计算脉冲在非线性耦合器中演化的Matlab 程序 m3bCZ 9iE ! -<p,z % This Matlab script file solves the coupled nonlinear Schrodinger equations of
|`TgX@,#9 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
1)m@?CaI` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}e2VY
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Ep9W- n?} zc rY>t#l %fid=fopen('e21.dat','w');
": a\z(*t N = 128; % Number of Fourier modes (Time domain sampling points)
3cdTed-MIh M1 =3000; % Total number of space steps
d?wc*N3 J =100; % Steps between output of space
+M'
H0-[ T =10; % length of time windows:T*T0
J N+_| ` T0=0.1; % input pulse width
&i+ Ce MN1=0; % initial value for the space output location
B"yFS7Rrj dt = T/N; % time step
=X\^ J n = [-N/2:1:N/2-1]'; % Index
,R%q}IH# t = n.*dt;
[e[<p\] u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
BTgG4F/) u20=u10.*0.0; % input to waveguide 2
I[)% , jd u1=u10; u2=u20;
Wbr+ KX8) U1 = u1;
7f rTTS Z U2 = u2; % Compute initial condition; save it in U
f+8wl!M+6 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
.*m>\>Gsgw w=2*pi*n./T;
*na?n2Yzt g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
<sK4#!K L=4; % length of evoluation to compare with S. Trillo's paper
q 9Y9w( dz=L/M1; % space step, make sure nonlinear<0.05
[
ol9|sdu for m1 = 1:1:M1 % Start space evolution
`x%'jPP1 ^ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Z}$TKO*u u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
BauU{:Sh ca1 = fftshift(fft(u1)); % Take Fourier transform
F*"}aP$ ca2 = fftshift(fft(u2));
okbQ<{9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
7}M2bH} \K c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
/|*
Y2ETOr u2 = ifft(fftshift(c2)); % Return to physical space
93Co}@Y;Y+ u1 = ifft(fftshift(c1));
'>r7V if rem(m1,J) == 0 % Save output every J steps.
i3rH'B -I. U1 = [U1 u1]; % put solutions in U array
F u!RhsW5j U2=[U2 u2];
'yMF~r3 J MN1=[MN1 m1];
&=VDASEu z1=dz*MN1'; % output location
^0/j0]O end
nBk)WX&[K end
(sh)TBb5 hg=abs(U1').*abs(U1'); % for data write to excel
0PlO(" ,a ha=[z1 hg]; % for data write to excel
v`M3eh@$A t1=[0 t'];
z`:lcF{V hh=[t1' ha']; % for data write to excel file
RzWXKBI\E] %dlmwrite('aa',hh,'\t'); % save data in the excel format
Y "/]|'p figure(1)
o!)3 ? waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
[VE 8V- figure(2)
+E{|63~q waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
yu ;P +G
iof-7{+3_ 非线性超快脉冲耦合的数值方法的Matlab程序 6I%5Q4Ll iyg*Xbmi~. 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。
O#F4WWF 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
EOCN&_Z; [eC2 "&} tCdqh- V,%=AR5 % This Matlab script file solves the nonlinear Schrodinger equations
,^C--tgZJg % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
H ' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
DQ r Y*nH % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0tXS3+@n = ;C2K~8, C=1;
NuQdSj_> M1=120, % integer for amplitude
>Wv;R2| M3=5000; % integer for length of coupler
T\D}kQM N = 512; % Number of Fourier modes (Time domain sampling points)
"vOwd.(?N dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
,%M$0poKM T =40; % length of time:T*T0.
tNbN7y I dt = T/N; % time step
v_De dVhe n = [-N/2:1:N/2-1]'; % Index
/ G7vwC t = n.*dt;
s+<Yg$) ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8|\8O@ w=2*pi*n./T;
Sy0$z3 9 g1=-i*ww./2;
a ?)NC g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
0 eDHu g3=-i*ww./2;
Zcx`SC-0 P1=0;
= ,6z4" ) P2=0;
Zg{KFM% P3=1;
tM'P m P=0;
1pgU}sRk for m1=1:M1
<nT
+$ p=0.032*m1; %input amplitude
}khV'6"'| s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
v@
lM3_rbO s1=s10;
{+Rog/;S' s20=0.*s10; %input in waveguide 2
|l]XpWV s30=0.*s10; %input in waveguide 3
^f4s"T s2=s20;
k@k&}N0{ s3=s30;
r E.; g^4p p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
8|l\E VV6 %energy in waveguide 1
paCV!tP p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
P*3BB>FO %energy in waveguide 2
1cpiHZa p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
.uMn0PE %energy in waveguide 3
n'E(y)9| for m3 = 1:1:M3 % Start space evolution
Bf ~vA4 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
r{L>
F]Tw s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
U@uGNMKR s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
0dE@c./R i sca1 = fftshift(fft(s1)); % Take Fourier transform
S.-TOE sca2 = fftshift(fft(s2));
C26>BU< sca3 = fftshift(fft(s3));
- "' j7t: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
w"-Lc4t+ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
,9zjFI sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
3q\,$*D. s3 = ifft(fftshift(sc3));
5K>3My# s2 = ifft(fftshift(sc2)); % Return to physical space
iJ1"at s1 = ifft(fftshift(sc1));
F Q<Ju. end
4;yKOQD| p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!Prg_6
` p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
&8Cu#^3
p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Q ayPo]O P1=[P1 p1/p10];
3Q.#c,`jV P2=[P2 p2/p10];
7&jTtKLj P3=[P3 p3/p10];
n|9-KTe7|* P=[P p*p];
5YE'L. end
-#u=\8 figure(1)
r1 !@hT plot(P,P1, P,P2, P,P3);
Hq:X{)" I9_RlAd 转自：
http://blog.163.com/opto_wang/
