计算脉冲在非线性耦合器中演化的Matlab 程序 Sjp ]TWj D {r M % This Matlab script file solves the coupled nonlinear Schrodinger equations of
v>/_U % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
4n} a%ocv^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Ay0.D FL % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
SS 6K7 I8 f=' %fid=fopen('e21.dat','w');
dJ {q}U N = 128; % Number of Fourier modes (Time domain sampling points)
]j0/. pG M1 =3000; % Total number of space steps
h + <Jv J =100; % Steps between output of space
L;-V Yo# T =10; % length of time windows:T*T0
.Ta (v3om% T0=0.1; % input pulse width
CE @[Z MN1=0; % initial value for the space output location
g OK dt = T/N; % time step
UM<!bNz` n = [-N/2:1:N/2-1]'; % Index
Z& of-[) t = n.*dt;
cH6++r u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
-B&
Nou u20=u10.*0.0; % input to waveguide 2
+c$:#9$ | u1=u10; u2=u20;
Wv||9[Rd U1 = u1;
VWc)AfKe U2 = u2; % Compute initial condition; save it in U
{ H* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mKs J[)#. w=2*pi*n./T;
:DrF )1C g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
zGNmc7 L=4; % length of evoluation to compare with S. Trillo's paper
_2TL>1KZt dz=L/M1; % space step, make sure nonlinear<0.05
erh ez for m1 = 1:1:M1 % Start space evolution
NFyKTA6 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
= Z ql6D u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
qKr xln/T ca1 = fftshift(fft(u1)); % Take Fourier transform
[RF 6mWQ ca2 = fftshift(fft(u2));
x4K A8 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
6 {quO# ! c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
qOy0QZ#0 u2 = ifft(fftshift(c2)); % Return to physical space
oL~?^`cGZ u1 = ifft(fftshift(c1));
2u$rloc$b if rem(m1,J) == 0 % Save output every J steps.
*M/ :W =,t U1 = [U1 u1]; % put solutions in U array
>p'{! k U2=[U2 u2];
p zZ+!d MN1=[MN1 m1];
~1{ppc+
z1=dz*MN1'; % output location
3l"8_zLP end
a 7685Y end
O?O=]s
u hg=abs(U1').*abs(U1'); % for data write to excel
4fL`.n1^ ha=[z1 hg]; % for data write to excel
BO WOH t1=[0 t'];
bO bsj] hh=[t1' ha']; % for data write to excel file
dI|D c %dlmwrite('aa',hh,'\t'); % save data in the excel format
D^gS.X ^ figure(1)
%lD+57= waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
%DA&txX}w figure(2)
R a"hdxH waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
7MGvw-Tpb7 Qj'Ik`o 非线性超快脉冲耦合的数值方法的Matlab程序 dyk(/# *7W '4SDAa2f 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。
:yRv:`r3Lt 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
oKCv$>Y #IJe q0TVB A $ ]s{` jwUX?`6jX % This Matlab script file solves the nonlinear Schrodinger equations
]T'7+5w % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
a{@}vZx>3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
T];dFv-GT % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[(gXjt- ;s;3cC! C=1;
~>HzAo9e M1=120, % integer for amplitude
0)M8Tm0$ M3=5000; % integer for length of coupler
s <rV1D N = 512; % Number of Fourier modes (Time domain sampling points)
,ryL( "G dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
gq"d$Xh$x7 T =40; % length of time:T*T0.
tbWf m5 $ dt = T/N; % time step
YM};85 K n = [-N/2:1:N/2-1]'; % Index
* k<@ t = n.*dt;
hf^<lJh~= ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
V$sY3,J7A% w=2*pi*n./T;
@Ns[qn;9 g1=-i*ww./2;
UoPY:(?;i g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
P#,; )HF g3=-i*ww./2;
X6",Xr! { P1=0;
zh|9\ lf P2=0;
*ziR &Fr! P3=1;
l#`G4Vf P=0;
IvT><8<G for m1=1:M1
o<G#%9j p=0.032*m1; %input amplitude
0 ZM(heQ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
g;v;xlY`N s1=s10;
Xl$, f`f~ s20=0.*s10; %input in waveguide 2
tAF?. \x"g s30=0.*s10; %input in waveguide 3
nYFrp)DLK s2=s20;
5nUJ9sqA s3=s30;
p F4Z4?W p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
<S041KF.{6 %energy in waveguide 1
MUAs(M; p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2ozh!8aL %energy in waveguide 2
Rd& DH_<+^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
An$2='=/ %energy in waveguide 3
Xv|=RNz for m3 = 1:1:M3 % Start space evolution
Vv45w#w; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
3iIy_n WC s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
nuXL{ tg6 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
3f] ;y<Km sca1 = fftshift(fft(s1)); % Take Fourier transform
#3QPcoxa sca2 = fftshift(fft(s2));
IQRuqp KL sca3 = fftshift(fft(s3));
Jsysk $R sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
z@i4 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
d<6F'F^w.7 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
mAtqF
%V s3 = ifft(fftshift(sc3));
D2?H"PH s2 = ifft(fftshift(sc2)); % Return to physical space
@Fb1D"! s1 = ifft(fftshift(sc1));
%'yrI R end
.VCY|KZ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
_r*\ BM8y p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
,|{`(y/v
p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
E4L?4>V@\ P1=[P1 p1/p10];
U} RBgPX! P2=[P2 p2/p10];
;^5k _\ P3=[P3 p3/p10];
{ aUnOyX_ P=[P p*p];
+ cfEyiub end
`8ac;b figure(1)
N) H "'#- plot(P,P1, P,P2, P,P3);
>ESVHPj] P [ 2!D)A 转自：
http://blog.163.com/opto_wang/
