计算脉冲在非线性耦合器中演化的Matlab 程序 K($+ILZ ; 6 d-+(@ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
<<qzZ+u % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
;dZ ZOocV1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+7WpJ;C4 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@/As|) dm kGIg} %fid=fopen('e21.dat','w');
U"@p3$2QW N = 128; % Number of Fourier modes (Time domain sampling points)
|I"&Z+m M1 =3000; % Total number of space steps
@f o(#i& J =100; % Steps between output of space
JM0+-,dl[ T =10; % length of time windows:T*T0
^o Ds*F T0=0.1; % input pulse width
!T)_(}|6} MN1=0; % initial value for the space output location
jZ5ac=D&I dt = T/N; % time step
?t\GHQ$$? n = [-N/2:1:N/2-1]'; % Index
rFC9y o t = n.*dt;
V0,5c`H c u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
yP-$@Ry u20=u10.*0.0; % input to waveguide 2
m#Z9w f] F u1=u10; u2=u20;
po ]<sB U1 = u1;
90J WU$K U2 = u2; % Compute initial condition; save it in U
"3 2Ua3m:G ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
>3 p8o@: w=2*pi*n./T;
rjfWty%6pX g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1$ }Tn L=4; % length of evoluation to compare with S. Trillo's paper
Xsb.xxK. dz=L/M1; % space step, make sure nonlinear<0.05
B B1_EdoG for m1 = 1:1:M1 % Start space evolution
j}@LiH'Q u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
P%w!4v ~" u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
^N ;TCn ca1 = fftshift(fft(u1)); % Take Fourier transform
'R$/Qt; uA ca2 = fftshift(fft(u2));
hQzT
=0 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
H,/ =<Th;i c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
YyYp-0# u2 = ifft(fftshift(c2)); % Return to physical space
Rdj3dg'< u1 = ifft(fftshift(c1));
5``usn/&Kj if rem(m1,J) == 0 % Save output every J steps.
Bz,Xg-k+ U1 = [U1 u1]; % put solutions in U array
) cOBP}j+ U2=[U2 u2];
VD,g3B p MN1=[MN1 m1];
|l|$ Q ; z1=dz*MN1'; % output location
j~Ci*'*L end
Y?oeP^V'u end
| t$%kpp hg=abs(U1').*abs(U1'); % for data write to excel
\dB z-H'@ ha=[z1 hg]; % for data write to excel
|a0@4
: t1=[0 t'];
L)H/t6}i hh=[t1' ha']; % for data write to excel file
4
;6,h6a %dlmwrite('aa',hh,'\t'); % save data in the excel format
V2m=
m}HQ figure(1)
qvh8~[ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
~-yq,x figure(2)
33"!K>wC waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Oeg^%Y
\H PB{
; 非线性超快脉冲耦合的数值方法的Matlab程序 ~WmA55 =':SOO7 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
mX @xV*
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
HXB &
6 Q`=d5Uvw k1D|Cpnp ` apCu % This Matlab script file solves the nonlinear Schrodinger equations
)DQcf]I % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
R C!~eJG! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7Sycy#D % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
(3m^@2i u3 4.
C=1;
6D4u ?P, M1=120, % integer for amplitude
Lp{uA4:=K M3=5000; % integer for length of coupler
*2m{i:3 N = 512; % Number of Fourier modes (Time domain sampling points)
py/ #h$eY dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
l n09_Lr T =40; % length of time:T*T0.
P>] *pD dt = T/N; % time step
;T!ZO @1X n = [-N/2:1:N/2-1]'; % Index
%wq;<'W t = n.*dt;
KW36nY\7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-0*z"a9<p8 w=2*pi*n./T;
S]c& T`jx g1=-i*ww./2;
^{O1+7d[. g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
?j8_ j g3=-i*ww./2;
s<LYSr d P1=0;
R {Me~L? P2=0;
7a%)/ )<D P3=1;
baR*4{] P=0;
N<HJ}geC " for m1=1:M1
H|d"45J_ p=0.032*m1; %input amplitude
{9 ./- s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
|198A, ^ s1=s10;
k`0m|< $ s20=0.*s10; %input in waveguide 2
jxgs!B> s30=0.*s10; %input in waveguide 3
7}fT7tsN s2=s20;
S1 *xM s3=s30;
u5P2* p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
K@!Gs'Op %energy in waveguide 1
F*,RDM'M p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
@ql S #( %energy in waveguide 2
E$5A
1 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
14 hE <u %energy in waveguide 3
/V>yF&p
for m3 = 1:1:M3 % Start space evolution
vq5o?$ :- s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Cl!qd h6 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6"c(5#H s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
843O}v' sca1 = fftshift(fft(s1)); % Take Fourier transform
5o Y^; )\/ sca2 = fftshift(fft(s2));
Wtj* Z.=: sca3 = fftshift(fft(s3));
\hqjk:o sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
!='L `. sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
J@(69 & sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
rIA br5CG s3 = ifft(fftshift(sc3));
G@6F<L~$1 s2 = ifft(fftshift(sc2)); % Return to physical space
6tBe,'* s1 = ifft(fftshift(sc1));
N?mQ50o~C end
Ibu 5 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
>B+!fi'SS> p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
O P\m~1 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
qbD[<T P1=[P1 p1/p10];
:sJQ r._L P2=[P2 p2/p10];
V \r2=ok@y P3=[P3 p3/p10];
!s[[X5 P=[P p*p];
O g !SFg* end
X32{y973hT figure(1)
U~Rs?JmTdD plot(P,P1, P,P2, P,P3);
C.?~D*Q yo!Y%9 转自：
http://blog.163.com/opto_wang/
