计算脉冲在非线性耦合器中演化的Matlab 程序 nVkx Q?2 T<(1)N1H` % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ITJ{]7N % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
F: %-x=q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
c' cK+32 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_DsA<SJ] EdFCaW}"" %fid=fopen('e21.dat','w');
CXt9 5O? N = 128; % Number of Fourier modes (Time domain sampling points)
hhd%j6 M1 =3000; % Total number of space steps
+GCN63 n X J =100; % Steps between output of space
O b'B? T =10; % length of time windows:T*T0
!/] F.0 T0=0.1; % input pulse width
:T^!<W4 MN1=0; % initial value for the space output location
U-Ia$b-5! dt = T/N; % time step
-^sW{s0Rc n = [-N/2:1:N/2-1]'; % Index
X[/>{rK t = n.*dt;
d: D`rpcC u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
gGF]Dq u20=u10.*0.0; % input to waveguide 2
"fK` F/ u1=u10; u2=u20;
{gh41G;n U1 = u1;
Z9 X<W` U2 = u2; % Compute initial condition; save it in U
Fp'qn'){:# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
I5]=\k($ w=2*pi*n./T;
ldp
x, g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
\kSoDY`l& L=4; % length of evoluation to compare with S. Trillo's paper
$pW6a %7 dz=L/M1; % space step, make sure nonlinear<0.05
^b|Z<oF for m1 = 1:1:M1 % Start space evolution
yg({g
" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
)9/.K'o,dy u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
+B(x:hzY 9 ca1 = fftshift(fft(u1)); % Take Fourier transform
x{K^u" ca2 = fftshift(fft(u2));
9/A$ 3#wF c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
aAM!;3j]B` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
l-s%3E3 u2 = ifft(fftshift(c2)); % Return to physical space
8vQGpIa, u1 = ifft(fftshift(c1));
+;z^qn if rem(m1,J) == 0 % Save output every J steps.
kc*zP= U1 = [U1 u1]; % put solutions in U array
^n8ioL\*i U2=[U2 u2];
| OW/-&) MN1=[MN1 m1];
!ie MhJ5r z1=dz*MN1'; % output location
N>h/!#
ZC end
= 5:L#` . end
` =m[(CLb hg=abs(U1').*abs(U1'); % for data write to excel
V~#e%&73FH ha=[z1 hg]; % for data write to excel
kk|7{83O t1=[0 t'];
aq~>$CHa hh=[t1' ha']; % for data write to excel file
w2*.3I,~)B %dlmwrite('aa',hh,'\t'); % save data in the excel format
Oi# 4|*b{W figure(1)
U'(Exr [ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
n(X {|? figure(2)
/V'^$enK!} waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
=BD} +(3 R&oC9< 非线性超快脉冲耦合的数值方法的Matlab程序 tW<i;2 l ] 5(T{ 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。
5x $/.U
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
+_^Rxx! XA )m8ve)l R Ln sy, Q` ?+w+y7 % This Matlab script file solves the nonlinear Schrodinger equations
$db]b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
j
/d? c5 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
. <xzf4C % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
V+\L@ mz; +65OR' d C=1;
3=[#(p: M1=120, % integer for amplitude
JFOto,6L: M3=5000; % integer for length of coupler
,m4M39MWJ N = 512; % Number of Fourier modes (Time domain sampling points)
2!-? dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
)-qWcf? T =40; % length of time:T*T0.
}iGpuoXT` dt = T/N; % time step
N5W;Zx] n = [-N/2:1:N/2-1]'; % Index
_(J;!, t = n.*dt;
IE;Fu67wi ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
4Vv~ w=2*pi*n./T;
By3y.}'Ub9 g1=-i*ww./2;
[^N8v;O g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
NxOiT#YH g3=-i*ww./2;
8]SJ=c"}Xf P1=0;
GUX! kj P2=0;
]V*ku% L0 P3=1;
i 4sd29v P=0;
|\HYq`!g%7 for m1=1:M1
0P M F)';R p=0.032*m1; %input amplitude
f j
14'T s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
A/bxxB7w s1=s10;
P<.
TiF?@ s20=0.*s10; %input in waveguide 2
l ~bjNhk s30=0.*s10; %input in waveguide 3
Drn{ucIs s2=s20;
J A=9EnTU s3=s30;
N 3M:|D p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Cx
N]fo %energy in waveguide 1
|)%]MK$; p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
/ 5x~3~ %energy in waveguide 2
o0yyP,?yh p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
q,e {t#t %energy in waveguide 3
1/ZvcdYB for m3 = 1:1:M3 % Start space evolution
Z.Otci> J s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
<5 Ye')+ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Yg @&@S] s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
.,-,@ZK sca1 = fftshift(fft(s1)); % Take Fourier transform
g Kp5* sca2 = fftshift(fft(s2));
Z` FEB0$ sca3 = fftshift(fft(s3));
"ITC P<+ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
y15 MWZ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
*8QESF9 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
V XE85 s3 = ifft(fftshift(sc3));
L&gC s2 = ifft(fftshift(sc2)); % Return to physical space
mbf'xGO s1 = ifft(fftshift(sc1));
i146@<\G{P end
3CKd[=-Z p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Ffv v8x p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
?M W *`U p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
"7]YvZYu0 P1=[P1 p1/p10];
<>|&%gmz P2=[P2 p2/p10];
{2A| F{7> P3=[P3 p3/p10];
'ycr/E&m{ P=[P p*p];
">8]Oi;g end
2
}9of[ figure(1)
kiah,7V/ plot(P,P1, P,P2, P,P3);
3 s @6pI U@ ; W^Mt 转自：
http://blog.163.com/opto_wang/
