计算脉冲在非线性耦合器中演化的Matlab 程序 ;X8eZQ Lx.X#n.]T % This Matlab script file solves the coupled nonlinear Schrodinger equations of
L~\Ir % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
,+ WDa%R % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
4oJ 0,u % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&Mol8=V) 7v{Dwg %fid=fopen('e21.dat','w');
qTG/7tn
" N = 128; % Number of Fourier modes (Time domain sampling points)
Up~#]X M1 =3000; % Total number of space steps
-LUKYGBK J =100; % Steps between output of space
z Mtx>VI T =10; % length of time windows:T*T0
gF&1e5`i T0=0.1; % input pulse width
{<V{ 0
s% MN1=0; % initial value for the space output location
flRok?iF dt = T/N; % time step
[S4< bh! n = [-N/2:1:N/2-1]'; % Index
&4LrV+`$V t = n.*dt;
{q:6;yzxl u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
v 81<K*w`P u20=u10.*0.0; % input to waveguide 2
p~qdkA< u1=u10; u2=u20;
Zv -#v U1 = u1;
3>ytpXUEGx U2 = u2; % Compute initial condition; save it in U
}5`Kn}rY ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
*~cq
(PFQ w=2*pi*n./T;
rOX\rI%0+ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
g/eE^o ~; L=4; % length of evoluation to compare with S. Trillo's paper
^I7iEv dz=L/M1; % space step, make sure nonlinear<0.05
`$05+UU for m1 = 1:1:M1 % Start space evolution
RK< uAiU u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
umI@ej+D u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
cJMp`DQzc ca1 = fftshift(fft(u1)); % Take Fourier transform
x tyOG ca2 = fftshift(fft(u2));
` KB; 3L c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
/C}u,dBf c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
^DD ]jx u2 = ifft(fftshift(c2)); % Return to physical space
5 y0 N }} u1 = ifft(fftshift(c1));
RGsgT ^ if rem(m1,J) == 0 % Save output every J steps.
.r 4 *?> U1 = [U1 u1]; % put solutions in U array
ka0Mu Q M U2=[U2 u2];
y2KR^/LN|Y MN1=[MN1 m1];
4S5U|n z1=dz*MN1'; % output location
Pd)mLs Jg end
A{MMY{K3 end
ZwM(H[iqL hg=abs(U1').*abs(U1'); % for data write to excel
H QX.oW ha=[z1 hg]; % for data write to excel
yhc}*BMZ t1=[0 t'];
!c W6dc^ hh=[t1' ha']; % for data write to excel file
Qhy!:\&1 %dlmwrite('aa',hh,'\t'); % save data in the excel format
<- L}N ' figure(1)
Y'*oW+K waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Q\rf J|| figure(2)
f3^An aa]l waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
xPCRT*Pd l|v`B6( 非线性超快脉冲耦合的数值方法的Matlab程序 WUrE1%u VYbH:4K@% 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。
F JCs$0 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@ q]4]U) zncKd{Q\tP a@!(o )> AT%6K. % This Matlab script file solves the nonlinear Schrodinger equations
x n?$ @ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
0Xb,ne
7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
bI+/0X x % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
R#HVrzOO|T 2D U Y4Ti C=1;
V_zU?}lZ^ M1=120, % integer for amplitude
5\V""fH M3=5000; % integer for length of coupler
F%P"T%| N = 512; % Number of Fourier modes (Time domain sampling points)
Uo?4o*} dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
z^vfha T =40; % length of time:T*T0.
ox*1F+Xri dt = T/N; % time step
w p\-LO~ n = [-N/2:1:N/2-1]'; % Index
<p/z m}?') t = n.*dt;
.d I".L ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
{8>g?4Q# w=2*pi*n./T;
,.Lwtp,n g1=-i*ww./2;
,oykOda:| g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
t0,=U8]w g3=-i*ww./2;
F/ x2}' P1=0;
DL`8qJ'mJs P2=0;
A3)"+`&PUl P3=1;
pT{is.RM P=0;
By waD? for m1=1:M1
EHN( K - p=0.032*m1; %input amplitude
}y Vx"e) s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
_K}q%In s1=s10;
s]]lB018O\ s20=0.*s10; %input in waveguide 2
,Qx]_gZ` s30=0.*s10; %input in waveguide 3
}`kiULC'= s2=s20;
BmKf%:l} s3=s30;
~m_{&,C A. p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
3Q'vVNFh< %energy in waveguide 1
l `.z^+!8@ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
?5F lbiT %energy in waveguide 2
LaO8)lqR p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
d?&`Z Vl %energy in waveguide 3
M6mgJonN| for m3 = 1:1:M3 % Start space evolution
< rtKPlb// s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
:.4O
Hp1 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
QEg[ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ynv{
rMl sca1 = fftshift(fft(s1)); % Take Fourier transform
)X-'Q - sca2 = fftshift(fft(s2));
,A'| Z sca3 = fftshift(fft(s3));
"MU-&** sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
(?m{G Q sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
d7Vp^^}( sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
1~t.2eU G s3 = ifft(fftshift(sc3));
Tf~eH!~0 s2 = ifft(fftshift(sc2)); % Return to physical space
,VS(4 s1 = ifft(fftshift(sc1));
>ei~ :z]R end
(P `=9+ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
LD ]-IX&L p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
+N=HI1^54R p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
vo f8bQ{& P1=[P1 p1/p10];
@ 4hzNi+ P2=[P2 p2/p10];
OKAU*}_ P3=[P3 p3/p10];
&nDXn| P=[P p*p];
<Xl#}6 II end
VE-l6@` figure(1)
`Jk0jj6Z plot(P,P1, P,P2, P,P3);
X8VBs#tLE 0S^&A?$= 转自：
http://blog.163.com/opto_wang/
