计算脉冲在非线性耦合器中演化的Matlab 程序 W:G *t4i Qpc>5p![3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Vow+,,oh % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
~yV0SpL % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
j~0hAKHG % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
(nm&\b~j q.4DwY5 L %fid=fopen('e21.dat','w');
GzX@Av$ N = 128; % Number of Fourier modes (Time domain sampling points)
Rh|&{Tf M1 =3000; % Total number of space steps
S_zE+f+
2 J =100; % Steps between output of space
V Puzu| T =10; % length of time windows:T*T0
IZGty=Q_ T0=0.1; % input pulse width
"A7tb39* MN1=0; % initial value for the space output location
? p]w _l dt = T/N; % time step
Sk xaS J" n = [-N/2:1:N/2-1]'; % Index
ESAh(A)8 t = n.*dt;
mb/Y u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
O \?ei+(H7 u20=u10.*0.0; % input to waveguide 2
{ .AFg/Z u1=u10; u2=u20;
]4PG[9J@ U1 = u1;
/C" E*a U2 = u2; % Compute initial condition; save it in U
:Fh* 4
&Z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
JkTL+obu w=2*pi*n./T;
8@!SM g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
3't?%$'5 L=4; % length of evoluation to compare with S. Trillo's paper
U}NNb GQj dz=L/M1; % space step, make sure nonlinear<0.05
6xwC1V?:0t for m1 = 1:1:M1 % Start space evolution
Xv9C D u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Z(#a-_ g u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
\|k U{d0 ca1 = fftshift(fft(u1)); % Take Fourier transform
SRMy#j- ca2 = fftshift(fft(u2));
/ wEr>[8S c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
JP#m} W c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
`#~@f!'; u2 = ifft(fftshift(c2)); % Return to physical space
!HFwQGP.Y u1 = ifft(fftshift(c1));
(5SI! 1N if rem(m1,J) == 0 % Save output every J steps.
~{J.br` U1 = [U1 u1]; % put solutions in U array
r(RJ& \ ! U2=[U2 u2];
) s M}BY MN1=[MN1 m1];
'n\ZmG{ z1=dz*MN1'; % output location
*%8d W end
g\ 2Y605DM end
r*$KF!-dg hg=abs(U1').*abs(U1'); % for data write to excel
:t(}h!7 ha=[z1 hg]; % for data write to excel
%k"-rmW t1=[0 t'];
~&g:7f|X hh=[t1' ha']; % for data write to excel file
I3A](`
%dlmwrite('aa',hh,'\t'); % save data in the excel format
rkV ZP!7! figure(1)
tUzuel* waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
r]TeR$NJ figure(2)
3=` UX waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
I;=}@]9 { aU~[5L3( 非线性超快脉冲耦合的数值方法的Matlab程序 :iq1-Pw >LLFe~9`g 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。
avdi9!J2 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
?=6zgb"9- Oa{M9d,l o o`mVRV f ).LJY<A % This Matlab script file solves the nonlinear Schrodinger equations
Xf:-K(%e % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
=r`>tWs % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8L0#<"'0 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
g8^ $, rN
OwB2e C=1;
W;2y.2* M1=120, % integer for amplitude
=>&d[G[m! M3=5000; % integer for length of coupler
jQc$>M<"o N = 512; % Number of Fourier modes (Time domain sampling points)
?'^xO: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
a93Aj T =40; % length of time:T*T0.
&}6=V+J; dt = T/N; % time step
[<6ez;2q' n = [-N/2:1:N/2-1]'; % Index
^,,|ED\M{m t = n.*dt;
*P D7H9m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|ML|P\1&V w=2*pi*n./T;
B \BP:;" g1=-i*ww./2;
s %/3X\_ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
+hi!=^b] g3=-i*ww./2;
NU81 V0:jG P1=0;
L_O m<LO2 P2=0;
<.#i3! P3=1;
C&r&&Pw P=0;
~r+;i ,,X for m1=1:M1
A+>+XA' p=0.032*m1; %input amplitude
U",kAQY s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Ak&eGd$d s1=s10;
k]w; (< s20=0.*s10; %input in waveguide 2
XNsMXeO]& s30=0.*s10; %input in waveguide 3
1InG %=jLo s2=s20;
whr[rWt@> s3=s30;
0jG8Gmh! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
|G } qY5_ %energy in waveguide 1
eWE7 >kwh p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
p v%`aQ]o{ %energy in waveguide 2
qo/`9%^E? p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
kec t)=T( %energy in waveguide 3
sZA7)Z`7 for m3 = 1:1:M3 % Start space evolution
vT)FLhH6* s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
\\xo OA. s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
~}+F$& s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
VI/77 sca1 = fftshift(fft(s1)); % Take Fourier transform
)$XcO] sca2 = fftshift(fft(s2));
Gg8F>y<[R sca3 = fftshift(fft(s3));
b dP @^Q sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
/c6:B5G sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
e+Vn@-L; sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Gg$4O 8 s3 = ifft(fftshift(sc3));
L3pNna s2 = ifft(fftshift(sc2)); % Return to physical space
_ 5n Lrn,~ s1 = ifft(fftshift(sc1));
M*<Ee]u end
]?M3X_Mq p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
@T)kqT p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
B _k+Oa2! p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
B 'SLyf P1=[P1 p1/p10];
Z^wogIAV P2=[P2 p2/p10];
9bwG3jn4? P3=[P3 p3/p10];
) G
a5c P=[P p*p];
EIug)S~ end
,%6!8vX figure(1)
$MhfGMk!' plot(P,P1, P,P2, P,P3);
N3"O#C ]O]6O%.ao 转自：
http://blog.163.com/opto_wang/
