计算脉冲在非线性耦合器中演化的Matlab 程序 <dD)>Y. Uhw:XV@m % This Matlab script file solves the coupled nonlinear Schrodinger equations of
/<R[X>]<F % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Irc(5rD7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
u_Wftb?9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*el~sor;S t@;r~Sb
%fid=fopen('e21.dat','w');
yrF"`/zv6| N = 128; % Number of Fourier modes (Time domain sampling points)
;4'pucq5/ M1 =3000; % Total number of space steps
m]?C @ina J =100; % Steps between output of space
W"v"mjYud T =10; % length of time windows:T*T0
sGp]jqX2,m T0=0.1; % input pulse width
lEYAq'= MN1=0; % initial value for the space output location
W{is 2s dt = T/N; % time step
+F4SU(T n = [-N/2:1:N/2-1]'; % Index
6Mj(B*c t = n.*dt;
0! W$Cz[ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
(M-Wea!q u20=u10.*0.0; % input to waveguide 2
tW
-f_0a. u1=u10; u2=u20;
?'IY0^ U1 = u1;
Q
H57[Yg U2 = u2; % Compute initial condition; save it in U
fEB&)mM ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
fZtuP1-4 w=2*pi*n./T;
1EemVZdY g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1!=^mu8 L=4; % length of evoluation to compare with S. Trillo's paper
q2e=(]rKE{ dz=L/M1; % space step, make sure nonlinear<0.05
K(3_1*e for m1 = 1:1:M1 % Start space evolution
*DcB?8% u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
di4>Ir~] u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
v;o/M6GL5 ca1 = fftshift(fft(u1)); % Take Fourier transform
f.G"[p ca2 = fftshift(fft(u2));
=#>F' A c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
)>]@@Trx c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
O>3f*Cc u2 = ifft(fftshift(c2)); % Return to physical space
,<t)aZL,A; u1 = ifft(fftshift(c1));
[vTk*#Cl4 if rem(m1,J) == 0 % Save output every J steps.
I/hq8v~S U1 = [U1 u1]; % put solutions in U array
ms{iQ:'9 U2=[U2 u2];
*hIjVKTu79 MN1=[MN1 m1];
skP'- ^F~ z1=dz*MN1'; % output location
b[rVr
J end
C0}@0c end
H7{I[>: hg=abs(U1').*abs(U1'); % for data write to excel
ZZ324UuATX ha=[z1 hg]; % for data write to excel
sW&5Mu- t1=[0 t'];
B2^*Sr[ hh=[t1' ha']; % for data write to excel file
#GuN.`__n, %dlmwrite('aa',hh,'\t'); % save data in the excel format
z(n Ba]^[F figure(1)
uZml.#@4 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
80%L!x| figure(2)
P47x-; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
>/+R~ n isU4D 非线性超快脉冲耦合的数值方法的Matlab程序 NHQi_U ez14f$cJ+ 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。
)wNcz~
Y 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
dT7!+)s5- [.'9Sw rlQ=rNrG&E KA? J: % This Matlab script file solves the nonlinear Schrodinger equations
uqv S % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
*t300`x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\IP
9EF A % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\YPvpUg (9Of,2]&E C=1;
QTospHf` M1=120, % integer for amplitude
u K=)65] M3=5000; % integer for length of coupler
mRIBE9K+& N = 512; % Number of Fourier modes (Time domain sampling points)
r1BL?&X- dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
J,*+Ak
~ T =40; % length of time:T*T0.
8?LHYdJ dt = T/N; % time step
n.=Zw2FE n = [-N/2:1:N/2-1]'; % Index
3}lIY7O t = n.*dt;
8`z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
6xLQ w=2*pi*n./T;
>BZ,g!N,J} g1=-i*ww./2;
L:\>)6]Ls g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
<DN7 g3=-i*ww./2;
3<>DDY2bl P1=0;
.q<5OE(f P2=0;
yRR[M@Y P3=1;
p$}/~5b}4 P=0;
t=fr`|! for m1=1:M1
_%u t# p=0.032*m1; %input amplitude
"hnvND4= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
n.XgGT=L s1=s10;
{_4`0J`3 s20=0.*s10; %input in waveguide 2
^Rh}[ s30=0.*s10; %input in waveguide 3
Gkm{b[ s2=s20;
[)?yH3 s3=s30;
%c@PTpAM p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Q^8/"aV\ %energy in waveguide 1
=E62N7_`= p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
%-[*G;c'w %energy in waveguide 2
B'I_i$g4w p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
_
glB<r$ %energy in waveguide 3
LkWY6
?$U for m3 = 1:1:M3 % Start space evolution
~gaWZQXyu s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
s Fx0 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|rI;OvZ\ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
OAaLCpRp sca1 = fftshift(fft(s1)); % Take Fourier transform
Sx1|Oq] sca2 = fftshift(fft(s2));
1DlXsup&?# sca3 = fftshift(fft(s3));
<cO
`jK sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
??f,(om sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
^VEaOKMr sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
b&6lu4D s3 = ifft(fftshift(sc3));
Uy|Tu~ s2 = ifft(fftshift(sc2)); % Return to physical space
PZVH=dagq s1 = ifft(fftshift(sc1));
M+I9k;N6& end
5,+fM6^V p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s4j]kH p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
y>cLG5v p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
3WpQzuHPT P1=[P1 p1/p10];
)q`.tsR> P2=[P2 p2/p10];
tt|P-p- P3=[P3 p3/p10];
97/ 4J P=[P p*p];
v\E6N2.S end
4"UH~A;^ figure(1)
b~2LD3"3 plot(P,P1, P,P2, P,P3);
+BDW1% {<1uV']x 转自:
http://blog.163.com/opto_wang/