计算脉冲在非线性耦合器中演化的Matlab 程序 p),* 4@2< un!v1g9O % This Matlab script file solves the coupled nonlinear Schrodinger equations of
JW><&hY$" % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
P 0+@,kM % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
2G-" HOG % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
yU/?4/G! "|J6*s %fid=fopen('e21.dat','w');
aY,Bt N = 128; % Number of Fourier modes (Time domain sampling points)
|uz<) M1 =3000; % Total number of space steps
t oDi70o J =100; % Steps between output of space
gfN=0Xj4 T =10; % length of time windows:T*T0
'{~[e** T0=0.1; % input pulse width
Kv1~ ,j6 MN1=0; % initial value for the space output location
k ?6d\Q dt = T/N; % time step
Hc<@T_h+2 n = [-N/2:1:N/2-1]'; % Index
IQC [ewk t = n.*dt;
^{IZpT3 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
'l!\2Wv2 u20=u10.*0.0; % input to waveguide 2
\WnTpl>B u1=u10; u2=u20;
S]%,g%6i U1 = u1;
SX'NFdY U2 = u2; % Compute initial condition; save it in U
rxMo7px@}I ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
q$yg^:]2 w=2*pi*n./T;
>Ho=L)u g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
F~E)w5?\O L=4; % length of evoluation to compare with S. Trillo's paper
u SI@Cjp dz=L/M1; % space step, make sure nonlinear<0.05
P X^ k ; for m1 = 1:1:M1 % Start space evolution
rxol7"2l u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
2uT6M%OC u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
t>%b[(a ca1 = fftshift(fft(u1)); % Take Fourier transform
3 } phg ca2 = fftshift(fft(u2));
z8S]FpM6 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
HH6H4K3Zj c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
d)biMI}<5 u2 = ifft(fftshift(c2)); % Return to physical space
k0PwAt)65 u1 = ifft(fftshift(c1));
$$0 <
& if rem(m1,J) == 0 % Save output every J steps.
w DoCc: U1 = [U1 u1]; % put solutions in U array
]<YS7.pT U2=[U2 u2];
_8K8Ai-~.> MN1=[MN1 m1];
8r[TM z1=dz*MN1'; % output location
a w lq/ end
[];wP '* end
,%x2SyA hg=abs(U1').*abs(U1'); % for data write to excel
%nq<nfDT ha=[z1 hg]; % for data write to excel
,Js_ d t1=[0 t'];
%YF
/ =l hh=[t1' ha']; % for data write to excel file
fk?!0M6d %dlmwrite('aa',hh,'\t'); % save data in the excel format
@VOegf+N figure(1)
FdnLxw waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
@V^.eVM\R figure(2)
O"TVx P: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
=Oh$pZRymu P%yL { 非线性超快脉冲耦合的数值方法的Matlab程序 Z| UVH 6=JJ!`"<2 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
q3/4l%"X Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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a H*0g*( % This Matlab script file solves the nonlinear Schrodinger equations
HES$ . a % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Fq+Cr?- % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
"N &ix* ($ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ph(LsPT- [ -Y~g%M C=1;
~MB)}!S: M1=120, % integer for amplitude
F:<+}{Av M3=5000; % integer for length of coupler
N`N=}&v ] N = 512; % Number of Fourier modes (Time domain sampling points)
]
X ]!xvN@ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
/i@. Xg@: T =40; % length of time:T*T0.
hB\BFVUSn/ dt = T/N; % time step
s/~[/2[bnf n = [-N/2:1:N/2-1]'; % Index
:&z!o"K t = n.*dt;
Q2)5A& U\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
s 2N'Ip w=2*pi*n./T;
\& V[<] g1=-i*ww./2;
8aRmHy"9l g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
BSSeh e* g3=-i*ww./2;
@g#| srYD P1=0;
3 Z SU^v P2=0;
* Z .{1 P3=1;
cJwe4c6.m P=0;
r?0w5I for m1=1:M1
d^IX(y* $ p=0.032*m1; %input amplitude
5)k/ 4l ' s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
y< `:I|y s1=s10;
~ KGE(o4 p s20=0.*s10; %input in waveguide 2
u|ihUE!h s30=0.*s10; %input in waveguide 3
y}U'8*, s2=s20;
@c8RlW/A s3=s30;
q(s0dkrj p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
w\Q(wH' %energy in waveguide 1
bfJ<~ss/ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
qB $QC %energy in waveguide 2
&V &beq4)p p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
5>1c4u`x %energy in waveguide 3
FRPdfo37 for m3 = 1:1:M3 % Start space evolution
Ug gg!zA s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
=.m/ X> s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
k-s|gC4 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
oM#+Z
qP sca1 = fftshift(fft(s1)); % Take Fourier transform
\:n<&<aVSr sca2 = fftshift(fft(s2));
2" Unk\Y sca3 = fftshift(fft(s3));
9*n?V ;E sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
[["eK9 }0 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
LG(" <CU sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
i}<fg*6@E s3 = ifft(fftshift(sc3));
P a|*Jcr s2 = ifft(fftshift(sc2)); % Return to physical space
ZL!5dT&@W s1 = ifft(fftshift(sc1));
rO1N@kd/ end
Iz#jR2:yn p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
vf?m6CMU ! p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
rF?QI*`Y( p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
cZ .p P1=[P1 p1/p10];
Ve"M8-{oKk P2=[P2 p2/p10];
R >[G6LOG P3=[P3 p3/p10];
3ox|Mz<aZX P=[P p*p];
[Q8vS ;. end
l i')U figure(1)
&)!N5Veb plot(P,P1, P,P2, P,P3);
6k37RpgH eVbT<9k 转自：
http://blog.163.com/opto_wang/
