计算脉冲在非线性耦合器中演化的Matlab 程序 lp4sO#>` S6cSeRmw % This Matlab script file solves the coupled nonlinear Schrodinger equations of
&9 8qAO]Z % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
]SK (cfA` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
DRw%~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
qoOHWh& IUzRE?Kzf %fid=fopen('e21.dat','w');
Y~Zg^x2 N = 128; % Number of Fourier modes (Time domain sampling points)
2t_E\W7w+ M1 =3000; % Total number of space steps
#* w$JH J =100; % Steps between output of space
\2 W( >_ z T =10; % length of time windows:T*T0
2-2'c?% T0=0.1; % input pulse width
CvlAn7r,@ MN1=0; % initial value for the space output location
)U8F6GIC&} dt = T/N; % time step
MECR0S9 n = [-N/2:1:N/2-1]'; % Index
fz<Y9h= t = n.*dt;
m"u 9AOH k u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
jk) U~KGcg u20=u10.*0.0; % input to waveguide 2
5-n N8qs u1=u10; u2=u20;
lnTl"9F U1 = u1;
9;.dNdg> U2 = u2; % Compute initial condition; save it in U
u K 8 r ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-6#i ~a] w=2*pi*n./T;
RL($h4d9 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ci ,o'`Q L=4; % length of evoluation to compare with S. Trillo's paper
3<B{-z dz=L/M1; % space step, make sure nonlinear<0.05
!iITX,'8 for m1 = 1:1:M1 % Start space evolution
P^+Og_$ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Jg^t r>I~ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
8iq~ha$]| ca1 = fftshift(fft(u1)); % Take Fourier transform
r/8,4 :rh ca2 = fftshift(fft(u2));
OG0ro(|dI c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
^fH]Rlx c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
9'O<d/xj/ u2 = ifft(fftshift(c2)); % Return to physical space
Bojm lVg u1 = ifft(fftshift(c1));
D4_D{\xhO if rem(m1,J) == 0 % Save output every J steps.
GMd81@7 U1 = [U1 u1]; % put solutions in U array
tBdvk>d U2=[U2 u2];
-j<m0XUQ MN1=[MN1 m1];
g`\Vy4w z1=dz*MN1'; % output location
AQ@A$ end
N\mV+f3A@, end
SrU,-mA W hg=abs(U1').*abs(U1'); % for data write to excel
{_PV~8u ha=[z1 hg]; % for data write to excel
:Ruj;j t1=[0 t'];
>KC *xa" hh=[t1' ha']; % for data write to excel file
h1J-AfV %dlmwrite('aa',hh,'\t'); % save data in the excel format
eF!c<
Kcr figure(1)
UI |D?z< waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ePB=aCZ figure(2)
e( j"u;= waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
H`m| R Ywlym\
[+ 非线性超快脉冲耦合的数值方法的Matlab程序 $
5 o"K{^ L~u 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。
v='7 .A 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
@^/JNtbH! yP~ D." dEns|r <"aPoGda % This Matlab script file solves the nonlinear Schrodinger equations
a!4'}gHR % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
;\( wJ{u?Y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
t~ gnai % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
no^I![_M (~,Q-w" C=1;
'N0d==aI M1=120, % integer for amplitude
;w[|IRa M3=5000; % integer for length of coupler
d(42ob.Tr N = 512; % Number of Fourier modes (Time domain sampling points)
|\Jpjm)? dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
LR'F/.Dx T =40; % length of time:T*T0.
m`E8 g VC dt = T/N; % time step
rn U2EL n = [-N/2:1:N/2-1]'; % Index
KYd2=P6 t = n.*dt;
`[/BG)4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
f`P%aX'cBQ w=2*pi*n./T;
`fc2vaSH = g1=-i*ww./2;
,]1K^UeZ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
8BC}D +q g3=-i*ww./2;
|_
E)2b:h P1=0;
\*1pFX# P2=0;
-0Y8/6]( P3=1;
tb^3-ZUb P=0;
L0_R2E A for m1=1:M1
Ptw E[YDu p=0.032*m1; %input amplitude
X{<j%PdC s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
eB^:+h#A_ s1=s10;
@v a)j s20=0.*s10; %input in waveguide 2
)# M*@e$k s30=0.*s10; %input in waveguide 3
YjoN: z`b s2=s20;
jo0p/5; s3=s30;
'l!tQD! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
3Q Z w %energy in waveguide 1
E;9SsA
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
SPn0D9 b] %energy in waveguide 2
z9u"?vdA p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
rW&8#& %energy in waveguide 3
zf4@:GM` for m3 = 1:1:M3 % Start space evolution
VLkK6W.u s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
e(,sFhR s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
~;3N'o s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
@ $4(!80- sca1 = fftshift(fft(s1)); % Take Fourier transform
y!)Z ^u sca2 = fftshift(fft(s2));
iw1 2x: sca3 = fftshift(fft(s3));
y`! 3Z} 7 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
` ` 6?;Y sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Nq"/:3@4 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
zgJ%Z r!~ s3 = ifft(fftshift(sc3));
P<km?\Xp( s2 = ifft(fftshift(sc2)); % Return to physical space
8 U B?X s1 = ifft(fftshift(sc1));
v](7c2; end
Yhb=^)@)) p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\:'=ccf p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3z!\Z[ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
ZH~ T'Bg P1=[P1 p1/p10];
ZB B^?FF P2=[P2 p2/p10];
.3t[M0sd P3=[P3 p3/p10];
Wm7Dy7#l P=[P p*p];
Yvcd (2 end
@c9VCG D figure(1)
( B}+uI{ plot(P,P1, P,P2, P,P3);
(sq4 '@3hU|jO! 转自：
http://blog.163.com/opto_wang/
