计算脉冲在非线性耦合器中演化的Matlab 程序 N+ y&,N, ()3O =! % This Matlab script file solves the coupled nonlinear Schrodinger equations of
l!g]a2x* % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
1rDqa(7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
g'|MA~4yB % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
6 %VV,$p 6MxKl
D7kl %fid=fopen('e21.dat','w');
?A )hN8 N = 128; % Number of Fourier modes (Time domain sampling points)
YR;^hs? M1 =3000; % Total number of space steps
x4/M}%h!;B J =100; % Steps between output of space
Y>&Ew*Y T =10; % length of time windows:T*T0
m:/ wG&
! T0=0.1; % input pulse width
,Uy|5zv MN1=0; % initial value for the space output location
2[ r^M'J dt = T/N; % time step
91xB9k1zO n = [-N/2:1:N/2-1]'; % Index
xQp|;oW;z t = n.*dt;
h`H ,a7 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
C|o`k9I# u20=u10.*0.0; % input to waveguide 2
QQV~?iW{~ u1=u10; u2=u20;
J:kmqk! U1 = u1;
@, W vvh U2 = u2; % Compute initial condition; save it in U
T0]*{k(FR ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
w&x!,yd; w=2*pi*n./T;
!eUDi( g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
bpxe znz L=4; % length of evoluation to compare with S. Trillo's paper
kGN+rHo dz=L/M1; % space step, make sure nonlinear<0.05
(S
v~2 for m1 = 1:1:M1 % Start space evolution
A+UU~?3y u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,DZX$Ug~+E u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
uy}%0vLo ca1 = fftshift(fft(u1)); % Take Fourier transform
Usta0Ag ca2 = fftshift(fft(u2));
b ? j< BvQ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
%bdjBa} c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
3dDX8M? u2 = ifft(fftshift(c2)); % Return to physical space
0]jA<vLR u1 = ifft(fftshift(c1));
>N.]|\V if rem(m1,J) == 0 % Save output every J steps.
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%cTK)a U1 = [U1 u1]; % put solutions in U array
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U2=[U2 u2];
A<B=f<N3gV MN1=[MN1 m1];
"k A*Vc# z1=dz*MN1'; % output location
pm6>_K z end
:Pv*, qHE end
c-Pw]Ju hg=abs(U1').*abs(U1'); % for data write to excel
?]4>rl} ha=[z1 hg]; % for data write to excel
V$ uk6# t1=[0 t'];
! XzF67 hh=[t1' ha']; % for data write to excel file
b%Eei2Gm% %dlmwrite('aa',hh,'\t'); % save data in the excel format
&EpAg@9! figure(1)
{iq3|x2[ : waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
q@jq 0D)g figure(2)
8dlw-Q'S waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
XduV+$ 03 [S@}T
zE 非线性超快脉冲耦合的数值方法的Matlab程序 }E7:ihy W\L`5CW 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。
ts8+V<g 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
CV{r5Sye \fjMc }' ~%2pp~1 K e*.b3 z % This Matlab script file solves the nonlinear Schrodinger equations
_H^^y$+1 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
wm+})SOX9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
G5FaYL.7 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>[1W:KQA +GAf O0 C=1;
8L1oh j M1=120, % integer for amplitude
NzW`B^p M3=5000; % integer for length of coupler
Z,.G%"i3C N = 512; % Number of Fourier modes (Time domain sampling points)
kZ=s'QRgL dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
d
O~O
|Xsb T =40; % length of time:T*T0.
\))=gu)I dt = T/N; % time step
Ia'ZV7' n = [-N/2:1:N/2-1]'; % Index
Nlj^D m t = n.*dt;
tM#lFmdd\P ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
^Eo=W/
w=2*pi*n./T;
Cz8f1suO4 g1=-i*ww./2;
Gx
72 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
e9E\% p g3=-i*ww./2;
_aPh(qprc P1=0;
wI5Yn
h P2=0;
uZi.HG{<) P3=1;
;2m<CSv!D P=0;
1+7GUSIb for m1=1:M1
I_q~*/<h p=0.032*m1; %input amplitude
$@i"un; s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2:LHy[{5 s1=s10;
emW:C-/h/@ s20=0.*s10; %input in waveguide 2
&'' WRgZ} s30=0.*s10; %input in waveguide 3
y4Er @8I` s2=s20;
RJeSi`19T) s3=s30;
/(8a~f&%r p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
DS xUdEK6 %energy in waveguide 1
wJlX4cT4YV p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
DK m Z %energy in waveguide 2
R3X{:1{j p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
,Os? f:Y6 %energy in waveguide 3
W~Z<1[ for m3 = 1:1:M3 % Start space evolution
HWm#t./ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
{5|("0[F s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|*mL1#bB s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
:3$}^uzIq sca1 = fftshift(fft(s1)); % Take Fourier transform
rbZ[ !LA sca2 = fftshift(fft(s2));
aV1lJ ;0 sca3 = fftshift(fft(s3));
p#KW$OQ]8 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
H7[6yh sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
0L^u2HZYL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
aJqeD'\> s3 = ifft(fftshift(sc3));
A*tKF&U5 s2 = ifft(fftshift(sc2)); % Return to physical space
\b*X:3g* s1 = ifft(fftshift(sc1));
rNl.7O9b end
x&A vU J p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s4H2/EC p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
M|i o4+sy p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
A`6ra}U<
P1=[P1 p1/p10];
V| MY!uV P2=[P2 p2/p10];
tD$lNh^ P3=[P3 p3/p10];
Fd \ e*ww' P=[P p*p];
5y4u5Tm-% end
{I{:GcS figure(1)
X%9*O[6{ plot(P,P1, P,P2, P,P3);
i.1U|Pi
StYzGJ 转自：
http://blog.163.com/opto_wang/
