计算脉冲在非线性耦合器中演化的Matlab 程序 xD # I&. mzB#O;3= % This Matlab script file solves the coupled nonlinear Schrodinger equations of
2w|u)ow ) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?ev G=S4> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
IKDjat n % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|u ;BAb wmE,k1 G %fid=fopen('e21.dat','w');
[ |n-x3h N = 128; % Number of Fourier modes (Time domain sampling points)
xqWrW) M1 =3000; % Total number of space steps
^3|$wB= J =100; % Steps between output of space
4 sBoD=e T =10; % length of time windows:T*T0
Kw0V4UF T0=0.1; % input pulse width
DD 5EHJR MN1=0; % initial value for the space output location
]8>UII ,US dt = T/N; % time step
MD4 j~q\ g n = [-N/2:1:N/2-1]'; % Index
DG*o
w^ t = n.*dt;
+N$7=oGC u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Jf<yTAm u20=u10.*0.0; % input to waveguide 2
$lAb6e$n u1=u10; u2=u20;
\G=R hx f U1 = u1;
jfP J5]Z U2 = u2; % Compute initial condition; save it in U
[RFK-E ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
qV8\/7'A0a w=2*pi*n./T;
N E 2sD g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ilp;@O6 L=4; % length of evoluation to compare with S. Trillo's paper
m2uML*&O5K dz=L/M1; % space step, make sure nonlinear<0.05
L +rySP for m1 = 1:1:M1 % Start space evolution
0 , Qj: u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
*<1x:PR u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
9=~H6(m> ca1 = fftshift(fft(u1)); % Take Fourier transform
w+9C/U;|s ca2 = fftshift(fft(u2));
3b)T}g c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
uM)9b*Vbo c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
0rJ\e u2 = ifft(fftshift(c2)); % Return to physical space
W|rFl]~a u1 = ifft(fftshift(c1));
# 1dTM- if rem(m1,J) == 0 % Save output every J steps.
% r U1 = [U1 u1]; % put solutions in U array
_Kl{50}] U2=[U2 u2];
EXW
6yXLV MN1=[MN1 m1];
sJI - z1=dz*MN1'; % output location
.V 3X#t end
M |Q end
Q `p}X&^a hg=abs(U1').*abs(U1'); % for data write to excel
h[je _^5 ha=[z1 hg]; % for data write to excel
b|ksMB>) t1=[0 t'];
?Y6la.bc{ hh=[t1' ha']; % for data write to excel file
4R*<WdT( %dlmwrite('aa',hh,'\t'); % save data in the excel format
JIb zh?$aD figure(1)
95?5=T F waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
C+(Gg^ w figure(2)
t:"=]zUU waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
C*y6~AYN# QV'3O| 非线性超快脉冲耦合的数值方法的Matlab程序 Y 6<0% ~?`9i>3W~ 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。
G9'YgW+$7 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\B>[je-d ??zABV 8~s-t Fe& n, % This Matlab script file solves the nonlinear Schrodinger equations
OZC/+"\, % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
X \p`pw$ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
JM+sHHs % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
uU[[[LQq tU)r[2H2 C=1;
*@G(3 n M1=120, % integer for amplitude
}lC64;yo M3=5000; % integer for length of coupler
K+ 7yUF8XP N = 512; % Number of Fourier modes (Time domain sampling points)
g=oeS%>E dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
wwK~H T =40; % length of time:T*T0.
ndKvJH 4 dt = T/N; % time step
Ic{ 'H2~4, n = [-N/2:1:N/2-1]'; % Index
q]iKz%|Z/ t = n.*dt;
@ wB'3q}( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m.HX2(&\3 w=2*pi*n./T;
.sJys SA\ g1=-i*ww./2;
*3F /Ft5 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
fV A=<: g3=-i*ww./2;
W p7@ P1=0;
> G4HZE P2=0;
CFkW@\] P3=1;
7S A-OFM P=0;
vSYun I for m1=1:M1
e}?1T7NPG] p=0.032*m1; %input amplitude
@;m@Luk s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-VreBKn s1=s10;
J/]o WC`u s20=0.*s10; %input in waveguide 2
2sd ) w s30=0.*s10; %input in waveguide 3
EG(`E9DZ s2=s20;
5Aa31"43n s3=s30;
7}#*3*] p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
B~V<n&< %energy in waveguide 1
"5o;z@(
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
&e HM#as %energy in waveguide 2
')P2O\YS p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
(^tr }?C %energy in waveguide 3
je- , S>U for m3 = 1:1:M3 % Start space evolution
X ]pR,\B s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
8u:v:>D.' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
@pqY9_:P1 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
kO..~@ aY sca1 = fftshift(fft(s1)); % Take Fourier transform
To# E@Nw sca2 = fftshift(fft(s2));
"q9~ C sca3 = fftshift(fft(s3));
y"|K
|QT sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#uD)0zdw sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
]HJ{dcF sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
;1 *m} uNz s3 = ifft(fftshift(sc3));
P<cMP)+K s2 = ifft(fftshift(sc2)); % Return to physical space
Xb(CH#*{z s1 = ifft(fftshift(sc1));
HQ| o%9~ end
F.~n p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
2d5}`> p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
(aDb^(]> p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[|:QE~U@ P1=[P1 p1/p10];
5 4ak <&? P2=[P2 p2/p10];
zmy4tsmX P3=[P3 p3/p10];
_" ?c9 P=[P p*p];
p |&ZJ@3 end
?
-v figure(1)
1&X}1 plot(P,P1, P,P2, P,P3);
b lRY7 _L&n&y1+% 转自：
http://blog.163.com/opto_wang/
