计算脉冲在非线性耦合器中演化的Matlab 程序 ?'+ kZ | N
Obw/9JO % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#Zt(g( T % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
,7mB`0j> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7dtkylW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s\3OqJo%) qpX sQim$~ %fid=fopen('e21.dat','w');
m9 D' yXZ N = 128; % Number of Fourier modes (Time domain sampling points)
vvmG46IgZ M1 =3000; % Total number of space steps
mB<*we J =100; % Steps between output of space
(hFyp}jkk T =10; % length of time windows:T*T0
P1I L ] T0=0.1; % input pulse width
~3,k8C"pRq MN1=0; % initial value for the space output location
.}e Pm( dt = T/N; % time step
XAw0Nn n = [-N/2:1:N/2-1]'; % Index
O 6Mxp - t = n.*dt;
kYnp$8 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
WI}cXXUKm0 u20=u10.*0.0; % input to waveguide 2
F0]xc u1=u10; u2=u20;
A#KfG1K> U1 = u1;
$fFh4O4 U2 = u2; % Compute initial condition; save it in U
|cIv&\ x ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
W 2T6JFv w=2*pi*n./T;
?3Y~q;I]O g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
5}NTqN0@ L=4; % length of evoluation to compare with S. Trillo's paper
['jr+gIfQ dz=L/M1; % space step, make sure nonlinear<0.05
1yV+~)by3 for m1 = 1:1:M1 % Start space evolution
g=L80$1 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^SC2k LI u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
TAp8x ca1 = fftshift(fft(u1)); % Take Fourier transform
AtYqD<hl: ca2 = fftshift(fft(u2));
L . DD c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
jN T+?2 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
fe8}2#<o u2 = ifft(fftshift(c2)); % Return to physical space
i.Z iLDs\7 u1 = ifft(fftshift(c1));
y ]D[JX[ if rem(m1,J) == 0 % Save output every J steps.
7-A/2/G< U1 = [U1 u1]; % put solutions in U array
Wf:LY L U2=[U2 u2];
iph}!3f MN1=[MN1 m1];
(Qf . S{ ; z1=dz*MN1'; % output location
I#PhzG C@ end
,Vfjt=6]} end
CWa~~h<r- hg=abs(U1').*abs(U1'); % for data write to excel
_bn
"c@s ha=[z1 hg]; % for data write to excel
4=qZ Z>[t t1=[0 t'];
?4cj" i hh=[t1' ha']; % for data write to excel file
E4,
J"T|@ %dlmwrite('aa',hh,'\t'); % save data in the excel format
r t'pc\|O& figure(1)
Fxv5kho waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
2Og<e| figure(2)
i !;9A6D waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
$Ts; o Q)Q1a; o 非线性超快脉冲耦合的数值方法的Matlab程序 sf"vi i,1A / }Pj^^6A< 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
.,F`*JVFq Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
BlfadM; 7j8lhrM}^ .t7ME{ K.Tob,5` % This Matlab script file solves the nonlinear Schrodinger equations
kgh0 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
M;9s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>Og| *g % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
,ygUy] x;{Hd;<YF C=1;
X& mD/1 M1=120, % integer for amplitude
'<{Jlz(u9 M3=5000; % integer for length of coupler
!< >*|a N = 512; % Number of Fourier modes (Time domain sampling points)
{5]c \_. dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
"x3x$JQZy T =40; % length of time:T*T0.
jN-!1O._G dt = T/N; % time step
4W#DLip9 n = [-N/2:1:N/2-1]'; % Index
XAZPbvG |$ t = n.*dt;
#I1q,fm ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%,(X R` w=2*pi*n./T;
n8tw8o%&[ g1=-i*ww./2;
+ZOKfX g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
,b4oV g3=-i*ww./2;
WK0:3q(P P1=0;
E0AbVa. P2=0;
QP/ZD|/ t1 P3=1;
\q\"=
P=0;
b] for m1=1:M1
Fw:_O2 p=0.032*m1; %input amplitude
C1>zwU_z o s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-lrcb/)Gz s1=s10;
n?U^vK _ s20=0.*s10; %input in waveguide 2
zf>*\pZE s30=0.*s10; %input in waveguide 3
) "Z6Q5k^ s2=s20;
/_qHF- s3=s30;
JIIc4fyy8s p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
rp+]f\] h %energy in waveguide 1
T%B z >K p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
=3 ovaP %energy in waveguide 2
W1521: p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
1nw\?r2 %energy in waveguide 3
'E&tEbY for m3 = 1:1:M3 % Start space evolution
S+"Bq:u" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
E]v?:!!ds s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
w{t]^w: s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
E*h!{)z@F sca1 = fftshift(fft(s1)); % Take Fourier transform
\t 5_ V)P sca2 = fftshift(fft(s2));
w3z'ZCcr;" sca3 = fftshift(fft(s3));
I{ h KN V sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Q :.i[ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
bYoBJ
#UX sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
P a eq s3 = ifft(fftshift(sc3));
?4oP=. s2 = ifft(fftshift(sc2)); % Return to physical space
I,< ?Kv s1 = ifft(fftshift(sc1));
S}a]Bt end
plp-[eKcD p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
2W 2 T p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
I&m' a p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
)ki
Gk}2 P1=[P1 p1/p10];
c& I P2=[P2 p2/p10];
?O3d Sxi P3=[P3 p3/p10];
Q6wa-Y, P=[P p*p];
@%G?Nht]o end
6ypLE@Mk figure(1)
DVVyWn[ plot(P,P1, P,P2, P,P3);
[uK{``" iP kCuLQ} 转自：
http://blog.163.com/opto_wang/
