计算脉冲在非线性耦合器中演化的Matlab 程序 /w| YNDA]j ,Vogo5~X % This Matlab script file solves the coupled nonlinear Schrodinger equations of
F>&8b^v bn % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
ka (xU#; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>+1bTt/-F % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
h0GXN\xI @8 pRI S"V %fid=fopen('e21.dat','w');
tIg_cY_y N = 128; % Number of Fourier modes (Time domain sampling points)
Uc/%4Gx M1 =3000; % Total number of space steps
|i| O9^*% J =100; % Steps between output of space
__a9}m4i7x T =10; % length of time windows:T*T0
3KqylC &. T0=0.1; % input pulse width
m~}nM |m% MN1=0; % initial value for the space output location
GK)hK-
dt = T/N; % time step
hfY2pG9N n = [-N/2:1:N/2-1]'; % Index
[P<oyd@# t = n.*dt;
u}pLO9V"` u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
].$N@t C u20=u10.*0.0; % input to waveguide 2
'rSM6j u1=u10; u2=u20;
^ *ZO@GNL U1 = u1;
D;Z\GnD U2 = u2; % Compute initial condition; save it in U
"Aynt_a. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#e=[W) ) w=2*pi*n./T;
B$ {Q Y)t g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
KjhOz%Yt[o L=4; % length of evoluation to compare with S. Trillo's paper
a^,Xm(Wb} dz=L/M1; % space step, make sure nonlinear<0.05
ETmfy}V8 for m1 = 1:1:M1 % Start space evolution
i#
QI}r u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Er{yQIi0L u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
j_k!9"bt ca1 = fftshift(fft(u1)); % Take Fourier transform
x]F:~(P ca2 = fftshift(fft(u2));
#
T vY*D, c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
m~2PpO c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
gI[x O K# u2 = ifft(fftshift(c2)); % Return to physical space
W & * 0F~ u1 = ifft(fftshift(c1));
z+;+c$X if rem(m1,J) == 0 % Save output every J steps.
/: B!hvpw U1 = [U1 u1]; % put solutions in U array
$[H3O(B0* U2=[U2 u2];
R+P1 +5 MN1=[MN1 m1];
SoCa_9*X z1=dz*MN1'; % output location
xw ` Pq6 end
Qv#]T, end
gVb;sk^ hg=abs(U1').*abs(U1'); % for data write to excel
aK 'BC>uFI ha=[z1 hg]; % for data write to excel
?xIw Q d0 t1=[0 t'];
y<kW2 <? hh=[t1' ha']; % for data write to excel file
orJN# 0v4 %dlmwrite('aa',hh,'\t'); % save data in the excel format
E-CZk_K9 figure(1)
}s? 9Hnqa waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
li (g?|AD figure(2)
U4Il1|
M& waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Zhf+u
r ^`ny]3JA 非线性超快脉冲耦合的数值方法的Matlab程序 3b~k)t4R H|5\c= 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
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X! d*4 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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k3/t qEE
V& 6,| !zaeS Z!D GCw % This Matlab script file solves the nonlinear Schrodinger equations
~~z} yCl % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Db@$' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
|BN^5m qP6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.O@T#0&=_ 4 1q|R[js! C=1;
]U82A**n M1=120, % integer for amplitude
4'[/gMUkw M3=5000; % integer for length of coupler
8!sl) R N = 512; % Number of Fourier modes (Time domain sampling points)
} Dp/K4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^i:%0"[*^i T =40; % length of time:T*T0.
/d*d '3{c dt = T/N; % time step
,Tjc\;~% n = [-N/2:1:N/2-1]'; % Index
OF-$* t = n.*dt;
"=@X>jUc ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
^- Bx zOp w=2*pi*n./T;
q-}q r g g1=-i*ww./2;
B^nE^"b g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
d#NG]V/
g3=-i*ww./2;
^\KZE|^3@ P1=0;
WS6'R P2=0;
NH~\kV P3=1;
muc6gwBp P=0;
l$
^LY)i for m1=1:M1
>cJf D9-<h p=0.032*m1; %input amplitude
Yv >kToa\^ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
(l}W\iB' d s1=s10;
F! ZE4S_ s20=0.*s10; %input in waveguide 2
~Z-o2+xA s30=0.*s10; %input in waveguide 3
Qh3BI?GZ'3 s2=s20;
UU'0WIbY6 s3=s30;
juIi-*R! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
_Oc5g5_{ %energy in waveguide 1
_Fkz^B* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Kjzo>fIC{ %energy in waveguide 2
=S#9\W& 6Q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
|kG j}v3 %energy in waveguide 3
O3 NI for m3 = 1:1:M3 % Start space evolution
#83`T&Xw* s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}JI@f14 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
H< 51dJn~ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
e|>
5
R sca1 = fftshift(fft(s1)); % Take Fourier transform
Gu@n1/m@o sca2 = fftshift(fft(s2));
m55|&Ux| sca3 = fftshift(fft(s3));
X)Zc*9XA sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
?&U g"$v sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
M47t(9krV sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
4]G J+a s3 = ifft(fftshift(sc3));
.7BJq?K. s2 = ifft(fftshift(sc2)); % Return to physical space
w#}[=jy s1 = ifft(fftshift(sc1));
duQ , 6 end
x 4bmV@b p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!{q_ Q ! p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
m )Ta5w^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
#fy3 i+ P1=[P1 p1/p10];
X rl# DN P2=[P2 p2/p10];
~)CGwST [ P3=[P3 p3/p10];
7 D&O5Z=%+ P=[P p*p];
Ua%;h I)j$ end
g~p43sVV figure(1)
j[CXIz?c plot(P,P1, P,P2, P,P3);
q\Q'9Rl0( T {:8,CiW 转自：
http://blog.163.com/opto_wang/
