[P p*p];
py:L- 5 end
* @]wT ' figure(1)
C /Tk`C& plot(P,P1, P,P2, P,P3);
(m:Q'4Ep 1 >rQ).eT 转自：
http://blog.163.com/opto_wang/
