计算脉冲在非线性耦合器中演化的Matlab 程序 }#bZ 8tm& @ h9K % This Matlab script file solves the coupled nonlinear Schrodinger equations of
qlvwK&W<QM % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
7D9]R#-K % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
a%*_2 # % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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aA;<# wPgDy %fid=fopen('e21.dat','w');
P7UJ-2%Y+ N = 128; % Number of Fourier modes (Time domain sampling points)
\XDmK M1 =3000; % Total number of space steps
ai9 J =100; % Steps between output of space
#a'r_K=ch) T =10; % length of time windows:T*T0
JnHNkCaU T0=0.1; % input pulse width
x,uBJ MN1=0; % initial value for the space output location
N|<bVq% dt = T/N; % time step
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9 =8@ n = [-N/2:1:N/2-1]'; % Index
5k~\or 5_ t = n.*dt;
#C x%OIi[f u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+A\ V ) u20=u10.*0.0; % input to waveguide 2
N<n8'XDdG u1=u10; u2=u20;
ZB0+GG\ U1 = u1;
R[Nbtbv9Q U2 = u2; % Compute initial condition; save it in U
I=odMw7Hj ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
P5P< " w=2*pi*n./T;
cm ,4&x6 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
R{`gR"* L=4; % length of evoluation to compare with S. Trillo's paper
}hq^+fC? dz=L/M1; % space step, make sure nonlinear<0.05
Z'ao[CG for m1 = 1:1:M1 % Start space evolution
*IqVY& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
~1ps7[ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
o3\,gzJ ca1 = fftshift(fft(u1)); % Take Fourier transform
AAo0M/U' ca2 = fftshift(fft(u2));
}AJ L,Q7q c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
(!-;T c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
DJ|BM+ u2 = ifft(fftshift(c2)); % Return to physical space
I=5dYq4 l u1 = ifft(fftshift(c1));
ib; yu_ if rem(m1,J) == 0 % Save output every J steps.
oLw|uU-| U1 = [U1 u1]; % put solutions in U array
I*( 1.%:m U2=[U2 u2];
H `5Ct MN1=[MN1 m1];
Kr]W
o8dWy z1=dz*MN1'; % output location
&~ y{'zoL end
B j= @&; end
1!1DuQ hg=abs(U1').*abs(U1'); % for data write to excel
FJF3B)Va| ha=[z1 hg]; % for data write to excel
ThiN9! Y t1=[0 t'];
lvPpC AXY hh=[t1' ha']; % for data write to excel file
b}}y=zO|$ %dlmwrite('aa',hh,'\t'); % save data in the excel format
om> VQ3 figure(1)
gCL{Cw waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
vnZ4( figure(2)
C ]Q>*=r waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
PT05DH ZMJ3NN]F 非线性超快脉冲耦合的数值方法的Matlab程序 o X@nP?\ <5k&)EoT 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。
UO1$UF!
QC Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
I{EIHD< kF?S 2(vH LyV#j>gD 1J&#&\,f& % This Matlab script file solves the nonlinear Schrodinger equations
i pwW%"6 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
w?S8@|MK % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
VfRs[ 3Q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
sS|<&3 )WmZP3$^TX C=1;
=1IEpxh% M1=120, % integer for amplitude
vbedk+dd?A M3=5000; % integer for length of coupler
BvQUn@ XE N = 512; % Number of Fourier modes (Time domain sampling points)
%z2oDAjX dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
PU"S;4m T =40; % length of time:T*T0.
WAv@F[ dt = T/N; % time step
0$l&i=L n = [-N/2:1:N/2-1]'; % Index
M/l95fp t = n.*dt;
U&X. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/cYk+c
w=2*pi*n./T;
hR0]8l | g1=-i*ww./2;
]1tN|ODY*W g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
77tZp @>hn g3=-i*ww./2;
RPY 6Wh| 4 P1=0;
O /$ v69: P2=0;
ExQ--!AC= P3=1;
O'fc/cvh=' P=0;
9>IsqYc for m1=1:M1
aX]y` p=0.032*m1; %input amplitude
7>
)l{7 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
.T{U^0 ) s1=s10;
q 7` s20=0.*s10; %input in waveguide 2
K)Ge s30=0.*s10; %input in waveguide 3
..aK sSm( s2=s20;
OoSa95#x s3=s30;
9T/<x-FD p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
`!_? uT %energy in waveguide 1
eiOi3q p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
\wTW?>o Z %energy in waveguide 2
yG4 MUf6 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
WFXx 70n %energy in waveguide 3
9a-]T=5Ee for m3 = 1:1:M3 % Start space evolution
oR7 7` s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
|N XFla s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
m8p4U-*j s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
|]I# CdO sca1 = fftshift(fft(s1)); % Take Fourier transform
CO7CNN sca2 = fftshift(fft(s2));
uQ-WTz|* sca3 = fftshift(fft(s3));
X=\x&Wt sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
oUCVd}wH sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
} cR i
A sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
UX?X]ZYVR s3 = ifft(fftshift(sc3));
31H|?cg< s2 = ifft(fftshift(sc2)); % Return to physical space
lf}?!*V`+ s1 = ifft(fftshift(sc1));
ayHn _ end
5t TLMZ `o p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
L{zamVQG p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
rC=f#YjR p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
dnk1M u< P1=[P1 p1/p10];
VB}P Ng P2=[P2 p2/p10];
Gl=@>Dc% P3=[P3 p3/p10];
m79 m{!q$- P=[P p*p];
/\Jc:v#Q end
A-}PpH~.Z figure(1)
sY&r bJ(P plot(P,P1, P,P2, P,P3);
4D0( Fl iFY]0@yt 转自：
http://blog.163.com/opto_wang/
