计算脉冲在非线性耦合器中演化的Matlab 程序 T mK[^ 1%$t;R % This Matlab script file solves the coupled nonlinear Schrodinger equations of
E4$y|Ni" % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
A^c
( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
M
~ ;]d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0"} =A,o(w ){LU>MW{& %fid=fopen('e21.dat','w');
.wV-g:2 N = 128; % Number of Fourier modes (Time domain sampling points)
(: P#l&f M1 =3000; % Total number of space steps
LC7%Bfn! J =100; % Steps between output of space
82)%`$yZw[ T =10; % length of time windows:T*T0
g@'2 :'\ T0=0.1; % input pulse width
(A )f
r4 MN1=0; % initial value for the space output location
Nwj M=GG dt = T/N; % time step
G#Kw6 n = [-N/2:1:N/2-1]'; % Index
x4i&;SP0 t = n.*dt;
W|Cs{rBc? u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
uZTbJ3$$ u20=u10.*0.0; % input to waveguide 2
n8E3w:A- u1=u10; u2=u20;
@Q7^caG U1 = u1;
\sAkKPI U2 = u2; % Compute initial condition; save it in U
]eUD3WUe>q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
OI_Px3)
y w=2*pi*n./T;
N\"Hf=Y(~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
*JRM(V+IEv L=4; % length of evoluation to compare with S. Trillo's paper
b0sj0w / dz=L/M1; % space step, make sure nonlinear<0.05
:-_"[:t 5Z for m1 = 1:1:M1 % Start space evolution
7z_ZD0PxPc u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
6?ky~ CV u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_?]W%R| ca1 = fftshift(fft(u1)); % Take Fourier transform
nA(5p?D+YB ca2 = fftshift(fft(u2));
^RE[5h6^q c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&_q8F,I \< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
d/3bE*gr
u2 = ifft(fftshift(c2)); % Return to physical space
xS(VgP&YGO u1 = ifft(fftshift(c1));
i[4!% FxB if rem(m1,J) == 0 % Save output every J steps.
|{ =Jp<} s U1 = [U1 u1]; % put solutions in U array
%ikPz~( U2=[U2 u2];
JqUft=p5 MN1=[MN1 m1];
l, 9r d[ z1=dz*MN1'; % output location
2Lytk OMf end
KRX\< @ end
Y[| 9
+T hg=abs(U1').*abs(U1'); % for data write to excel
Aj]/A ha=[z1 hg]; % for data write to excel
1g,Ofr t1=[0 t'];
O6vHo3k hh=[t1' ha']; % for data write to excel file
p-m\0tQ %dlmwrite('aa',hh,'\t'); % save data in the excel format
Ci 'V figure(1)
$VjMd f waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
QL @SE@" figure(2)
^F
qs,^~W waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
aT fc>A; #]QS 非线性超快脉冲耦合的数值方法的Matlab程序 *Kpw@4G wy^mh.= UX 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
sOVpDtZ]LR Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
He$v '87] 3kh!dL3D z}iz ~WZ G*=&yx."E % This Matlab script file solves the nonlinear Schrodinger equations
v-8{ mK`9\ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
S?zP;
iFj % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5R)IL 2~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~Y{]yBGoF *%\Xw*\0 C=1;
%__ @G_M M1=120, % integer for amplitude
r oPC
^Q M3=5000; % integer for length of coupler
R%~~'/2V N = 512; % Number of Fourier modes (Time domain sampling points)
++UxzUd dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
fT{jD_Q+3 T =40; % length of time:T*T0.
[VLq/lg* dt = T/N; % time step
:#\jx
n = [-N/2:1:N/2-1]'; % Index
4`'Rm/) t = n.*dt;
N?8nlrDQ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-7XaS&.4 w=2*pi*n./T;
-GCU6U| g1=-i*ww./2;
$m-C6xC/ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
lYS " g3=-i*ww./2;
aK(e%Ed t" P1=0;
:?}> Q P2=0;
l: kW| P3=1;
5z_Kkf?o P=0;
1NG[ for m1=1:M1
=(~*8hJ p=0.032*m1; %input amplitude
*y(UI/c s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
fB&i{_J s1=s10;
Z"KrirZ s20=0.*s10; %input in waveguide 2
-;;m/QM s30=0.*s10; %input in waveguide 3
_{
2`sL) s2=s20;
)Jw$&%/{1 s3=s30;
6;@:/kl t p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Bs|#7mA[ %energy in waveguide 1
fh66Gn, p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
.Wi%V" %energy in waveguide 2
K{9Vyt9,$ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
&|h9L' mr %energy in waveguide 3
T!pA$eE for m3 = 1:1:M3 % Start space evolution
@ *uZ+$ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
E(z|LS*3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
(LMT ' s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
[g}0.J`_ sca1 = fftshift(fft(s1)); % Take Fourier transform
$VP\Ac,! sca2 = fftshift(fft(s2));
U ]B-B+- sca3 = fftshift(fft(s3));
a1ps'^Qhh sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
7Bd=K=3u sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
hQz1zG`z7 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
h`eHoKJ #w s3 = ifft(fftshift(sc3));
5|`./+Ghk s2 = ifft(fftshift(sc2)); % Return to physical space
c >T)Rc s1 = ifft(fftshift(sc1));
Eg2SC? 5 end
<]_[o:nOP p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
D{q r N6g# p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Zlt, Us` p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
z5D*UOy5M P1=[P1 p1/p10];
meXwmO P2=[P2 p2/p10];
K|Xe) P3=[P3 p3/p10];
x8C
* P=[P p*p];
%Na` \`L{F end
d/ @P;YN! figure(1)
%h;1}SFl0 plot(P,P1, P,P2, P,P3);
d DAl n+ 4Me3{!HJ z 转自：
http://blog.163.com/opto_wang/
