计算脉冲在非线性耦合器中演化的Matlab 程序 ^ g vTc+| I{g.V|+ x % This Matlab script file solves the coupled nonlinear Schrodinger equations of
)^{}ov % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
'Tjvq%ks % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xt?-X%oY8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
? PMbbqa0 !9_(y~g{N %fid=fopen('e21.dat','w');
2 wY|E<E N = 128; % Number of Fourier modes (Time domain sampling points)
`hj,r F+4 M1 =3000; % Total number of space steps
b~,e(D9DG J =100; % Steps between output of space
Mt-r`W3 q T =10; % length of time windows:T*T0
+:; ddV T0=0.1; % input pulse width
lxL. ztL MN1=0; % initial value for the space output location
F5
]<=i dt = T/N; % time step
H)D|lt5xy n = [-N/2:1:N/2-1]'; % Index
.A<Hk1(-) t = n.*dt;
F &czD;F u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
0<\|D^m=&h u20=u10.*0.0; % input to waveguide 2
3 Vc}Q'&Y u1=u10; u2=u20;
0d_)C>gcF U1 = u1;
6(`N!]e*L U2 = u2; % Compute initial condition; save it in U
FHr)xqo=~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`w:kY9
w=2*pi*n./T;
vw2E$ya g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
G9Uc
}z L=4; % length of evoluation to compare with S. Trillo's paper
xjo`u:BH dz=L/M1; % space step, make sure nonlinear<0.05
`-pw P for m1 = 1:1:M1 % Start space evolution
(O0 Ry2u k u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
KM?4 J6jH u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
w g?}c ;
ca1 = fftshift(fft(u1)); % Take Fourier transform
V'XEz;Ze ca2 = fftshift(fft(u2));
[ Xu8~c X c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
,w#lUg p c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
"?3=FBp& u2 = ifft(fftshift(c2)); % Return to physical space
UGO;5! u1 = ifft(fftshift(c1));
_ f%s] if rem(m1,J) == 0 % Save output every J steps.
4<#ItQ( U1 = [U1 u1]; % put solutions in U array
|})s 0TU U2=[U2 u2];
Hloe7+5UD MN1=[MN1 m1];
]H
n:c'aT z1=dz*MN1'; % output location
kzRvLs4xM end
7_1 Iadb end
y5j:+2|I hg=abs(U1').*abs(U1'); % for data write to excel
OOSf<I*> ha=[z1 hg]; % for data write to excel
-iDs:J4Iq t1=[0 t'];
ZTzec zXpQ hh=[t1' ha']; % for data write to excel file
8/aJ4w[A %dlmwrite('aa',hh,'\t'); % save data in the excel format
;]-08lzO<4 figure(1)
| KYl'"5\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
OCx'cSs-= figure(2)
;\0|1Eem` waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
HqWWWCW al );.$ `0 非线性超快脉冲耦合的数值方法的Matlab程序 !
*sXLlS .Od:#(aq 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。
k _V+;&: % 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
utZI'5i } gv'r
"; qIZ+%ZOu ,zoHmV1Wd+ % This Matlab script file solves the nonlinear Schrodinger equations
.z,-ThTH@\ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
'r!!W0-K % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
s5@BVD'}E % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
cn} C I 7He"IJ C=1;
"rn M1=120, % integer for amplitude
8UjIC4' M3=5000; % integer for length of coupler
w PR Ns9^ N = 512; % Number of Fourier modes (Time domain sampling points)
\XB,)XDB dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
fF0K ]. T =40; % length of time:T*T0.
HKJCiQ|k dt = T/N; % time step
9Ad%~qciY n = [-N/2:1:N/2-1]'; % Index
\7LL neq t = n.*dt;
Eg`~mE+a ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G ky*EY w=2*pi*n./T;
wMCMrv: g1=-i*ww./2;
"> Qxb .Y} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
vX }iA|`# g3=-i*ww./2;
pqO3(2F9 P1=0;
>k"O3Pc@ P2=0;
i\IpS@/{-v P3=1;
bKS/T^UQ P=0;
*/K[ B(G for m1=1:M1
2@a 'n@- p=0.032*m1; %input amplitude
%.$!VTO" s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
_K#7#qp2 s1=s10;
_ooHB>sH s20=0.*s10; %input in waveguide 2
VzSkqWF/" s30=0.*s10; %input in waveguide 3
@TALZk'% s2=s20;
la{?&75] s3=s30;
[1(e SH p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
w~B1TfqNo %energy in waveguide 1
_W(xO
|,M p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
;b [>{Q; %energy in waveguide 2
LE}`rW3 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
wBpt
W2jA %energy in waveguide 3
%@:>hQ2 ; for m3 = 1:1:M3 % Start space evolution
G%~V b s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
PNAvT$0LaZ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Q+Nnj(AQY s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
]CP5s5 sca1 = fftshift(fft(s1)); % Take Fourier transform
rrU(>jA! sca2 = fftshift(fft(s2));
RgoF4 g+@ sca3 = fftshift(fft(s3));
i}LQ}35@ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
<T7@,_T sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
h:Gs9]Lvtv sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
l atm_\ s3 = ifft(fftshift(sc3));
TS Frv8L s2 = ifft(fftshift(sc2)); % Return to physical space
, zZH>P s1 = ifft(fftshift(sc1));
:gRrM)n end
`{YOl\d_ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
]Qe~|9I p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
AT
t.}- p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
D 7pQWlN\ P1=[P1 p1/p10];
>
U3 >I^Y P2=[P2 p2/p10];
g s1 P3=[P3 p3/p10];
5L6.7}B P=[P p*p];
aEdMZ+P. end
Jy: @&c figure(1)
Q']'KU. plot(P,P1, P,P2, P,P3);
){GJgk|P fQ~~%#z1 转自：
http://blog.163.com/opto_wang/
