计算脉冲在非线性耦合器中演化的Matlab 程序 hH HQmK<r
hD=.rDvO % This Matlab script file solves the coupled nonlinear Schrodinger equations of
v2_` iwE % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
yM~bU mSg % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
MqJ5 |C.q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'%82pZ,? a>x6n3{ %fid=fopen('e21.dat','w');
2,wwI<=E' N = 128; % Number of Fourier modes (Time domain sampling points)
()48 > || M1 =3000; % Total number of space steps
aCI3Tx&2qT J =100; % Steps between output of space
'NZ=DSGIy T =10; % length of time windows:T*T0
*~>p;* T0=0.1; % input pulse width
T;?k]4.X MN1=0; % initial value for the space output location
1X&.po dt = T/N; % time step
x x4GP2 n = [-N/2:1:N/2-1]'; % Index
yOt#6Vw t = n.*dt;
rlD!%gG2x u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
&a;?o~%*]i u20=u10.*0.0; % input to waveguide 2
IzJq:G. u1=u10; u2=u20;
I}m2 0|vv U1 = u1;
N!Rt040.% U2 = u2; % Compute initial condition; save it in U
}z x
~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
3 y e w=2*pi*n./T;
Rq%Kw > {& g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|?s sHW L=4; % length of evoluation to compare with S. Trillo's paper
? *%_:fB dz=L/M1; % space step, make sure nonlinear<0.05
5|nc^
1 2 for m1 = 1:1:M1 % Start space evolution
r4fHD~#l{ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
P.q zP/Ny u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
#K6cBf qI ca1 = fftshift(fft(u1)); % Take Fourier transform
P /d nH ca2 = fftshift(fft(u2));
8'HS$J;C c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
F,{mF2U*$ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
o$buoGS Pc u2 = ifft(fftshift(c2)); % Return to physical space
9&5<ZC -D u1 = ifft(fftshift(c1));
uO`MA%
z< if rem(m1,J) == 0 % Save output every J steps.
2Jio _Hk U1 = [U1 u1]; % put solutions in U array
dWPQp*f2 U2=[U2 u2];
&8z<~q MN1=[MN1 m1];
G %6P`: z1=dz*MN1'; % output location
KGHSEZi] end
Ca
PHF@6WN end
~e 1l7H; hg=abs(U1').*abs(U1'); % for data write to excel
NOuG# P ha=[z1 hg]; % for data write to excel
pX
^^ 0 t1=[0 t'];
6e B; hh=[t1' ha']; % for data write to excel file
`om+p ?j %dlmwrite('aa',hh,'\t'); % save data in the excel format
C=/B\G/.9 figure(1)
X S [L-NHG waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
. \" k49M` figure(2)
U8w_C\Q waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
<aJQV)]\ wOl?(w=| 非线性超快脉冲耦合的数值方法的Matlab程序 a/,>fv9;$ `;E/\eG" 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。
hd(FO KOP 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
.mt%8GM 2t-w0~O Ki2!sADd cKe %P|8 % This Matlab script file solves the nonlinear Schrodinger equations
]:59c{O % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
>H!Mx_fDL % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
W(`QbNJ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
l9I r@.m 6!ve6ZB[p C=1;
H<Oo./8+ M1=120, % integer for amplitude
/Hyz]46 M3=5000; % integer for length of coupler
Sw\ *$g] N = 512; % Number of Fourier modes (Time domain sampling points)
ViPC Yt`of dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
DH-M|~.sf^ T =40; % length of time:T*T0.
8AuBs;i dt = T/N; % time step
_1p8(n n = [-N/2:1:N/2-1]'; % Index
?)xIn)#l s t = n.*dt;
ej`%}e%2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
h'):/}JPl w=2*pi*n./T;
d,b4q&^ X8 g1=-i*ww./2;
6lSz/V; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
wZiUzS ;v g3=-i*ww./2;
;Y$>WKsV P1=0;
5&&4- P2=0;
xzOa9w/ P3=1;
(+>
2&@@< P=0;
~#A}=, 4> for m1=1:M1
xH-d<Ht,7 p=0.032*m1; %input amplitude
CubQ6@, s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
` p\=NP!n s1=s10;
c=oDzAzuV\ s20=0.*s10; %input in waveguide 2
cz>,sz~i s30=0.*s10; %input in waveguide 3
2 |s ohF s2=s20;
7K1-.uQ s3=s30;
QJ GGce p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
jwDlz.sW! %energy in waveguide 1
=
xO03|T;6 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Fb5U@X/vE %energy in waveguide 2
I&;>(@K p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
#j Q auO %energy in waveguide 3
\G" S7 for m3 = 1:1:M3 % Start space evolution
OSgJj MQ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
!Zz;;Z s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
A`c%p7Z% s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
*@2Bh 4 sca1 = fftshift(fft(s1)); % Take Fourier transform
x sryXex; sca2 = fftshift(fft(s2));
]pax,| +$C sca3 = fftshift(fft(s3));
t]yxL l\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Z2% HQL2 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Rh!UbEPjC sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
" O& 93#8 s3 = ifft(fftshift(sc3));
HN5m %R&` s2 = ifft(fftshift(sc2)); % Return to physical space
M!UTq f7XL s1 = ifft(fftshift(sc1));
mmAm @/ end
Xn6#q3;^| p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Ys"wG B> p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
c/;;zc p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
h0GoF A< P1=[P1 p1/p10];
aF{_"X2 P2=[P2 p2/p10];
*o6}>; P3=[P3 p3/p10];
^ X =Q{nB P=[P p*p];
WRh5v8Wz0 end
R 'Sd'pSDN figure(1)
fE#(M +(< plot(P,P1, P,P2, P,P3);
QQ*sjK.( {%V(Dd[B6 转自：
http://blog.163.com/opto_wang/
