计算脉冲在非线性耦合器中演化的Matlab 程序 :hMuxHr mnil1*-c0 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
3N]pN<3@ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
t4gD*j6J3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!5A
nr % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p~3CXmUc~ k ,<L#?,a %fid=fopen('e21.dat','w');
(Mtc&+n{ N = 128; % Number of Fourier modes (Time domain sampling points)
~Zj?%4 M1 =3000; % Total number of space steps
k.lnG5e J =100; % Steps between output of space
c7iu[vE'+ T =10; % length of time windows:T*T0
u8?ceM^r T0=0.1; % input pulse width
%{HqF>=~ MN1=0; % initial value for the space output location
'kh%^_FH7 dt = T/N; % time step
r`S]`& #}( n = [-N/2:1:N/2-1]'; % Index
x7NxHTL t = n.*dt;
( j-(fS u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
5n9F\T5 u20=u10.*0.0; % input to waveguide 2
dvL '>'g u1=u10; u2=u20;
P%/+?(? U1 = u1;
8AefgjE U2 = u2; % Compute initial condition; save it in U
s L\|y38' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
MnX2sX| w=2*pi*n./T;
S>"d UM g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
{ X"X.`p L=4; % length of evoluation to compare with S. Trillo's paper
ax 3:rl dz=L/M1; % space step, make sure nonlinear<0.05
'6xn!dK for m1 = 1:1:M1 % Start space evolution
QPFpGS{ d u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
0 \h2& u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
(O<l Vz@8 ca1 = fftshift(fft(u1)); % Take Fourier transform
}XXE
hOO ca2 = fftshift(fft(u2));
9s7B1Pf c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Y/$SriC_+' c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+m+HC(Z u2 = ifft(fftshift(c2)); % Return to physical space
G4RsH/ u1 = ifft(fftshift(c1));
k~q[qKb8y: if rem(m1,J) == 0 % Save output every J steps.
m.^6e f U1 = [U1 u1]; % put solutions in U array
F(XWnfUv U2=[U2 u2];
D:F!;n9 MN1=[MN1 m1];
>Y \4 v}- z1=dz*MN1'; % output location
\4vFEJSh end
x`lBG%Y[-v end
Mq7|37(N[ hg=abs(U1').*abs(U1'); % for data write to excel
9Q. j
< ha=[z1 hg]; % for data write to excel
z ?gJHN< t1=[0 t'];
{==Q6BG* hh=[t1' ha']; % for data write to excel file
b#y}V Y)? %dlmwrite('aa',hh,'\t'); % save data in the excel format
DX!$k[ figure(1)
5S7Z]DXiT8 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
[ wu%t8O2 figure(2)
4o=G) KO{ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Tl1?5 &G"]v]V 非线性超快脉冲耦合的数值方法的Matlab程序 9<YB &:< 3{_+dE"9 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。
'{+hti,Lh 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
+Rh'VZJs (&gCVf %(e=Q^= brVT % This Matlab script file solves the nonlinear Schrodinger equations
]':C~ -RV{ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
j xoEOEA % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
A9R}74e4g % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
m0#hG
x x [? _F C=1;
e U12*( M1=120, % integer for amplitude
/J6CSk M3=5000; % integer for length of coupler
EP8LJzd" N = 512; % Number of Fourier modes (Time domain sampling points)
1rKR =To dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
I&v B\A T =40; % length of time:T*T0.
m2}& 5vD8- dt = T/N; % time step
*PI3L/* n = [-N/2:1:N/2-1]'; % Index
D H.ljGb t = n.*dt;
[Ytia#Vv ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%*/[aq, # w=2*pi*n./T;
._R82 gy g1=-i*ww./2;
3a 5H<3w_ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
|/s.P NP2 g3=-i*ww./2;
~W#f,mf P1=0;
MVj@0W33m P2=0;
?y
'.sQ P3=1;
jsG9{/Ov3 P=0;
4R0_%x6vG for m1=1:M1
O3_Mrn(R p=0.032*m1; %input amplitude
*H$nydQ: s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
/qCYNwWH9 s1=s10;
H{V-C_ s20=0.*s10; %input in waveguide 2
m0edkt-x s30=0.*s10; %input in waveguide 3
hw7_8pAbh s2=s20;
lAGxE-B^a" s3=s30;
mA."*)8VNg p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
CJC|%i3 %energy in waveguide 1
d}G?iX;c} p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
`SG70/ %energy in waveguide 2
>hhd 9 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
she`_'?5 %energy in waveguide 3
l?~ci
;lG for m3 = 1:1:M3 % Start space evolution
IQ_0[ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
dOhV`8l s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
AVJk s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
EvYw$ j sca1 = fftshift(fft(s1)); % Take Fourier transform
Vy9n3W"FB1 sca2 = fftshift(fft(s2));
GW W@8GNI sca3 = fftshift(fft(s3));
pta%%8": sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
U %4g:s sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
^4[\-L8Lpq sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
S ~_ % s3 = ifft(fftshift(sc3));
\w:u&6,0O s2 = ifft(fftshift(sc2)); % Return to physical space
j\vK`.z s1 = ifft(fftshift(sc1));
8x{vgx @M end
J.&q[ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
OBl8kH(b> p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
MJb = +L p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
QA3l:D}u P1=[P1 p1/p10];
<H p"ZCN P2=[P2 p2/p10];
*"5a5.`%, P3=[P3 p3/p10];
R*y[/Aw P=[P p*p];
rNAu@B end
z>{KeX: figure(1)
EH3G|3^xz plot(P,P1, P,P2, P,P3);
)k1,o Ux H>] z=w~ 转自：
http://blog.163.com/opto_wang/
