计算脉冲在非线性耦合器中演化的Matlab 程序 TRSOO} ;rNd701p" % This Matlab script file solves the coupled nonlinear Schrodinger equations of
:L]-'\y % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
=8O}t+U % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
i B%XBR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!-KCF MvT e-~hS6p( %fid=fopen('e21.dat','w');
b+W)2rFO N = 128; % Number of Fourier modes (Time domain sampling points)
;
Z h9^0 M1 =3000; % Total number of space steps
`f%&<, i J =100; % Steps between output of space
P `}$-#D F T =10; % length of time windows:T*T0
S2Zx &D/_ T0=0.1; % input pulse width
+VwV5iy[` MN1=0; % initial value for the space output location
~GSpl24W< dt = T/N; % time step
w-J"z C n = [-N/2:1:N/2-1]'; % Index
a4% `" t = n.*dt;
,r@xPZPz:e u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
YQN.Ohtv*F u20=u10.*0.0; % input to waveguide 2
}bZ
8-v u1=u10; u2=u20;
M#ZT2~+CT U1 = u1;
>g=^,G}y U2 = u2; % Compute initial condition; save it in U
n.@#rBKZ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
y*w"J3|29 w=2*pi*n./T;
8098y,mQe g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
j z|VF,l L=4; % length of evoluation to compare with S. Trillo's paper
FU[*8^Z dz=L/M1; % space step, make sure nonlinear<0.05
g&Z"_7L~ for m1 = 1:1:M1 % Start space evolution
vxb@9 eb!H u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
x,w8r+~5 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
|4=ihB9+ ca1 = fftshift(fft(u1)); % Take Fourier transform
SK?I. ca2 = fftshift(fft(u2));
? 'Cb-C_ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
H4W1\u c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Umij!=GPG^ u2 = ifft(fftshift(c2)); % Return to physical space
?qy*s3 j'M u1 = ifft(fftshift(c1));
Qr<AV: if rem(m1,J) == 0 % Save output every J steps.
$Tfm/ =e U1 = [U1 u1]; % put solutions in U array
Qy/uB$q{A U2=[U2 u2];
L,#^&9bHa# MN1=[MN1 m1];
YDW|-HI F z1=dz*MN1'; % output location
]7*kWc2 end
VDG|>#[! end
3eWJt\}?B hg=abs(U1').*abs(U1'); % for data write to excel
lHcA j{6 ha=[z1 hg]; % for data write to excel
s u}& ".e^ t1=[0 t'];
f# 1/}Hq/I hh=[t1' ha']; % for data write to excel file
[8.-(-/; %dlmwrite('aa',hh,'\t'); % save data in the excel format
V- /YNRV figure(1)
XJc
,uj7 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
, }KwP *:Z figure(2)
pKq ]X}[^c waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
9YAM#LBTWi 0',[J 非线性超快脉冲耦合的数值方法的Matlab程序 Cpe #[mE
QPX`l0V 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。
z4bN)W )p 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
eIsT!V" 7 p=H3Q?HJ} ~JLYhA^'+< @cPf lb % This Matlab script file solves the nonlinear Schrodinger equations
a#$ N% =j % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
!W ~QT} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0t+])> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
H$Kw=kMw ~}K {e C=1;
_H8*ReFG M1=120, % integer for amplitude
S!`:E M3=5000; % integer for length of coupler
"-P/jk N = 512; % Number of Fourier modes (Time domain sampling points)
Ia#"/`|| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
_W}(!TKO T =40; % length of time:T*T0.
XC 2FF&B& dt = T/N; % time step
+ mLD/gK` n = [-N/2:1:N/2-1]'; % Index
zSKKr?{ t = n.*dt;
JYQ.EAsr! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
>n K%^T w=2*pi*n./T;
Y[@0qc3UO g1=-i*ww./2;
O>%$q8x@i g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
9n " V\e_R g3=-i*ww./2;
D#ZPq,f P1=0;
sBU_Ft P2=0;
V 9Hl1\j^ P3=1;
t0.;nv @A0 P=0;
e}e6r3faz for m1=1:M1
y6FKg ) p=0.032*m1; %input amplitude
_4v"")Xe s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
8ljuc5,J s1=s10;
yPN+W8}f s20=0.*s10; %input in waveguide 2
W~yLl% s30=0.*s10; %input in waveguide 3
zq f[Z3 s2=s20;
!b63ik15O~ s3=s30;
U <rI!!# 9 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
'60//"9>k/ %energy in waveguide 1
xCq' [9oU p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
d8o ewkiR %energy in waveguide 2
^BiP LQ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
G,|KL" H6 %energy in waveguide 3
-?z\5 z for m3 = 1:1:M3 % Start space evolution
/?P!.!W& s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
|z*>ixK s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
mf9hFy* <4 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
WqQU@s A sca1 = fftshift(fft(s1)); % Take Fourier transform
Ha)np sca2 = fftshift(fft(s2));
iD714+N( sca3 = fftshift(fft(s3));
G?ig1PB"# sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
p/&HUQQk sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
96}eR, sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
u Y]0dyI s3 = ifft(fftshift(sc3));
V^sc1ak1Q s2 = ifft(fftshift(sc2)); % Return to physical space
!}t-j3bCs s1 = ifft(fftshift(sc1));
n"Z |e tZ4 end
;A"\?i Q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
*HeVACxo p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
kP^*h O!% p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
\=fh-c (J, P1=[P1 p1/p10];
#c:kCZt# P2=[P2 p2/p10];
``4?a7!! P3=[P3 p3/p10];
!i Jipe5 P=[P p*p];
P)hi||[ end
w
&
P&7 figure(1)
"V}qf3 qU plot(P,P1, P,P2, P,P3);
9!#EwPD$# kceyuD$3G 转自：
http://blog.163.com/opto_wang/
