计算脉冲在非线性耦合器中演化的Matlab 程序 _;J9q} X CyK$XDHa % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Io4:$w % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
{YKMQI^O/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
PgG |7=' % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
T956L'.+G &x0TnW"g %fid=fopen('e21.dat','w');
}N#>q.M N = 128; % Number of Fourier modes (Time domain sampling points)
OJ_2z| f< M1 =3000; % Total number of space steps
CI~;B J =100; % Steps between output of space
{Y* ]Qc T =10; % length of time windows:T*T0
WKrZTPD'm T0=0.1; % input pulse width
Nh\8+v*+{ MN1=0; % initial value for the space output location
fD#&: ) dt = T/N; % time step
U3 8wGSG n = [-N/2:1:N/2-1]'; % Index
YqY6\ mo t = n.*dt;
kX ,FQG> u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
d-N"m I- u20=u10.*0.0; % input to waveguide 2
@+CSY-g$ u1=u10; u2=u20;
Q@ ) rw0$ U1 = u1;
1=q?#PQ U2 = u2; % Compute initial condition; save it in U
M%5$-;6~_ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
WtdkA Sj w=2*pi*n./T;
oCd OC5 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
M(h H#_ $ L=4; % length of evoluation to compare with S. Trillo's paper
W$t}3R u dz=L/M1; % space step, make sure nonlinear<0.05
wM4g1H%s for m1 = 1:1:M1 % Start space evolution
k>0cTBY& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
rIFC#Jd/ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
D N 8pJa ca1 = fftshift(fft(u1)); % Take Fourier transform
V\M!]Nnxr ca2 = fftshift(fft(u2));
V+a%,sI c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
'3u]-GU2_ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
pTX'5 u2 = ifft(fftshift(c2)); % Return to physical space
@H# kvYWmn u1 = ifft(fftshift(c1));
ep}/dBg if rem(m1,J) == 0 % Save output every J steps.
\lbiz4^> U1 = [U1 u1]; % put solutions in U array
K!:
,l U2=[U2 u2];
g/X =#! MN1=[MN1 m1];
~Ro:mH: w z1=dz*MN1'; % output location
w%o4MFK=! end
NdSxWrD`m end
uF3p1by hg=abs(U1').*abs(U1'); % for data write to excel
5B.??;xtaV ha=[z1 hg]; % for data write to excel
])wMUJWg2 t1=[0 t'];
]o+|jgkt] hh=[t1' ha']; % for data write to excel file
9]F&Fz/G %dlmwrite('aa',hh,'\t'); % save data in the excel format
yg[; figure(1)
@[b:([ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
MqBATW.pmJ figure(2)
OYtus7q< waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
y yR8VO{ 5WJkeG ba 非线性超快脉冲耦合的数值方法的Matlab程序 !g&B)0u]* *,[=}v1 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。
iCSM1W3 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
%^%-h} 1 >T*g'954xF rnhf(K.{3 VaI P % This Matlab script file solves the nonlinear Schrodinger equations
Q
fyERa\rb % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
KP7RrgOan& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
DPxu3,Y % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&?` &X=Q IC-xCzR C=1;
;yER
V M1=120, % integer for amplitude
fh)`kZDk M3=5000; % integer for length of coupler
@?=)}2=|?i N = 512; % Number of Fourier modes (Time domain sampling points)
x7 1!r dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2P=~3g* T =40; % length of time:T*T0.
%=<NqINM[ dt = T/N; % time step
q4k o}jn n = [-N/2:1:N/2-1]'; % Index
_r5Ild @n t = n.*dt;
?~Ed
n-" Y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"l,EcZRjTz w=2*pi*n./T;
h_G7T1;L g1=-i*ww./2;
eC`f8=V g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
<({eOh5 N g3=-i*ww./2;
rtF 6Lg P1=0;
nkj'AH"2 P2=0;
j<P%Uy+ P3=1;
hJ*E"{xs P=0;
bNU^tL3QZ for m1=1:M1
yaYt/?| p=0.032*m1; %input amplitude
L0VR( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
v
4b`19} s1=s10;
HP dwx
V s20=0.*s10; %input in waveguide 2
E=*Q\3G~ s30=0.*s10; %input in waveguide 3
i@^`~ vj s2=s20;
(*Q|; s3=s30;
[f(^vlK p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
c@B%`6kF %energy in waveguide 1
.u;TeP p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
K y 2xWd8 %energy in waveguide 2
OjEA;;qq p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
t -(7Q8( %energy in waveguide 3
_NnO mwK7 for m3 = 1:1:M3 % Start space evolution
}t-|^mY> s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
+i!M[ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
0_pwY=P s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
W1`ZS*12D sca1 = fftshift(fft(s1)); % Take Fourier transform
qm5pEort sca2 = fftshift(fft(s2));
3D
dG$@ sca3 = fftshift(fft(s3));
[
=2In; sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Df3v"iCq } sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
2U+p@}cQUA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
r3vj o( s3 = ifft(fftshift(sc3));
$rYu4^ s2 = ifft(fftshift(sc2)); % Return to physical space
J5IJy3d s1 = ifft(fftshift(sc1));
- XG$ 0 end
z))[Lg p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
OBSJbDqT p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
bK1`a{ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
@}!$NI8 P1=[P1 p1/p10];
qM !q,Q P2=[P2 p2/p10];
\^LR5S& P3=[P3 p3/p10];
Ud*[2Oi|R P=[P p*p];
8|Y^Jn\p5u end
*bSG48W(" figure(1)
K3D $
hb plot(P,P1, P,P2, P,P3);
G_m u7w P`9A?aG.Z 转自：
http://blog.163.com/opto_wang/
