计算脉冲在非线性耦合器中演化的Matlab 程序 kYhV1I ZveNe~D7C % This Matlab script file solves the coupled nonlinear Schrodinger equations of
,i jB3J % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&SG5 f[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
4U8N7 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
eRqPZb"6MR pCf9"LLer %fid=fopen('e21.dat','w');
_/czH<
N = 128; % Number of Fourier modes (Time domain sampling points)
f,|g|&C M1 =3000; % Total number of space steps
$ >8O2p7W J =100; % Steps between output of space
J9*i`8kU. T =10; % length of time windows:T*T0
qfkd Q/fP T0=0.1; % input pulse width
"{S6iH)]8 MN1=0; % initial value for the space output location
lak,lDt] dt = T/N; % time step
mm9uhlV8 n = [-N/2:1:N/2-1]'; % Index
s{Og3qUy t = n.*dt;
EI9;J-c u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
-Qn l)JB u20=u10.*0.0; % input to waveguide 2
4]HW!J u1=u10; u2=u20;
d,b]#fj U1 = u1;
yq?\.~ax U2 = u2; % Compute initial condition; save it in U
'3w%K+eJY ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<vE|QxpR w=2*pi*n./T;
A<]
$[2qPj g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
abAw#X Q8 L=4; % length of evoluation to compare with S. Trillo's paper
m-qu<4A/U| dz=L/M1; % space step, make sure nonlinear<0.05
=9Vo [ for m1 = 1:1:M1 % Start space evolution
.Y|wG<E u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
V'tqsKQ! u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
G|*&owJ ca1 = fftshift(fft(u1)); % Take Fourier transform
p+pu_T;~ ca2 = fftshift(fft(u2));
A^E 6)A= c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
[8<0Q_?, c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
(wFoI}s u2 = ifft(fftshift(c2)); % Return to physical space
\11+~ u1 = ifft(fftshift(c1));
cij8'( "+! if rem(m1,J) == 0 % Save output every J steps.
PqIsk v+ U1 = [U1 u1]; % put solutions in U array
&1f3e U2=[U2 u2];
?@z/#3b MN1=[MN1 m1];
!PA ><F z1=dz*MN1'; % output location
!>"fDz<w` end
k*u6'IKi.4 end
_s+G02/q1 hg=abs(U1').*abs(U1'); % for data write to excel
diNAT`|?# ha=[z1 hg]; % for data write to excel
b9ud8wLE[ t1=[0 t'];
(&1.!R[X hh=[t1' ha']; % for data write to excel file
@tJ4^<`P{ %dlmwrite('aa',hh,'\t'); % save data in the excel format
r7sA;Y\ figure(1)
2">de/jS waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
OTGy[jY" figure(2)
k+%&dEE|vH waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
bEB2q\|J e W':b6}? 非线性超快脉冲耦合的数值方法的Matlab程序 qDTdYf v
k= |TE 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。
d&+ 0JI< 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
hj& ~Dn( gkX 7,J-0 tUuARo7# d/T&J= % This Matlab script file solves the nonlinear Schrodinger equations
}a/z.&x]V % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Fg 8lX9L % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@)x*6 2r+ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
qe 'ssX; ?E_;[(Mcr C=1;
Z wz co M1=120, % integer for amplitude
m[(_fOd M3=5000; % integer for length of coupler
7AS_Aw1L N = 512; % Number of Fourier modes (Time domain sampling points)
Vhh=GJ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
9=j) g T =40; % length of time:T*T0.
_g
fmo dt = T/N; % time step
{NQCe0S+p n = [-N/2:1:N/2-1]'; % Index
Q-!gO t = n.*dt;
+zd /< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
YF-A8gXS w=2*pi*n./T;
0{ua SR g1=-i*ww./2;
o <iU; 15 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
\m~p;B g3=-i*ww./2;
: 8j7}' P1=0;
O@
H.k<zn P2=0;
c{dabzL y P3=1;
t, dm3+R P=0;
u#rbc" for m1=1:M1
>MKj~Ud p=0.032*m1; %input amplitude
u]7wd3( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
(X
Oz0.W s1=s10;
P[-do s20=0.*s10; %input in waveguide 2
MoQ\~/Z| s30=0.*s10; %input in waveguide 3
-C i&h s2=s20;
(hdu+^Qj= s3=s30;
~ b m'i%$k p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
oPF]]Imu %energy in waveguide 1
jDqG9] p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
,~&HL7 v %energy in waveguide 2
GA$fueiQNs p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
<ShA_+Nd %energy in waveguide 3
;9WUt,R for m3 = 1:1:M3 % Start space evolution
\y:48zd s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
T)OR HJ&, s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
rX /' s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
m2"e ]I sca1 = fftshift(fft(s1)); % Take Fourier transform
@M B)B5 sca2 = fftshift(fft(s2));
+-(,'slov sca3 = fftshift(fft(s3));
Z)$@1Q4P?1 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
$H[q5(_~ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
H8[A*uYL
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
4oH ,_sr s3 = ifft(fftshift(sc3));
}) P!7t s2 = ifft(fftshift(sc2)); % Return to physical space
[`qdpzUp& s1 = ifft(fftshift(sc1));
0+ $gR~^^ end
d"miPR p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
dr}PjwW% p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
8
/t'; p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Uavl%Q P1=[P1 p1/p10];
knYp"<qj P2=[P2 p2/p10];
ls&H oJ7 P3=[P3 p3/p10];
~gW^9nWYU P=[P p*p];
ky vl>I0q@ end
fglfnx0{ figure(1)
LtX53c plot(P,P1, P,P2, P,P3);
xQDQgv wa [2Zy~`*y { 转自：
http://blog.163.com/opto_wang/
