计算脉冲在非线性耦合器中演化的Matlab 程序 cP]5Qz Xv5|j/< ~p % This Matlab script file solves the coupled nonlinear Schrodinger equations of
`akbzHOM % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
LK?V`J5wY % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
-9 L [eYn % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
j gk JF[t` ?)60JWOJ1 %fid=fopen('e21.dat','w');
A18 &9gY N = 128; % Number of Fourier modes (Time domain sampling points)
#Fl5]> | M1 =3000; % Total number of space steps
nJ ZQRRa:C J =100; % Steps between output of space
X-Q;4M-C J T =10; % length of time windows:T*T0
=s\RK
T0=0.1; % input pulse width
6{ qI MN1=0; % initial value for the space output location
>o #^)LN dt = T/N; % time step
ToNRY<! n = [-N/2:1:N/2-1]'; % Index
J4xJGO t = n.*dt;
IIrXI8'} u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
fV\ eksBF u20=u10.*0.0; % input to waveguide 2
%)|_&Rh u1=u10; u2=u20;
gk*Md+ U1 = u1;
xIrRFK9[Q U2 = u2; % Compute initial condition; save it in U
r 2Wx31j{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
M[Kk43;QY! w=2*pi*n./T;
3XOf-v:~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
)(Z)yz L=4; % length of evoluation to compare with S. Trillo's paper
Z Rjqjx dz=L/M1; % space step, make sure nonlinear<0.05
B!#F!Wk" for m1 = 1:1:M1 % Start space evolution
W $l%= / u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
<gdKuoY u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Gz>M`M`[4 ca1 = fftshift(fft(u1)); % Take Fourier transform
}`SXUM_sD` ca2 = fftshift(fft(u2));
Sv E|" c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
z@_ 9.n] c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
#]BpTpRAe< u2 = ifft(fftshift(c2)); % Return to physical space
AIx,c1G]K u1 = ifft(fftshift(c1));
RC S 91[ if rem(m1,J) == 0 % Save output every J steps.
HifU65"8 U1 = [U1 u1]; % put solutions in U array
+&T;jad2 U2=[U2 u2];
1VH$l(7IQ MN1=[MN1 m1];
B;r o(R z1=dz*MN1'; % output location
[q MFLY$ end
-quWnn/ end
@_O,0d
g hg=abs(U1').*abs(U1'); % for data write to excel
=> PBdW ha=[z1 hg]; % for data write to excel
z_jTR[d Y t1=[0 t'];
] [b2Q> hh=[t1' ha']; % for data write to excel file
pxF<L\L?: %dlmwrite('aa',hh,'\t'); % save data in the excel format
iTt#%Fs)4M figure(1)
nt"8kv waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
jv"^_1 figure(2)
`#m>3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Hko(@ z >/kwy2 非线性超快脉冲耦合的数值方法的Matlab程序 w'Kc#2 mNvK|bTUT 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。
P p}N-me>_ 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
Cw =wU/) PR&D67:Jy iz2I4 _N B Bub' % This Matlab script file solves the nonlinear Schrodinger equations
ATeXOe % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
}x[d]fcC % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
s1[_Pk;! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4zF|}ai Q l*+"0 C=1;
K{
s=k/h M1=120, % integer for amplitude
t*fG;YOg M3=5000; % integer for length of coupler
`VT0wAe2; N = 512; % Number of Fourier modes (Time domain sampling points)
pvz*(u dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
.>(?c92 T =40; % length of time:T*T0.
'.@'^80iQ dt = T/N; % time step
"hRY+{m n = [-N/2:1:N/2-1]'; % Index
J.`z;0]op t = n.*dt;
jU#/yM "Y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
O1o.^i$-M w=2*pi*n./T;
&wZ ggp g1=-i*ww./2;
Kb_R "b3v g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
!U,^+"l'GP g3=-i*ww./2;
8 e'0AI_> P1=0;
;x[F4d P2=0;
0d-w< lg9 P3=1;
~IHjj1s P=0;
s[yIvlHw` for m1=1:M1
62BJ;/ ] p=0.032*m1; %input amplitude
;%1ob f 89 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3^LSK7.: s1=s10;
q2I;Ly\3o s20=0.*s10; %input in waveguide 2
XA[G F6W,Y s30=0.*s10; %input in waveguide 3
s*g y k s2=s20;
#\ + TKK s3=s30;
fw y -M: p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
5XNIX)H %energy in waveguide 1
LhZWK^!{S p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
CI+dIv> %energy in waveguide 2
#]s> p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Z\=].[,w4 %energy in waveguide 3
:<%q9)aPf` for m3 = 1:1:M3 % Start space evolution
wz *QB6QtU s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
H=vrF - # s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
{cF7h)j s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
n9;+RhxA sca1 = fftshift(fft(s1)); % Take Fourier transform
O&# bC sca2 = fftshift(fft(s2));
>'i
d/ sca3 = fftshift(fft(s3));
/j]r ?KAzw sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
t)o #!)| sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Ejdw"P" sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
-aiQp@^/J s3 = ifft(fftshift(sc3));
n: ?fv=9n s2 = ifft(fftshift(sc2)); % Return to physical space
j+3~ s1 = ifft(fftshift(sc1));
\lK iUy/ end
a;Ic !:L p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
/Yk2 |L p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
IMY?L p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
"C $z) P1=[P1 p1/p10];
.>0e?A4,5? P2=[P2 p2/p10];
-ob_]CKtJ~ P3=[P3 p3/p10];
s-eC' )w~E P=[P p*p];
LxkT oO{ end
d\`A
^ figure(1)
^4 Ra$< plot(P,P1, P,P2, P,P3);
P sDks3cG SGW2 ' 转自：
http://blog.163.com/opto_wang/
