计算脉冲在非线性耦合器中演化的Matlab 程序 >#gDk K p8?"} % This Matlab script file solves the coupled nonlinear Schrodinger equations of
9`"#OQPn1 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
vCK+v
r! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
PRFl%M.H` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ufw[Ei$I: M"qS#*{ %fid=fopen('e21.dat','w');
N>Uxq& )! N = 128; % Number of Fourier modes (Time domain sampling points)
}s6Veosl M1 =3000; % Total number of space steps
-yBj7F| J =100; % Steps between output of space
iE_[]Vgc T =10; % length of time windows:T*T0
EQw7(r|v: T0=0.1; % input pulse width
Z#^|h0 MN1=0; % initial value for the space output location
]ZW-`U MO dt = T/N; % time step
$"MVr5q6 n = [-N/2:1:N/2-1]'; % Index
wf\7sz t = n.*dt;
8K8jz9.s u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
WB<MU:.Vc u20=u10.*0.0; % input to waveguide 2
FgrVXb_q u1=u10; u2=u20;
"!eq~/nk U1 = u1;
@de0)AJG6 U2 = u2; % Compute initial condition; save it in U
/ iAhGY ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
D/;[x{;E w=2*pi*n./T;
\1n (Jr.< g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
H5
:,hrZY L=4; % length of evoluation to compare with S. Trillo's paper
Zg>]!^X8 dz=L/M1; % space step, make sure nonlinear<0.05
4PkKL/ E for m1 = 1:1:M1 % Start space evolution
Z5*(xo ny0 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
D@ !r?E` u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
gX(Xj@=(& ca1 = fftshift(fft(u1)); % Take Fourier transform
T/ eX7p1 ca2 = fftshift(fft(u2));
#T{)y c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
D`'Cnt/ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
VZ">vIRyi| u2 = ifft(fftshift(c2)); % Return to physical space
utl-#Wwt/ u1 = ifft(fftshift(c1));
0S'@(p[A if rem(m1,J) == 0 % Save output every J steps.
s16, *;Z U1 = [U1 u1]; % put solutions in U array
G)M! ,
Q U2=[U2 u2];
>ke.ZZV? MN1=[MN1 m1];
]s E)-8 z1=dz*MN1'; % output location
ct
OCj$$u end
}; M@JMu, end
P>_9>k@;Q hg=abs(U1').*abs(U1'); % for data write to excel
:2/ jI:L~ ha=[z1 hg]; % for data write to excel
Oo FMOlb.Z t1=[0 t'];
\7#w@3* hh=[t1' ha']; % for data write to excel file
GRVF/hPn %dlmwrite('aa',hh,'\t'); % save data in the excel format
?$uF(>LD
figure(1)
~{-Ka>A waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
PlK3; figure(2)
Gr)G-zE waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
=PNkzFU o J|^z>gP( 非线性超快脉冲耦合的数值方法的Matlab程序 D]rYg' B.;@i;7L 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。
XzqB=iX 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
6K<o0=,jm2 oOAkwc%)b 4<)*a]\c5M z 0zB &} % This Matlab script file solves the nonlinear Schrodinger equations
suW|hh1/Ya % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
*QI Yq % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
v6[VdWOx5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s,!vBSn8 ST~YO C=1;
?z6K/'? M1=120, % integer for amplitude
Ex|Z@~T12 M3=5000; % integer for length of coupler
NXDkGO/* N = 512; % Number of Fourier modes (Time domain sampling points)
!<VP [%2L~ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
DHuvHK0# T =40; % length of time:T*T0.
SDNRcSbOD6 dt = T/N; % time step
5K682+^5 n = [-N/2:1:N/2-1]'; % Index
'irwecd8 t = n.*dt;
#w \x-i| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
yJO Jw o^ w=2*pi*n./T;
,O:p`"3`0= g1=-i*ww./2;
v WrTB g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
7(
Z9\ g3=-i*ww./2;
:hW(2= % P1=0;
G (Hr*T% P2=0;
!F xn1Z, P3=1;
N;BuBm5K P=0;
T5e#Ll/ for m1=1:M1
X eY[;}9 p=0.032*m1; %input amplitude
`d4xX@
s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
,/TmTX--d s1=s10;
G %\/[
B s20=0.*s10; %input in waveguide 2
B]}gfVO s30=0.*s10; %input in waveguide 3
E_[a|N"D s2=s20;
/-m ) s3=s30;
M"{*))O\-c p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
@JLN3 %energy in waveguide 1
Tz.okCo]z p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
#f_'&m %energy in waveguide 2
"oFi+']* p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
c=bK_Z_ %energy in waveguide 3
2J$vX( for m3 = 1:1:M3 % Start space evolution
+Zr~mwM=x s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
w9RBT(u s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
aaN/HE_ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
E4Ez)IaKyi sca1 = fftshift(fft(s1)); % Take Fourier transform
J|be'V#]1 sca2 = fftshift(fft(s2));
?$tD sca3 = fftshift(fft(s3));
!O }e)t sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
c C| sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4b`Fi@J\ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
c+T`X? .j s3 = ifft(fftshift(sc3));
NG:4Q.G1g s2 = ifft(fftshift(sc2)); % Return to physical space
3PL0bejaT7 s1 = ifft(fftshift(sc1));
|r?0!;bN0 end
s6 (md<r p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
F1B/cd p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@2d9
7.X p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
C 2=PGq P1=[P1 p1/p10];
Ygkf}n P2=[P2 p2/p10];
%{cVG-<_iz P3=[P3 p3/p10];
O{7#Xj
:_ P=[P p*p];
~UQ<8`@a end
:"Tkl$@, figure(1)
V51k X{S plot(P,P1, P,P2, P,P3);
-b8SaLak }U5$~, *p 转自：
http://blog.163.com/opto_wang/
