计算脉冲在非线性耦合器中演化的Matlab 程序 ivP#qM1*; (-hGb: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
P(~vqo>! % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
5VK.Zs\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=LojRY % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
bLyaJ%pa\/ c>yqq' %fid=fopen('e21.dat','w');
nQ^ c{Bm: N = 128; % Number of Fourier modes (Time domain sampling points)
629 #t`W\ M1 =3000; % Total number of space steps
(b;*8 J =100; % Steps between output of space
"tg ?V T =10; % length of time windows:T*T0
*waaM]u T0=0.1; % input pulse width
-gy@sSfvkv MN1=0; % initial value for the space output location
Eh|v>Yew dt = T/N; % time step
_Rm1-,3 n = [-N/2:1:N/2-1]'; % Index
^z}$ '<D9 t = n.*dt;
{K >}eO:K u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
E@92hB4D" u20=u10.*0.0; % input to waveguide 2
_*LgpZ-2( u1=u10; u2=u20;
" /qm,$ U1 = u1;
@0U={qX U2 = u2; % Compute initial condition; save it in U
Eh/Z4 pz T ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
s|o+
Im w=2*pi*n./T;
2H2Yxe7? - g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
oTLpq:9J L=4; % length of evoluation to compare with S. Trillo's paper
Xi81?F?[ dz=L/M1; % space step, make sure nonlinear<0.05
5 p! rZ for m1 = 1:1:M1 % Start space evolution
[mA\,ny9 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
5.zv0tJku u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
$ { 5 |{` ca1 = fftshift(fft(u1)); % Take Fourier transform
p1B~F ca2 = fftshift(fft(u2));
MtKM#@ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
D:vX/mf;7 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
OVa38Aucr3 u2 = ifft(fftshift(c2)); % Return to physical space
.|z8WF* u1 = ifft(fftshift(c1));
Y>To k|PV if rem(m1,J) == 0 % Save output every J steps.
U6yZKK U1 = [U1 u1]; % put solutions in U array
Hw
1cc3! U2=[U2 u2];
Z@ QJ5F1y MN1=[MN1 m1];
dE ]y b|Ld z1=dz*MN1'; % output location
GLE"[!s]f end
F%^)oQT+c end
iFkXt<_A hg=abs(U1').*abs(U1'); % for data write to excel
_0 E KE ha=[z1 hg]; % for data write to excel
Uy5G,! t1=[0 t'];
9@yi
UX hh=[t1' ha']; % for data write to excel file
kP,^c { %dlmwrite('aa',hh,'\t'); % save data in the excel format
IJ#+"(?7,u figure(1)
v2; ' F waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
qM8"* dL figure(2)
5><KTya?= waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
c%vtg.A (~OP)F). 非线性超快脉冲耦合的数值方法的Matlab程序 Gx/kel [Y} 8D6rShx = 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。
l7vxTj@(- 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
x#c%+ bT bF nC ( <eL /;clxtus % This Matlab script file solves the nonlinear Schrodinger equations
s5
($b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
M"
R= ;n % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
r%412 # % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;\(X;kQi p` /c& } C=1;
fF]w[lLDv M1=120, % integer for amplitude
, Aw
Z% M3=5000; % integer for length of coupler
KuJNKuHa. N = 512; % Number of Fourier modes (Time domain sampling points)
Z,1b$:+ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
J1g+H2 T =40; % length of time:T*T0.
Nn='9s9F?} dt = T/N; % time step
Wf:LY L n = [-N/2:1:N/2-1]'; % Index
iph}!3f t = n.*dt;
(Qf . S{ ; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
SI,
t:=D w=2*pi*n./T;
(C.<H6]= g1=-i*ww./2;
*"Uf| g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
l?) !^}Qc g3=-i*ww./2;
OAo;vC:^ P1=0;
L25%KGg' o P2=0;
uZe"M(3r$ P3=1;
7(l>Ck3B# P=0;
Y1R?, 5 for m1=1:M1
C2C 1 @=w p=0.032*m1; %input amplitude
kJK*wq]U6 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
\[&&4CN{ s1=s10;
s`gfz}/ s20=0.*s10; %input in waveguide 2
8F9x2CM-[C s30=0.*s10; %input in waveguide 3
qT~a`ou: s2=s20;
6_g:2=6S s3=s30;
sf"vi i,1A p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
/ }Pj^^6A< %energy in waveguide 1
.,F`*JVFq p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
BlfadM; %energy in waveguide 2
7j8lhrM}^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Y49&EQ %energy in waveguide 3
+t%1FkI\ for m3 = 1:1:M3 % Start space evolution
3 # "!Hg s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
)kD B*(? s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Vw]!Kb7tA s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
bs0[ a 1/ sca1 = fftshift(fft(s1)); % Take Fourier transform
(0E<Fz
V sca2 = fftshift(fft(s2));
U^8S@#1Q sca3 = fftshift(fft(s3));
NG_7jZzXA9 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
hBi/lHu' sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
eZ BC@y sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
<$? ?Z;6 s3 = ifft(fftshift(sc3));
D)tL}X$ s2 = ifft(fftshift(sc2)); % Return to physical space
{mUt|m 7! s1 = ifft(fftshift(sc1));
+{0v@6<(02 end
/j -c29nz p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
>t{-_4Yv? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@FZbp p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
+xd@un[r< P1=[P1 p1/p10];
=Cd{bj.8 P2=[P2 p2/p10];
uS5G(} [ P3=[P3 p3/p10];
6MNr H P=[P p*p];
7=/iFv[ end
?d Pr HSy figure(1)
C1>zwU_z o plot(P,P1, P,P2, P,P3);
!jvl"+_FV zf>*\pZE 转自：
http://blog.163.com/opto_wang/
