计算脉冲在非线性耦合器中演化的Matlab 程序 gMXs&`7P p\;\hHai % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#}M\ J0QG % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
j-~x==c-; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=sm<B^yj % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
(Dat`: '=s{9lxn^ %fid=fopen('e21.dat','w');
n*gr(S N = 128; % Number of Fourier modes (Time domain sampling points)
"|N58% M1 =3000; % Total number of space steps
ar&j1"" J =100; % Steps between output of space
W4OL{p-\/ T =10; % length of time windows:T*T0
3(2WO^zX { T0=0.1; % input pulse width
/Pbytu);ds MN1=0; % initial value for the space output location
BE0Ov{' dt = T/N; % time step
(-}:'5|Yj n = [-N/2:1:N/2-1]'; % Index
K#"J8h;x t = n.*dt;
1iA0+Ex(j u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
EF>vu+YK u20=u10.*0.0; % input to waveguide 2
i2+r#Hw#5R u1=u10; u2=u20;
\eF_Xk[ U1 = u1;
#}PQ !gZ U2 = u2; % Compute initial condition; save it in U
A&?8 rc ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
5taR[ukM w=2*pi*n./T;
UWW^g@d4 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
0sMNp L=4; % length of evoluation to compare with S. Trillo's paper
bA_/6r)u dz=L/M1; % space step, make sure nonlinear<0.05
kC,=E9)O for m1 = 1:1:M1 % Start space evolution
J#>)+ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
O'Mo/
u1- u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
%fT%,(
w}t ca1 = fftshift(fft(u1)); % Take Fourier transform
jo-2D[Q{ ca2 = fftshift(fft(u2));
!Y8+Z&^2 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
T}}T`Ce c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Vjdu9Ez u2 = ifft(fftshift(c2)); % Return to physical space
._E 6? u1 = ifft(fftshift(c1));
|2Vhj<6 if rem(m1,J) == 0 % Save output every J steps.
3 as~yF0 U1 = [U1 u1]; % put solutions in U array
qix$ }(P U2=[U2 u2];
VGYx( MN1=[MN1 m1];
ndmsXls z1=dz*MN1'; % output location
8t;vZ& end
XnwVK end
7"_m?c8 hg=abs(U1').*abs(U1'); % for data write to excel
QGCg~TV; ha=[z1 hg]; % for data write to excel
> `1K0?_ t1=[0 t'];
+P &S0/ hh=[t1' ha']; % for data write to excel file
exZgk2[0 %dlmwrite('aa',hh,'\t'); % save data in the excel format
H|Y*TI2vf8 figure(1)
`<3%`4z/ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
/Hs\`Kg"! figure(2)
A'tv[Td8, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
} =p e;l
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^tg 非线性超快脉冲耦合的数值方法的Matlab程序 -k?K|w*X SHc?C&^S 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。
4<j7F4 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
S.zY0 sv.?C pE s||c#+j"8 mz2 v2ma % This Matlab script file solves the nonlinear Schrodinger equations
O:]e4r,' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
yMz dM&a!* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
[t6Y,yo&h4 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
cq`!17"k Al3*? H& C=1;
3Q#Tut M1=120, % integer for amplitude
`Hx JE"/ M3=5000; % integer for length of coupler
N!//m?} N = 512; % Number of Fourier modes (Time domain sampling points)
hcqg94R#_ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
{UFs1 T =40; % length of time:T*T0.
hz+O.k],? dt = T/N; % time step
vn+~P9SHQ n = [-N/2:1:N/2-1]'; % Index
[ KDNKK t = n.*dt;
}*P?KV ( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[k]3#<sS w=2*pi*n./T;
n%ypxY0 g1=-i*ww./2;
|})v,
oB g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
NI:3hfs g3=-i*ww./2;
35H.ZXQp- P1=0;
Qp;FVUw9 P2=0;
V2SHF P3=1;
~_F <"40 P=0;
eMLcmZJR for m1=1:M1
Y<t(m$s p=0.032*m1; %input amplitude
KJ 7-Vl> s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
0m,q3 s1=s10;
aF{1V\e s20=0.*s10; %input in waveguide 2
#=T^XHjQ s30=0.*s10; %input in waveguide 3
Ov#G 7a" s2=s20;
(@Kc(>(: Y s3=s30;
^&lkh@Y1q p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
6IJH%qUx' %energy in waveguide 1
z?t75#u9. p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
,B:r^(}0j %energy in waveguide 2
pLe[<N p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
iOtf7.@ %energy in waveguide 3
fCbd]X for m3 = 1:1:M3 % Start space evolution
n}dLfg* s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Db*&'32W s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6@VgLa, s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
e0M'\'J sca1 = fftshift(fft(s1)); % Take Fourier transform
y
q!{\@- sca2 = fftshift(fft(s2));
!-m 'diE sca3 = fftshift(fft(s3));
25;(`Td5 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
FY)US> sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
N<O<wtXIj sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
*LEI@ s3 = ifft(fftshift(sc3));
C;%1XFzM s2 = ifft(fftshift(sc2)); % Return to physical space
X2E=2tXl`7 s1 = ifft(fftshift(sc1));
K@vU_x0Sl end
bZ#5\L2 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
VsDY,=Ww p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3i#'osq p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
4>Y*owa4 P1=[P1 p1/p10];
s &f\gp1 P2=[P2 p2/p10];
BZ,{gy7g7X P3=[P3 p3/p10];
+OZ\rs P=[P p*p];
2AW*PDncxP end
{TvB3QOsj figure(1)
mRy0zN>? plot(P,P1, P,P2, P,P3);
3:>hHQi ]QQeUxi 转自:
http://blog.163.com/opto_wang/