计算脉冲在非线性耦合器中演化的Matlab 程序 m)g:@^$ .kyp5CD}4 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
m.Yj{u8zX % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
SW#
5px` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
FUiEayM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
NRgN h5/ sO,,i]a0 %fid=fopen('e21.dat','w');
w+z~Mz}Vz N = 128; % Number of Fourier modes (Time domain sampling points)
L;wzvz\+ M1 =3000; % Total number of space steps
[y&yy|*\ J =100; % Steps between output of space
jgK8} C T =10; % length of time windows:T*T0
hCuUX) >Bt T0=0.1; % input pulse width
#px74EeI\ MN1=0; % initial value for the space output location
Am{Vtl)i dt = T/N; % time step
J7c(qGJI2 n = [-N/2:1:N/2-1]'; % Index
sWa`-gc t = n.*dt;
{ ZrIA+eH u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
4'P otv@/ u20=u10.*0.0; % input to waveguide 2
.SAOE'Foo u1=u10; u2=u20;
s\@RJ[(<
U1 = u1;
>kU$bh.( U2 = u2; % Compute initial condition; save it in U
. =yF ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
GHa D 3 2 w=2*pi*n./T;
l`>|XUf6 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
3"!h+dXw L=4; % length of evoluation to compare with S. Trillo's paper
p.~hZ+ x_ dz=L/M1; % space step, make sure nonlinear<0.05
U9 [QdC for m1 = 1:1:M1 % Start space evolution
vtk0 j u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
o9*}>J<+RQ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
@Fvp~]jCb ca1 = fftshift(fft(u1)); % Take Fourier transform
k[#<=G_=/E ca2 = fftshift(fft(u2));
pMndyuoJl c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
{DlQTgP c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
THEpW{.E u2 = ifft(fftshift(c2)); % Return to physical space
/Ps/ m! u1 = ifft(fftshift(c1));
-Ri/I4 Xj if rem(m1,J) == 0 % Save output every J steps.
g3B%}!| U1 = [U1 u1]; % put solutions in U array
__LR!F]=i U2=[U2 u2];
w#0/&\ b= MN1=[MN1 m1];
~XU% _Hz z1=dz*MN1'; % output location
L6<.>\^Z" end
[
*P~\' U end
PuO5@SP~ hg=abs(U1').*abs(U1'); % for data write to excel
%wil' ha=[z1 hg]; % for data write to excel
W2yNwB+{ t1=[0 t'];
)d(F]uV:y hh=[t1' ha']; % for data write to excel file
?gYQE&M ! %dlmwrite('aa',hh,'\t'); % save data in the excel format
Z{XF!pS%H figure(1)
Wz{,N07Q#{ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
u]0{#wu;g figure(2)
wB'GV1|jL waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Y2$wL9"> H. o=4[ 非线性超快脉冲耦合的数值方法的Matlab程序 `O,^oD 4 Q%>6u@' 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。
7C / ^ Gw 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
b,h@. s t9l]ie{"o. <Fo~|Nh| '< =77yDg % This Matlab script file solves the nonlinear Schrodinger equations
-qyhg-k6 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
BcXPgM!Xqz % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
tEuVn 5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>uLWfk+y1 >dK# tsp C=1;
E5iNuJj=f M1=120, % integer for amplitude
CWdpF>En M3=5000; % integer for length of coupler
unvS `>)Np N = 512; % Number of Fourier modes (Time domain sampling points)
Z X0 #I W dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
u!CcTE * T =40; % length of time:T*T0.
:;Xh`br dt = T/N; % time step
{Qba`lOkq n = [-N/2:1:N/2-1]'; % Index
E %%iVFPX t = n.*dt;
TGDrTyI?y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
um,G^R w=2*pi*n./T;
tNvjwgV\ g1=-i*ww./2;
>BWe"{ ; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
0<FT=tKm g3=-i*ww./2;
tqD=)0Uzs P1=0;
:l U#Dm] P2=0;
R :*1Y\o( P3=1;
4|/}~9/ P=0;
vJj}$Al I for m1=1:M1
)k o[_OJj p=0.032*m1; %input amplitude
Xk] uXx:TN s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
[Smqe>U 1 s1=s10;
: @4+ } s20=0.*s10; %input in waveguide 2
y$8S+N?> s30=0.*s10; %input in waveguide 3
tP1znJh>y s2=s20;
Cu! S|Xj. s3=s30;
@rP#ktz] p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
,K15KN.' %energy in waveguide 1
@6kkt~>: p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
mrQT:B\8 %energy in waveguide 2
M{t/B-'4 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
IOddu2.( %energy in waveguide 3
K%.t%)A_3 for m3 = 1:1:M3 % Start space evolution
9fy[%M s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
HDi_|{2^ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
'YB{W8bR s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
8;d./!|'&g sca1 = fftshift(fft(s1)); % Take Fourier transform
/$d #9Uv sca2 = fftshift(fft(s2));
9 K>~9Za sca3 = fftshift(fft(s3));
Nd
He:: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
cTja<*W^xv sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
LFAefl\ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
~^/BAc s3 = ifft(fftshift(sc3));
o'_eLp s2 = ifft(fftshift(sc2)); % Return to physical space
Z|B`n
SzH s1 = ifft(fftshift(sc1));
;w;+<Rd end
/b]+RXvxj p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
gb=tc` p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
DfjDw/{U3L p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
BPSi e0 P1=[P1 p1/p10];
4N)45@jk[ P2=[P2 p2/p10];
O[8wF86R P3=[P3 p3/p10];
=d$m@rc0r P=[P p*p];
W[LQ $uj end
&`}d;r|yn1 figure(1)
8iPA^b|sz{ plot(P,P1, P,P2, P,P3);
%_(^BZd q }]z8 L 转自：
http://blog.163.com/opto_wang/
