计算脉冲在非线性耦合器中演化的Matlab 程序 ;=VK _3" V@n(v\F % This Matlab script file solves the coupled nonlinear Schrodinger equations of
renmz,dJ, % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
.cT$h?+jyl % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
mGpkM?Y" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
k3 /JQ]'D 0?Tk* X %fid=fopen('e21.dat','w');
q8 xc70: R N = 128; % Number of Fourier modes (Time domain sampling points)
aRO_,n9 M1 =3000; % Total number of space steps
)-?uX.E{ J =100; % Steps between output of space
zNr_W[ T =10; % length of time windows:T*T0
?Y6la.bc{ T0=0.1; % input pulse width
4R*<WdT( MN1=0; % initial value for the space output location
JIb zh?$aD dt = T/N; % time step
95?5=T F n = [-N/2:1:N/2-1]'; % Index
qe6C|W~n t = n.*dt;
OwiWnS< u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
`k{ ff u20=u10.*0.0; % input to waveguide 2
FQ|LA[~ u1=u10; u2=u20;
Hu9-<upc& U1 = u1;
!OoaE* s U2 = u2; % Compute initial condition; save it in U
K jn& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&pMlt7 w=2*pi*n./T;
kL PO+lg+ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
AY/-j$5+? L=4; % length of evoluation to compare with S. Trillo's paper
Ro'4/{}+ dz=L/M1; % space step, make sure nonlinear<0.05
\p@nH%@v for m1 = 1:1:M1 % Start space evolution
o.A} `` u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
$~G0#JL u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
J ! A/r< ca1 = fftshift(fft(u1)); % Take Fourier transform
fJn3"D' ca2 = fftshift(fft(u2));
LF9aw4:>Ou c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
DA4edFAuE c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
cGpN4|*rQ u2 = ifft(fftshift(c2)); % Return to physical space
#}t 1 u1 = ifft(fftshift(c1));
M89-*1 if rem(m1,J) == 0 % Save output every J steps.
B=q)}aWc U1 = [U1 u1]; % put solutions in U array
%KJhtd"q U2=[U2 u2];
d )hzi MN1=[MN1 m1];
-@ UN]K z1=dz*MN1'; % output location
9#s95R O end
3<jAp#bE end
C6D=>%uY hg=abs(U1').*abs(U1'); % for data write to excel
36^C0uNdX ha=[z1 hg]; % for data write to excel
mHI4wS>()+ t1=[0 t'];
7S A-OFM hh=[t1' ha']; % for data write to excel file
VeD+U~ d %dlmwrite('aa',hh,'\t'); % save data in the excel format
nv_m!JG7 figure(1)
XC7Ty'#"KX waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
0$f_or9T figure(2)
`b^#quz waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
iJdrY 6qd y,y/P yN) 非线性超快脉冲耦合的数值方法的Matlab程序 C>J ekPeM OXIu>jF 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。
I!F}`d 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
i)@U.-*5m =q" w2b& ~ C/Yv&58 cYq' ]$] % This Matlab script file solves the nonlinear Schrodinger equations
je- , S>U % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
X ]pR,\B % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8u:v:>D.' % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@pqY9_:P1 kO..~@ aY C=1;
)tN?: l M1=120, % integer for amplitude
?dJ/)3I%F M3=5000; % integer for length of coupler
,u ?wYW; N = 512; % Number of Fourier modes (Time domain sampling points)
u@=+#q~/P dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
u|m[(- ` T =40; % length of time:T*T0.
S{^6iR dt = T/N; % time step
XI@6a9Uk n = [-N/2:1:N/2-1]'; % Index
e'k;A{Oh t = n.*dt;
{ (m+M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l5ZADK4 w=2*pi*n./T;
&jXca| wAR g1=-i*ww./2;
2A*X Hvwb g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
1AV1d%F g3=-i*ww./2;
jy\W_ CT P1=0;
?Kx6Sf<i P2=0;
A6?qIy P3=1;
AkYupP2]v P=0;
xQNw&'|UU for m1=1:M1
*<`7|BH 3 p=0.032*m1; %input amplitude
Lf,CxZL5 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
]+}ZfHp s1=s10;
`DgaO-Dg3 s20=0.*s10; %input in waveguide 2
71k!k&Im s30=0.*s10; %input in waveguide 3
F e_::NVvk s2=s20;
38V $ <w s3=s30;
%|: ;T i p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
IZ4W_NN %energy in waveguide 1
f
p v= P p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
@!z$Sp= %energy in waveguide 2
k%EWkM )? p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
ntrY =Y %energy in waveguide 3
! 6p>P4TT for m3 = 1:1:M3 % Start space evolution
A|p@\3 P*A s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
(
GFgt_ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
c8^+^.=pX s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
&ui:DZAxj| sca1 = fftshift(fft(s1)); % Take Fourier transform
C-s>1\ I sca2 = fftshift(fft(s2));
|Hx%f sca3 = fftshift(fft(s3));
kJ%{ [1fr sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
/[\6oa sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
33=Mm/<m$P sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
~mN g[] s3 = ifft(fftshift(sc3));
?60>'Xj j s2 = ifft(fftshift(sc2)); % Return to physical space
_v1bTg"? s1 = ifft(fftshift(sc1));
(\Rwf}gyR end
%iK%$ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Nc
G ,0K p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
AC 9{*K[ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
>}ro[x`K P1=[P1 p1/p10];
E)KB@f<g* P2=[P2 p2/p10];
R'S c P3=[P3 p3/p10];
e(?:g@]-r P=[P p*p];
n?y 'c^ end
jK3g iT figure(1)
sFbfFUd plot(P,P1, P,P2, P,P3);
8B}'\e 4i P YdIP\<V 转自：
http://blog.163.com/opto_wang/
