计算脉冲在非线性耦合器中演化的Matlab 程序 #4Z] /D2G 2S`D7R#6s % This Matlab script file solves the coupled nonlinear Schrodinger equations of
3$E\B=7/U % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
XX@@tzN % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
CG -^}xE: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<m7T`5+ beN(7jo %fid=fopen('e21.dat','w');
4PVkKP'/ N = 128; % Number of Fourier modes (Time domain sampling points)
xbeVq P M1 =3000; % Total number of space steps
}RT#V8oc J =100; % Steps between output of space
JC[G5$E T =10; % length of time windows:T*T0
,*Vt 53@E T0=0.1; % input pulse width
m:{ws~ MN1=0; % initial value for the space output location
8&0+Az"{O dt = T/N; % time step
'&<T;V% n = [-N/2:1:N/2-1]'; % Index
b}eBy t = n.*dt;
HU='Hk! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Ba]J3Yp,z u20=u10.*0.0; % input to waveguide 2
mV58&SZT u1=u10; u2=u20;
V6.w=6:`X U1 = u1;
@&7|Laa U2 = u2; % Compute initial condition; save it in U
[kjm EMF9i ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/1Q
i9uit w=2*pi*n./T;
iTgv8 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
GdxMHnn= L=4; % length of evoluation to compare with S. Trillo's paper
k~<b~V cU dz=L/M1; % space step, make sure nonlinear<0.05
N=`xoF
for m1 = 1:1:M1 % Start space evolution
6N^sUc0s u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
GOx+ %`.R\ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
\vU1*:3 ca1 = fftshift(fft(u1)); % Take Fourier transform
?[|T"bE5[ ca2 = fftshift(fft(u2));
BWd{xP y
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
jw^Pt~@ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
l_Ffbs_6t u2 = ifft(fftshift(c2)); % Return to physical space
e=]>T eqG0 u1 = ifft(fftshift(c1));
rTR4j>Ua~ if rem(m1,J) == 0 % Save output every J steps.
99<0xN(25 U1 = [U1 u1]; % put solutions in U array
~PoBvHi U2=[U2 u2];
vXio /m MN1=[MN1 m1];
)kq3q5*_ z1=dz*MN1'; % output location
b)5z'zQu end
ns{BU->f end
%Q0J$eC hg=abs(U1').*abs(U1'); % for data write to excel
%dyE F8) ha=[z1 hg]; % for data write to excel
o ZY2K3J) t1=[0 t'];
R-8/BTls7 hh=[t1' ha']; % for data write to excel file
JpFf O<uO %dlmwrite('aa',hh,'\t'); % save data in the excel format
gx* rxid figure(1)
)AX0x1I|E waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
* i}Nb* Z3 figure(2)
D`t }V waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
<N Lor55.] +:s]>R eDa 非线性超快脉冲耦合的数值方法的Matlab程序 b0~AN #Es 5g{L
-8XwI 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。
fC A/ 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
q66+x) 1>doa1 f-V8/ w_gPX0N}3n % This Matlab script file solves the nonlinear Schrodinger equations
k#4%d1O} % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
a!;]9}u7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7*7Z&1*3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=-ky%3:`@ T@n-^B !Xq C=1;
&*I\ ~;1 M1=120, % integer for amplitude
S_z }h M3=5000; % integer for length of coupler
, C#Mf@b N = 512; % Number of Fourier modes (Time domain sampling points)
Bh9 O<|E dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
yAu-BObD T =40; % length of time:T*T0.
hLVS}HE2 dt = T/N; % time step
M NE{mV( n = [-N/2:1:N/2-1]'; % Index
zS@"ITy t = n.*dt;
6z^Kg~a ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Yfk){1 w=2*pi*n./T;
0 L3 4)W g1=-i*ww./2;
O};U3=^0f g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
]7QRelMiz+ g3=-i*ww./2;
)C
@W_cfMN P1=0;
mulK(mp P2=0;
9. KOrg5}L P3=1;
H!F Cerg P=0;
UF[2Rb8? for m1=1:M1
-%&_LE9ZtS p=0.032*m1; %input amplitude
>u ok\sX s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
wff&ci28 s1=s10;
&CvNNDgrJ s20=0.*s10; %input in waveguide 2
00') Ol& s30=0.*s10; %input in waveguide 3
05(lh<C s2=s20;
}lzyl*. s3=s30;
Y",Fs( p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
uzO%+B! %energy in waveguide 1
U _~lpu p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
+ $MNG %energy in waveguide 2
ZQT14. $L p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
xw*T? !r=V %energy in waveguide 3
{Gnji] v for m3 = 1:1:M3 % Start space evolution
dbTPY` s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Y[AL!h s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
360V s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
h[D"O6 y sca1 = fftshift(fft(s1)); % Take Fourier transform
|Ire#0Nwx sca2 = fftshift(fft(s2));
& qki
NS sca3 = fftshift(fft(s3));
&zsaV m8 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
%nJ^0X_] sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
K~A$>0c sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
#zC_ ;u$ s3 = ifft(fftshift(sc3));
$_-f } E s2 = ifft(fftshift(sc2)); % Return to physical space
#>-_z s1 = ifft(fftshift(sc1));
.+<Ul ]e/ end
^CUeq"GYoZ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
AZ)H/#be p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
mie<jha p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
bk E4{P" P1=[P1 p1/p10];
*0)vsBi P2=[P2 p2/p10];
y]5O45E0 P3=[P3 p3/p10];
)v1n#m,W P=[P p*p];
L]L-000D( end
2R&msdF figure(1)
zbdmz plot(P,P1, P,P2, P,P3);
jX^uNmb 2f1WT g) 转自：
http://blog.163.com/opto_wang/
