计算脉冲在非线性耦合器中演化的Matlab 程序 v{[:7]b_= 74p=uQ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
!RD<" % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
4,]z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
j @HOU~x % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
cfP9b8JG f"}g5eg+ %fid=fopen('e21.dat','w');
e#t7 N = 128; % Number of Fourier modes (Time domain sampling points)
[ <,i}z M1 =3000; % Total number of space steps
FP_q?=~rFs J =100; % Steps between output of space
(/a#1Pd& T =10; % length of time windows:T*T0
^.HvuG},O T0=0.1; % input pulse width
6B=: P3Y MN1=0; % initial value for the space output location
!5}u \ dt = T/N; % time step
,|RN?1 ?U n = [-N/2:1:N/2-1]'; % Index
H6t'V%Ys t = n.*dt;
Qu;cl/& u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
00-cT9C3 u20=u10.*0.0; % input to waveguide 2
CVt:tV u1=u10; u2=u20;
aVvma= U1 = u1;
F!_8?=| U2 = u2; % Compute initial condition; save it in U
rijavZS6 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
LN0pC }F w=2*pi*n./T;
9> 6DA^ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
u$38"&cmA L=4; % length of evoluation to compare with S. Trillo's paper
) p^ " J| dz=L/M1; % space step, make sure nonlinear<0.05
x=M% QFe for m1 = 1:1:M1 % Start space evolution
?bH&F u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
!Soz??~o/ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
6|G&d>G$_ ca1 = fftshift(fft(u1)); % Take Fourier transform
Db`SNk= ca2 = fftshift(fft(u2));
d2a*xDkv c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
n(h9I'V8)F c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
xMs!FMn[ u2 = ifft(fftshift(c2)); % Return to physical space
E#!tXO&, u1 = ifft(fftshift(c1));
'w z6Zt if rem(m1,J) == 0 % Save output every J steps.
K'_qi8Z U1 = [U1 u1]; % put solutions in U array
B%^W$7
q U2=[U2 u2];
%;eD. If} MN1=[MN1 m1];
VtN1 [} z1=dz*MN1'; % output location
'CMbq Lk# end
, UsY0 YC end
xWnOOE$i hg=abs(U1').*abs(U1'); % for data write to excel
4OaU1Y[ ha=[z1 hg]; % for data write to excel
hGy[L3 { t1=[0 t'];
T!7B0_ hh=[t1' ha']; % for data write to excel file
lsaA
%dlmwrite('aa',hh,'\t'); % save data in the excel format
r@a]fTf figure(1)
~NMx:PP waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ve]hE} o/} figure(2)
2{Y~jYt{h waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
K0YQ b&*k 7tbY> U8 非线性超快脉冲耦合的数值方法的Matlab程序 @PT([1C OUk"aAo 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。
ZXIw^!8@/ 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
=(]Z%Q-V @jxP3:s *
'_(.Z: SK*z4 p % This Matlab script file solves the nonlinear Schrodinger equations
bu9.Hv T' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
3_ly"\I\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
W#P`Y < u$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
kV+%(Gl8 UCt}\IJ C=1;
>qz#& M1=120, % integer for amplitude
Y}]-o9Rl M3=5000; % integer for length of coupler
16ZyLt N = 512; % Number of Fourier modes (Time domain sampling points)
5-hnk'
~ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
|A/H*J, T =40; % length of time:T*T0.
i\,I)S%yJ dt = T/N; % time step
B<Q)z5KK n = [-N/2:1:N/2-1]'; % Index
H $+@O- t = n.*dt;
4*ZY#7h ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Sv_Nb > w=2*pi*n./T;
9=mc3m:Tb( g1=-i*ww./2;
N;`/>R4|I g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
vc :% g3=-i*ww./2;
YF)]B |I P1=0;
_i_P@I<M|~ P2=0;
pM^Z C P3=1;
\ h"U+Bv7 P=0;
Ptc+ypTu for m1=1:M1
.g 3=L p=0.032*m1; %input amplitude
P(3k1SM s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
/5<= m: s1=s10;
E.Q]X]q s20=0.*s10; %input in waveguide 2
Z}TLk^_[ s30=0.*s10; %input in waveguide 3
m"T}em# s2=s20;
sH.=Fao s s3=s30;
hrm<!uKn p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
/O5&)%N %energy in waveguide 1
9O - 2 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
m):*>o55 %energy in waveguide 2
X$;&M do. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
kU+|QBA@ %energy in waveguide 3
?=ffv]v| for m3 = 1:1:M3 % Start space evolution
?G5,}% s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
{#:31)P s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
{zWR)o .= s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
vQ
L$.A3> sca1 = fftshift(fft(s1)); % Take Fourier transform
EJ>&\I q sca2 = fftshift(fft(s2));
[ /YuI@C,@ sca3 = fftshift(fft(s3));
ei<0,w[V1{ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
CxTmW5l sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
> 1(J sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
V" Z8-u s3 = ifft(fftshift(sc3));
V^,eW! s2 = ifft(fftshift(sc2)); % Return to physical space
0'Si
^>bW s1 = ifft(fftshift(sc1));
. %s
U)$bH end
@zC6` p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Z4EmRa30 p p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
4 Wp5[(bg p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
R0}1:1}$Sn P1=[P1 p1/p10];
K Ax=C}9 P2=[P2 p2/p10];
ni&|;"Nt- P3=[P3 p3/p10];
+i!5<nn P=[P p*p];
-? -XO<I end
kzjuW figure(1)
0_eqO'" plot(P,P1, P,P2, P,P3);
ICb!AsL ]
\M+j u 转自：
http://blog.163.com/opto_wang/
