计算脉冲在非线性耦合器中演化的Matlab 程序 tJ* /5k
& %__ @G_M % This Matlab script file solves the coupled nonlinear Schrodinger equations of
elR1NhB|p % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?&!!(dWFH % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
QkWEVL@uM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
9ei<ou_s
'SXLnoeTa %fid=fopen('e21.dat','w');
^$mCF%e8H N = 128; % Number of Fourier modes (Time domain sampling points)
N
A _8<B^ M1 =3000; % Total number of space steps
6kME m)YjT J =100; % Steps between output of space
RameaFX8 T =10; % length of time windows:T*T0
C^LxJG{L5 T0=0.1; % input pulse width
aO}p"-' MN1=0; % initial value for the space output location
e\O625 dt = T/N; % time step
(uX"n`Dk n = [-N/2:1:N/2-1]'; % Index
h#Mx(q t = n.*dt;
B
qIN U u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@+_pj.D u20=u10.*0.0; % input to waveguide 2
ny!80I u1=u10; u2=u20;
?v-!`J>EF# U1 = u1;
UV</Nx)3 U2 = u2; % Compute initial condition; save it in U
5!wjYQt3 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-;;m/QM w=2*pi*n./T;
[,;O$j} g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[S-#}C? ~ L=4; % length of evoluation to compare with S. Trillo's paper
Z2-tDp(I dz=L/M1; % space step, make sure nonlinear<0.05
4#t=%} for m1 = 1:1:M1 % Start space evolution
[w-#
!X2y u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
>L8 & 6aU u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
z_#HJ}R= ca1 = fftshift(fft(u1)); % Take Fourier transform
:o87<)
_F ca2 = fftshift(fft(u2));
tkff\W[JU c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
k py) kS c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
4N1)+ W8k* u2 = ifft(fftshift(c2)); % Return to physical space
![eY%2;< u1 = ifft(fftshift(c1));
XF>!~D if rem(m1,J) == 0 % Save output every J steps.
2f{a|| U1 = [U1 u1]; % put solutions in U array
wzmQRn;s U2=[U2 u2];
#s#BYbF MN1=[MN1 m1];
jw uSne z1=dz*MN1'; % output location
@7;}6,) end
b7">IzAe
end
+VJyGbOcC hg=abs(U1').*abs(U1'); % for data write to excel
kIe)ocJg ha=[z1 hg]; % for data write to excel
2|(lKFkQ t1=[0 t'];
0bD\`Jiv, hh=[t1' ha']; % for data write to excel file
bYX.4(R %dlmwrite('aa',hh,'\t'); % save data in the excel format
snNB;hkj figure(1)
]l3Y=Cl waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
|oePB <N figure(2)
_ /Eg_dQ~@ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
%sPq*w. 8A/rkoht* 非线性超快脉冲耦合的数值方法的Matlab程序 )nq(XM7 cXr_,>k 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。
)c 79& S 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
Q4Qf/q;U ;#8 xR LW - a"b :Q :~ &# 9 % This Matlab script file solves the nonlinear Schrodinger equations
h2= w C. % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
b`J su! ?{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
g706*o)h % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
glkH??S !/! Fc'A C=1;
ux 17q>G M1=120, % integer for amplitude
?(}~ [ M3=5000; % integer for length of coupler
e?
|4O< @ N = 512; % Number of Fourier modes (Time domain sampling points)
Gv[(0 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
JW=q'ibR T =40; % length of time:T*T0.
+1\t 0P24 dt = T/N; % time step
4af^SZ )l n = [-N/2:1:N/2-1]'; % Index
v`Ja Bn t = n.*dt;
_Kh 8
<$h ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Cy)QS{YX w=2*pi*n./T;
NSR][h_ g1=-i*ww./2;
.ezZ+@LI+# g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ZsYY)<n g3=-i*ww./2;
= .) :tGDp P1=0;
%W X^']p P2=0;
o ,?h} @ P3=1;
}D3hP|.X P=0;
9A|9:OdG1 for m1=1:M1
K!2%8Ej,J p=0.032*m1; %input amplitude
wS
>S\,LV s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
%F}d'TPx s1=s10;
PeLzZ'$D s20=0.*s10; %input in waveguide 2
*<h )q)HS s30=0.*s10; %input in waveguide 3
Bo'v!bI7 s2=s20;
r0 29E- s3=s30;
ZqjLZ9?q p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
&]A0=h2{P* %energy in waveguide 1
'TA
!JB+ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
<7gv<N6BQf %energy in waveguide 2
b?, = |H p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
1F+JyZK}w %energy in waveguide 3
9ES V [ for m3 = 1:1:M3 % Start space evolution
5 v=e(Ph + s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
` joyHKZI. s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
kP^= s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
g'2; /// sca1 = fftshift(fft(s1)); % Take Fourier transform
N&|,!Cu sca2 = fftshift(fft(s2));
I\Cg-& e sca3 = fftshift(fft(s3));
^f ,%dM=i= sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
8kE3\#);\ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
1qm*#4x sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
r$x;rL4 s3 = ifft(fftshift(sc3));
T#[# w*w/ s2 = ifft(fftshift(sc2)); % Return to physical space
dx$ +,R~y s1 = ifft(fftshift(sc1));
!! cN4X end
i|28:FJA p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
mMO]l(a& p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
:-(qqC: p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
FC]n? 1?<( P1=[P1 p1/p10];
3~Ap1 _9 P2=[P2 p2/p10];
IlB*JJ nl P3=[P3 p3/p10];
X!@ Y , P=[P p*p];
7" )~JBH end
\BO6.;jA figure(1)
FJT0 lC plot(P,P1, P,P2, P,P3);
NYzBfL
x zw iS%-F 转自：
http://blog.163.com/opto_wang/
