计算脉冲在非线性耦合器中演化的Matlab 程序 IiJZ 5'{ -WJ? :?' % This Matlab script file solves the coupled nonlinear Schrodinger equations of
[?k8}B)mHB % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
k@dN$O%p % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
][&9]omB % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:A 1: IkPN?N %fid=fopen('e21.dat','w');
HKDID[d0 N = 128; % Number of Fourier modes (Time domain sampling points)
rl08 R M1 =3000; % Total number of space steps
2]cRXJ7h J =100; % Steps between output of space
)h{ ]k= T =10; % length of time windows:T*T0
4_/?: $KO T0=0.1; % input pulse width
/Ncm^b4 MN1=0; % initial value for the space output location
m
ci/'b Xt dt = T/N; % time step
n'1'!J; Q n = [-N/2:1:N/2-1]'; % Index
vy9 w$ls t = n.*dt;
8s{?v &p u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
l{j~Q^U}) u20=u10.*0.0; % input to waveguide 2
v'!a\b`9 u1=u10; u2=u20;
Ho;X4lo[j U1 = u1;
PwB1]p= U2 = u2; % Compute initial condition; save it in U
t. ='/` !N ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7!WA)@6 w=2*pi*n./T;
2-N ' ya g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
"VG +1r+]4 L=4; % length of evoluation to compare with S. Trillo's paper
HlvuW(,x= dz=L/M1; % space step, make sure nonlinear<0.05
;!!n{l$r' for m1 = 1:1:M1 % Start space evolution
u&mS8i } u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
~Wo)?q8UY, u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
4%nE*H% ca1 = fftshift(fft(u1)); % Take Fourier transform
H,nec<Jp ca2 = fftshift(fft(u2));
*!s; "U c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
y){
k3lm0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
scLn= u2 = ifft(fftshift(c2)); % Return to physical space
9RN-suE[ u1 = ifft(fftshift(c1));
Od4E x;F if rem(m1,J) == 0 % Save output every J steps.
? T9(Vw U1 = [U1 u1]; % put solutions in U array
#txE=e"&o U2=[U2 u2];
jB{4\) MN1=[MN1 m1];
Qham^ z1=dz*MN1'; % output location
WmY`` end
mGp.3 {j end
s7Ub@ hg=abs(U1').*abs(U1'); % for data write to excel
^?7`;/ ha=[z1 hg]; % for data write to excel
y{dTp t1=[0 t'];
/x_o!<M hh=[t1' ha']; % for data write to excel file
x8S7oO7 %dlmwrite('aa',hh,'\t'); % save data in the excel format
W`\R%>$H figure(1)
1%4sHSN waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
x=ul&|^7D figure(2)
a}%#* J)! waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
At7>V-f} ; ;L[e]Z 非线性超快脉冲耦合的数值方法的Matlab程序 *s9C!w YMZ 0"CG7Vg,zh 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。
+ qh[N @F 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
K+;e4 _\ ,lZB96r0 xx[9~z=d ZovW0 Q)m % This Matlab script file solves the nonlinear Schrodinger equations
O8 B\{T1 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
ne 4Q#P % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+L7n< U3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
cSXwYZDx? >-H {Z{VDd C=1;
S H! M1=120, % integer for amplitude
0NS<?p~_S M3=5000; % integer for length of coupler
G 6T_O N = 512; % Number of Fourier modes (Time domain sampling points)
l
c+g &f dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
b )B?
F T =40; % length of time:T*T0.
ee yHy"@ dt = T/N; % time step
!o:f$6EA~C n = [-N/2:1:N/2-1]'; % Index
{phNds% t = n.*dt;
&*+'>UEe5 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8C*c{(4 w=2*pi*n./T;
5H*\t 7 g1=-i*ww./2;
_lamn }(x0 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
~`aa5;Ab_ g3=-i*ww./2;
|Y ?H A& P1=0;
z6*X%6,8 P2=0;
Zl^\Q=*s P3=1;
u 6AA 4( P=0;
-[cTx[Z, for m1=1:M1
'.:z&gSqx0 p=0.032*m1; %input amplitude
vEJWFoeEFm s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
uScMn/ % s1=s10;
L DP UD' s20=0.*s10; %input in waveguide 2
3yVMXK s30=0.*s10; %input in waveguide 3
<sBbT ` s2=s20;
G3Z)Z) N s3=s30;
k?+?v?I
= p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
<g"{Wv: h %energy in waveguide 1
e )d`pQ6 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
4 o Fel.o %energy in waveguide 2
5 > [u ` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
sB7#
~p A %energy in waveguide 3
1*\o. for m3 = 1:1:M3 % Start space evolution
'Gj3:-xqL s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
MN\HDKN s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
GP N]9 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
I>W=x'PkLn sca1 = fftshift(fft(s1)); % Take Fourier transform
2LF/H$] o5 sca2 = fftshift(fft(s2));
l3)} qu sca3 = fftshift(fft(s3));
]'&LGA` sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
;ub;l h 3 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Z?h~{Mg sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Q'=x|K#xj s3 = ifft(fftshift(sc3));
b,7k)ND1F s2 = ifft(fftshift(sc2)); % Return to physical space
c2l@6<Ww s1 = ifft(fftshift(sc1));
|fK1/<sz# end
,Lr. 9I. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
NPy&O cRl p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
v[1aW v: p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
"~sW"n(F_ P1=[P1 p1/p10];
KcWN,!G P2=[P2 p2/p10];
wW>A_{Y P3=[P3 p3/p10];
zdB^S%cztS P=[P p*p];
TM%| '^) end
"\: `/k3 figure(1)
=$' 6(aDH plot(P,P1, P,P2, P,P3);
; ZA~p e"{{ TcNk 转自：
http://blog.163.com/opto_wang/
