计算脉冲在非线性耦合器中演化的Matlab 程序 bf/z
T0 `t2Y IwOK % This Matlab script file solves the coupled nonlinear Schrodinger equations of
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F O> % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
HJ!P]X_J1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
D:XjJMW3r % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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el q* %fid=fopen('e21.dat','w');
H'jo 3d ~+ N = 128; % Number of Fourier modes (Time domain sampling points)
in2m/q? M1 =3000; % Total number of space steps
s$xm J =100; % Steps between output of space
5$c*r$t_RK T =10; % length of time windows:T*T0
43Ua@KNi T0=0.1; % input pulse width
> Dq&[9,8 MN1=0; % initial value for the space output location
IhX P~C6 dt = T/N; % time step
^@;P -0Sy n = [-N/2:1:N/2-1]'; % Index
N2&h yM t = n.*dt;
M!
uE# | u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
B dxV [SF u20=u10.*0.0; % input to waveguide 2
Z;cA_}5 u1=u10; u2=u20;
-qpe;=g&f U1 = u1;
\8]("l}ms8 U2 = u2; % Compute initial condition; save it in U
T<U_Iq ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9%DLdc\z; w=2*pi*n./T;
b\C1qM4 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
xvW# ~T ] L=4; % length of evoluation to compare with S. Trillo's paper
~Z5Wwp]a dz=L/M1; % space step, make sure nonlinear<0.05
}M &hcw< for m1 = 1:1:M1 % Start space evolution
RIq\IQ_| u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
|qtZb}"| u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
2 P9 {?Y ca1 = fftshift(fft(u1)); % Take Fourier transform
A3Y}|7QA ca2 = fftshift(fft(u2));
@Wd1+Yky c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
kjj? X|Un c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
tTPjCl u2 = ifft(fftshift(c2)); % Return to physical space
g ]U! ] u1 = ifft(fftshift(c1));
goc"+ K if rem(m1,J) == 0 % Save output every J steps.
_Q}vPSJviC U1 = [U1 u1]; % put solutions in U array
' Xg9MS& U2=[U2 u2];
yi,Xs|%. MN1=[MN1 m1];
JjQ9AJ?-V z1=dz*MN1'; % output location
S=X_7V
end
8s>OO& end
[[KIuW~ot hg=abs(U1').*abs(U1'); % for data write to excel
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y&/d ha=[z1 hg]; % for data write to excel
J pKCux t1=[0 t'];
zJG=9C ? hh=[t1' ha']; % for data write to excel file
xi=Qxgx0I %dlmwrite('aa',hh,'\t'); % save data in the excel format
>RXDuCVi figure(1)
8:jakOeT waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Zmy:Etqi figure(2)
,pa=OF waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
_OJ19 Ry .%_=(C< E 非线性超快脉冲耦合的数值方法的Matlab程序 q[%SF=~<k{ |4F'Zu}g> 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。
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- 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
>{#QS"J# 2UEjn>2 o*xft6U 6<9gVh<=w % This Matlab script file solves the nonlinear Schrodinger equations
G/&Wc2k % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
YBQ{/"v%| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
z_ L ><}H % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
z=K hbh z&Lcl{<MA C=1;
Vn6]h|vm M1=120, % integer for amplitude
=B"^#n ; M3=5000; % integer for length of coupler
sF p% T4j N = 512; % Number of Fourier modes (Time domain sampling points)
vS G vv43G dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
#80M+m T =40; % length of time:T*T0.
z:JJ>mxV dt = T/N; % time step
}RZN3U= n = [-N/2:1:N/2-1]'; % Index
DQ= /Jr~ t = n.*dt;
I5w> *F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
L*1yK* w=2*pi*n./T;
U$j?2|v-x g1=-i*ww./2;
n<Z1i) g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
m]'P3^ <{P g3=-i*ww./2;
X!f` !tZ:{ P1=0;
>n pFg@A P2=0;
h3P ^W(=& P3=1;
i>z {QE P=0;
p$l'y""i for m1=1:M1
^-26K|{3 p=0.032*m1; %input amplitude
tQcn%C K s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
X> ck.}F s1=s10;
]McDN [h: s20=0.*s10; %input in waveguide 2
u51Lp s30=0.*s10; %input in waveguide 3
YUQKy2 s2=s20;
N6%M+R/Q s3=s30;
td(4Fw||1y p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~3qt<" %energy in waveguide 1
}Z8DVTpX} p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
v42Z&PO
%energy in waveguide 2
"$PX [: p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
nBGcf(BE.$ %energy in waveguide 3
S/x CX! for m3 = 1:1:M3 % Start space evolution
JG=z~ STz s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
NnqAr , s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
wZKEUJpQ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
T#-U\C~o sca1 = fftshift(fft(s1)); % Take Fourier transform
5ii:93Hlj sca2 = fftshift(fft(s2));
?a'P;&@7 sca3 = fftshift(fft(s3));
OQh4 MN#$ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
T :!Re*=JJ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
l jJR7< sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
? 7R&=B1g s3 = ifft(fftshift(sc3));
4' ` y5E s2 = ifft(fftshift(sc2)); % Return to physical space
z*G(AcS) s1 = ifft(fftshift(sc1));
e\' =#Hw end
ZoroK.N4A% p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
~?uch8H p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
p eGh- p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
tqicyNL P1=[P1 p1/p10];
R]"3^k* P2=[P2 p2/p10];
's 'H&sa P3=[P3 p3/p10];
3Tz~DdB P=[P p*p];
n_@cjO end
s:Io5C( figure(1)
n$y@a? al plot(P,P1, P,P2, P,P3);
::2(pgH > PONu]^ 转自：
http://blog.163.com/opto_wang/
