计算脉冲在非线性耦合器中演化的Matlab 程序 I ` `S%`h >[,ywRJ#_} % This Matlab script file solves the coupled nonlinear Schrodinger equations of
XUI9)Ne % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
N)F&c!anh % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
pKSn
3-A % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;3 N0) |I; tBqN{u %fid=fopen('e21.dat','w');
G9`;Z^<L N = 128; % Number of Fourier modes (Time domain sampling points)
hLs<g!*O M1 =3000; % Total number of space steps
j` fQN J =100; % Steps between output of space
D'{NEk@ T =10; % length of time windows:T*T0
Uavr>- T0=0.1; % input pulse width
[
" n+2; MN1=0; % initial value for the space output location
}]dK26pX dt = T/N; % time step
IJWUNKqo= n = [-N/2:1:N/2-1]'; % Index
:v=^-&t t = n.*dt;
ySfot`LQ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
2 kP0// u20=u10.*0.0; % input to waveguide 2
%kS4v,I u1=u10; u2=u20;
U9?fUS U1 = u1;
AXnuXa(j U2 = u2; % Compute initial condition; save it in U
x,U '!F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_*tU.x|DP w=2*pi*n./T;
/G{;?R g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
{6_M$"e. L=4; % length of evoluation to compare with S. Trillo's paper
e (e_p# dz=L/M1; % space step, make sure nonlinear<0.05
gdP Pk=LD for m1 = 1:1:M1 % Start space evolution
zmA]@'j u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
h/)kd3$*' u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
IE)$ .%q;) ca1 = fftshift(fft(u1)); % Take Fourier transform
-<g&U*/E ca2 = fftshift(fft(u2));
4AIo,{( c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
1Q5:Vo^B# c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
u[{j ;l( u2 = ifft(fftshift(c2)); % Return to physical space
&dH[lB u1 = ifft(fftshift(c1));
jOkc' if rem(m1,J) == 0 % Save output every J steps.
`Z#0kpXk_ U1 = [U1 u1]; % put solutions in U array
nrhzNW>] U2=[U2 u2];
)S:,q3g xJ MN1=[MN1 m1];
\
oY/h T _ z1=dz*MN1'; % output location
9\QeH'A end
Po)!vL"
end
mp !S<m hg=abs(U1').*abs(U1'); % for data write to excel
S'%|40U ha=[z1 hg]; % for data write to excel
|41NRGgY t1=[0 t'];
C`J> Gm hh=[t1' ha']; % for data write to excel file
4# L}& %dlmwrite('aa',hh,'\t'); % save data in the excel format
D]?eRO9' figure(1)
?Iin/ <y waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
xJ$/#UdP figure(2)
Z! /!4(Fh waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
z[cs /x q&DM*!Jq 非线性超快脉冲耦合的数值方法的Matlab程序 ]+"25V'L }&*wJ]j`L 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。
[%0{7pz} 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
[%uj+?}6O ~E8L,h~ hf JeVT-/v ~6Xr^An/Z % This Matlab script file solves the nonlinear Schrodinger equations
D 2y[?RG % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
o]@ Mg5(8Q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
n@JZ 2K4 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
O)aWTI cXd?48O C=1;
f`gs/R M1=120, % integer for amplitude
cIS?EW]S%X M3=5000; % integer for length of coupler
FwjmC%iY N = 512; % Number of Fourier modes (Time domain sampling points)
n9 %&HDl4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
anzt;V.;Y T =40; % length of time:T*T0.
N^TE
;BM dt = T/N; % time step
6CV9ewr n = [-N/2:1:N/2-1]'; % Index
Y'{F^VxA/ t = n.*dt;
H{BP7!t[V ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T2dv!}7p w=2*pi*n./T;
lz [s g1=-i*ww./2;
iW9o-W
a g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
~Z>!SMXp< g3=-i*ww./2;
xU!eT'Y P1=0;
iLbf:DXK( P2=0;
o bz|*1M? P3=1;
W^k|* Y| P=0;
@}<b42 for m1=1:M1
)ppIO"\ p=0.032*m1; %input amplitude
$<s;YhM:u) s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Wb%t6N? s1=s10;
\Q!I; s20=0.*s10; %input in waveguide 2
lDX\" Fq s30=0.*s10; %input in waveguide 3
PC<[ $~ s2=s20;
I^l\<1"] s3=s30;
|[W 7&@hF p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
EY^+ N>
%energy in waveguide 1
KNG7$i cG p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
P#l "`C
/ %energy in waveguide 2
_+6aD|7x p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
TY`t3 %energy in waveguide 3
_ *.ImD for m3 = 1:1:M3 % Start space evolution
Fz {T; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
mHF? t.y s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
(Zoo p kxw s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
V^%P}RFMc sca1 = fftshift(fft(s1)); % Take Fourier transform
od-yVE& sca2 = fftshift(fft(s2));
g2%fla7r sca3 = fftshift(fft(s3));
V%Ww;Ca]I sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
"j/j he6 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
a{@ gzB sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
60#eTo?}o s3 = ifft(fftshift(sc3));
HZ[.,DuW s2 = ifft(fftshift(sc2)); % Return to physical space
gZ >)
S@ s1 = ifft(fftshift(sc1));
045_0+r"@ end
&e \UlM22 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
'w8p[h
(, p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
'\% Kd+k p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
4q )+nh~s P1=[P1 p1/p10];
s4[PwD P2=[P2 p2/p10];
8P * d P3=[P3 p3/p10];
;J,`v5z0: P=[P p*p];
/^sk y! end
[ 0z-X 7=e figure(1)
b!JrdJO,DP plot(P,P1, P,P2, P,P3);
#Dp]S, e &&ZX<wOM 转自：
http://blog.163.com/opto_wang/
