计算脉冲在非线性耦合器中演化的Matlab 程序 Lf&p2p ?~c ync2X{9D % This Matlab script file solves the coupled nonlinear Schrodinger equations of
k+{ -iPm{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Z T Wbe % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
n@mWB UM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^TJn&k bBc<yaN %fid=fopen('e21.dat','w');
G@oY2sM" N = 128; % Number of Fourier modes (Time domain sampling points)
p-GlGEt_X M1 =3000; % Total number of space steps
*T*=~Y4kE J =100; % Steps between output of space
@H"~/ m_o T =10; % length of time windows:T*T0
aIpDf|~ T0=0.1; % input pulse width
cXFNX< MN1=0; % initial value for the space output location
KtU I(*$` dt = T/N; % time step
^1BQejD n = [-N/2:1:N/2-1]'; % Index
``)ys^V t = n.*dt;
G,e>dp_cPu u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
xN:ih*+,v u20=u10.*0.0; % input to waveguide 2
ns9iTU) u1=u10; u2=u20;
P&V,x`<Z U1 = u1;
p3` 'i U2 = u2; % Compute initial condition; save it in U
6&S;Nrg9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
XL>c TM w=2*pi*n./T;
x'{L %c>L g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
M2(+}gv;7p L=4; % length of evoluation to compare with S. Trillo's paper
3XYCtp8 dz=L/M1; % space step, make sure nonlinear<0.05
`@b+'L for m1 = 1:1:M1 % Start space evolution
ZWQrG'$?o8 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
k, & *d4 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
7c1xB.g
ca1 = fftshift(fft(u1)); % Take Fourier transform
V~t q
_ ca2 = fftshift(fft(u2));
v}!eJzeH c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
5 e~\o}] c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
{1;j1|CI u2 = ifft(fftshift(c2)); % Return to physical space
1@6dHFA`o u1 = ifft(fftshift(c1));
'3O@Nxof4 if rem(m1,J) == 0 % Save output every J steps.
3,+)3,N U1 = [U1 u1]; % put solutions in U array
t&T0E.kh*X U2=[U2 u2];
+ VkhM;'"C MN1=[MN1 m1];
Sg(fZ' - z1=dz*MN1'; % output location
Xi^3o end
H'Bo r\;[> end
oA%8k51>~K hg=abs(U1').*abs(U1'); % for data write to excel
0tv"tA; ha=[z1 hg]; % for data write to excel
w>>)3:Ytd t1=[0 t'];
3zo]*6p0 hh=[t1' ha']; % for data write to excel file
K9B _o, %dlmwrite('aa',hh,'\t'); % save data in the excel format
/_ 5I}{ figure(1)
:'9%~q.D4 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
T&c0j( figure(2)
4HQP, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
?Y 7'OlO 5@ecZ2`)+h 非线性超快脉冲耦合的数值方法的Matlab程序 zZ &L# OvqCuX 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。
6ziiV _p 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
REUWK#> WeNx9+2=Z =p ,+a/* yBqv'Y % This Matlab script file solves the nonlinear Schrodinger equations
{ </M C` % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
e6f:@ O? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\>0%E{CR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3^AycwNBA <NZ ^*] C=1;
}'mVD^<+ M1=120, % integer for amplitude
0g}+%5]yg M3=5000; % integer for length of coupler
.V G$ `g" N = 512; % Number of Fourier modes (Time domain sampling points)
-\6nT'P dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
\g< 9_ T =40; % length of time:T*T0.
Dnn$-W|NC dt = T/N; % time step
.|[ZEXq n = [-N/2:1:N/2-1]'; % Index
@ FVan t = n.*dt;
b fy `UZr ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[,[;'::=o4 w=2*pi*n./T;
}`#OA]NZ g1=-i*ww./2;
qplz != g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
]H<5]({F g3=-i*ww./2;
wQbN5*82 P1=0;
lc9aDt P2=0;
0vOt. LC/S P3=1;
B7r={P!0 P=0;
k~f3~- " for m1=1:M1
0f~7n*XH p=0.032*m1; %input amplitude
8}9|hT;
s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
v$c*3H.seM s1=s10;
d#P3
< s20=0.*s10; %input in waveguide 2
y3l3XLI*b s30=0.*s10; %input in waveguide 3
np3 $bqm s2=s20;
rvO7e cR" s3=s30;
# RAez:BI p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~wG.'d] %energy in waveguide 1
par| j ] p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
td!WgL,m %energy in waveguide 2
l9"4"+ ?j< p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
q>: >f+4 %energy in waveguide 3
(O {5L( for m3 = 1:1:M3 % Start space evolution
<tkxE!xF`J s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
lg` Qi& s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
d~+8ui{-U s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
~XAtt\WS
sca1 = fftshift(fft(s1)); % Take Fourier transform
]"bkB+I sca2 = fftshift(fft(s2));
9Fb|B sca3 = fftshift(fft(s3));
}YUUC q& sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#?%akQ+w sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
JTbg8b sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
3GVE/GtU s3 = ifft(fftshift(sc3));
BG:l Zj'I s2 = ifft(fftshift(sc2)); % Return to physical space
(2J_Y*N~> s1 = ifft(fftshift(sc1));
k^3 ?Z2a end
.b]
32Ww p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
AQkH3p/W p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
0tbximmDb p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
P<P4*cOV P1=[P1 p1/p10];
7^$PauAv P2=[P2 p2/p10];
$ nN`K*% P3=[P3 p3/p10];
}p-<+sFo P=[P p*p];
]D|sQPi]F end
1(!w xJ figure(1)
+g36,!q plot(P,P1, P,P2, P,P3);
VsS. \ 1 =Gsn4>~%n 转自：
http://blog.163.com/opto_wang/
