计算脉冲在非线性耦合器中演化的Matlab 程序 &QQ6F>'T UT{`'#iT % This Matlab script file solves the coupled nonlinear Schrodinger equations of
;=P!fvHk % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
G,WLca[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
*@@dO_%6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`N}V i6FG H^o_B1 %fid=fopen('e21.dat','w');
#t Pc<p6m N = 128; % Number of Fourier modes (Time domain sampling points)
LrdED[Z M1 =3000; % Total number of space steps
1)97AkN(O J =100; % Steps between output of space
e+#k\x T =10; % length of time windows:T*T0
By[M|4a T0=0.1; % input pulse width
/ioBc}] MN1=0; % initial value for the space output location
W 4P\H M>2 dt = T/N; % time step
+,7v bs3 n = [-N/2:1:N/2-1]'; % Index
Fku<|1}&y t = n.*dt;
NyC&j`d u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
uTO%O}D N u20=u10.*0.0; % input to waveguide 2
!% (kMN u1=u10; u2=u20;
X LYGhM U1 = u1;
X< W${L$G U2 = u2; % Compute initial condition; save it in U
3 TV4|&W; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
CO, { / w=2*pi*n./T;
e1V1A e g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
7z\ #"~(. L=4; % length of evoluation to compare with S. Trillo's paper
Y HS/|- dz=L/M1; % space step, make sure nonlinear<0.05
' qT\I8% for m1 = 1:1:M1 % Start space evolution
][//G|9 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
iM1E**WCtv u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
805oV(- ca1 = fftshift(fft(u1)); % Take Fourier transform
&>Z;>6J, ca2 = fftshift(fft(u2));
hZo f c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
e `JWY9% c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
~-sG& u> u2 = ifft(fftshift(c2)); % Return to physical space
p,(W?.ZDN? u1 = ifft(fftshift(c1));
64"DT3: if rem(m1,J) == 0 % Save output every J steps.
5L7 nEia' U1 = [U1 u1]; % put solutions in U array
Ks^wX U2=[U2 u2];
y=
8SD7P' MN1=[MN1 m1];
Fwvc+ a z1=dz*MN1'; % output location
5V/]7>b1 end
e:N;Jx# end
m9 c`"! hg=abs(U1').*abs(U1'); % for data write to excel
P,G
: 9x"e ha=[z1 hg]; % for data write to excel
Y>8 JHoV t1=[0 t'];
]70ZerQ~L hh=[t1' ha']; % for data write to excel file
oxnI/Z %dlmwrite('aa',hh,'\t'); % save data in the excel format
|,H 2ge figure(1)
.Tw:Y,G waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
p7izy$Wc figure(2)
/#t::b+>x waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
#tw_`yh Jko=E
非线性超快脉冲耦合的数值方法的Matlab程序 5vS[{;<& R S>qP;V*- 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
qf@P9M Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@1bl<27 BT3yrq9 (?GW/pLK] VS7 % This Matlab script file solves the nonlinear Schrodinger equations
ru1^. (W2 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
![I|hB % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
[yc7F0Aw % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
v< (+ l)Ln Q$k#q<+0 C=1;
+T,A^(&t M1=120, % integer for amplitude
p)m5|GH24 M3=5000; % integer for length of coupler
E1w8d4P,G N = 512; % Number of Fourier modes (Time domain sampling points)
7.)_H dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
O OABn* T =40; % length of time:T*T0.
79o=HiOF99 dt = T/N; % time step
7>0/$i#'Vl n = [-N/2:1:N/2-1]'; % Index
FK hgUnw t = n.*dt;
CeUXGa|C ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0$=U\[og w=2*pi*n./T;
6V6Mo}QF
s g1=-i*ww./2;
X1[zkb g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
TnKOr~ @* g3=-i*ww./2;
cBOt=vg,5 P1=0;
Be^"sC P2=0;
0 xvSi9 P3=1;
{ utnbt mu P=0;
utn,`v for m1=1:M1
4L97UhLL p=0.032*m1; %input amplitude
Z> X]'q03 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
S<i. O s1=s10;
V|awbff: s20=0.*s10; %input in waveguide 2
LN5q_ZvR s30=0.*s10; %input in waveguide 3
nYv keT s2=s20;
d@b2XCh< K s3=s30;
V pY,@qh p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
n!Y}D:6c6 %energy in waveguide 1
$
)2zz>4 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
)"2eN3H/ %energy in waveguide 2
mjk<FXW p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
b+f
' %energy in waveguide 3
C } L2'l, for m3 = 1:1:M3 % Start space evolution
Y~#F\ v s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
KilN`?EJ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
a^[s[j#^, s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
M[-/ &;`f@ sca1 = fftshift(fft(s1)); % Take Fourier transform
vI48*&]wTf sca2 = fftshift(fft(s2));
:C0)[L sca3 = fftshift(fft(s3));
^AXH}g sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
D)S_ p& sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
:w4N*lV- sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
J^ PFhu s3 = ifft(fftshift(sc3));
p`52 s2 = ifft(fftshift(sc2)); % Return to physical space
INCD5dihJ s1 = ifft(fftshift(sc1));
Q+_z*
end
r5$!41 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
n%02,pC6, p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
zx+}>(U\U p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
i!(5y>I_ P1=[P1 p1/p10];
E2`9H -6e P2=[P2 p2/p10];
<'hoN/g P3=[P3 p3/p10];
I,]q;lEMt P=[P p*p];
(b"q(:5oX end
#%#N.tB 5 figure(1)
*#?9@0b@ plot(P,P1, P,P2, P,P3);
^i3!1cS B=}QgXg 转自：
http://blog.163.com/opto_wang/
