计算脉冲在非线性耦合器中演化的Matlab 程序 Lc!%
3,#. t3.;W/0_ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
$UAmUQg)}_ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
% SL'X`j % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
iXt >!f* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
W~J@v@..4 jiMI&c l %fid=fopen('e21.dat','w');
E4aCL#}D N = 128; % Number of Fourier modes (Time domain sampling points)
Q"KD O-t M1 =3000; % Total number of space steps
PK@hf[YHe J =100; % Steps between output of space
L<encPJt T =10; % length of time windows:T*T0
F'DO46 T0=0.1; % input pulse width
0!YB.=\{_q MN1=0; % initial value for the space output location
xJ)hGPrAl dt = T/N; % time step
C3 ^QNhv n = [-N/2:1:N/2-1]'; % Index
A"8` 5qa t = n.*dt;
#8G (r9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
~{hcJ:bI u20=u10.*0.0; % input to waveguide 2
/pZ]:.A u1=u10; u2=u20;
b/:&iG; U1 = u1;
^b=9{.5 U2 = u2; % Compute initial condition; save it in U
1H{M0e ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Z> jk \[ w=2*pi*n./T;
,r T62w*e g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
M/XxiF L=4; % length of evoluation to compare with S. Trillo's paper
vq|o}6Et dz=L/M1; % space step, make sure nonlinear<0.05
lL.3$Rp; for m1 = 1:1:M1 % Start space evolution
5_@ u Be~ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
*Y'@|xf* u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
I6d4<#Q@L ca1 = fftshift(fft(u1)); % Take Fourier transform
#E %0 o ca2 = fftshift(fft(u2));
A` x_M! m c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
fX=o,=-f c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
[hE0 9W u2 = ifft(fftshift(c2)); % Return to physical space
pZ?7'+u$L u1 = ifft(fftshift(c1));
[m3[plwe if rem(m1,J) == 0 % Save output every J steps.
4vi P lO U1 = [U1 u1]; % put solutions in U array
5|> FM& U2=[U2 u2];
(he cvJ MN1=[MN1 m1];
j3`# v3 z1=dz*MN1'; % output location
Nf(Np1?;c end
dGf:0xE" end
WVUa:_5{ hg=abs(U1').*abs(U1'); % for data write to excel
Y;yt m
#= ha=[z1 hg]; % for data write to excel
,;LxFS5\ t1=[0 t'];
B -XM(C j hh=[t1' ha']; % for data write to excel file
bkfwsYZx %dlmwrite('aa',hh,'\t'); % save data in the excel format
f$Fa*O- figure(1)
;fLYO6 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
i`-,=RJ figure(2)
#p@8 m_g waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
"L'0" VPG+]> * 非线性超快脉冲耦合的数值方法的Matlab程序 UruD&=AMK YY~BNQn6d 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。
n\8;4]n 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
=SJw CT0; G RV#f06 5g9lO]WDI @Sb 86Ee % This Matlab script file solves the nonlinear Schrodinger equations
9 aYDi) % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
tHlKo0S$0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
bvY'=
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
: t Ka1vL sHC4iMIw C=1;
<x Ov0B M1=120, % integer for amplitude
thWQU" z4 M3=5000; % integer for length of coupler
;Ml??B]C N = 512; % Number of Fourier modes (Time domain sampling points)
>_3+s~ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
$F V!HD T =40; % length of time:T*T0.
X$:r dt = T/N; % time step
kkfwICBI n = [-N/2:1:N/2-1]'; % Index
Z|&Y1k-h t = n.*dt;
9Yih%d,
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
;4DqtR"7Y w=2*pi*n./T;
"YLH]9"= g1=-i*ww./2;
Xq"@Z g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
=Kdd+g! g3=-i*ww./2;
H]v" _!(\ P1=0;
tEEeek(! P2=0;
o (iv=(o P3=1;
|~Q`D dkX P=0;
lLD-QO}/ for m1=1:M1
VT.BHZ p=0.032*m1; %input amplitude
< YU+W"jQT s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
xs jJ8>G s1=s10;
/9/svPc] s20=0.*s10; %input in waveguide 2
V'vDXzk\ s30=0.*s10; %input in waveguide 3
ISo{>@a- s2=s20;
s':fv[% s3=s30;
rN3i5.*/t p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
0fc]RkHs" %energy in waveguide 1
4
I}xygV p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
V,>_L %energy in waveguide 2
Op] L#<&T p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
W )rE_tw,| %energy in waveguide 3
2?; =TJo$ for m3 = 1:1:M3 % Start space evolution
@)0-oa,u+ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
,/ V'(\>
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
q3 .L6M s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
oS'M sca1 = fftshift(fft(s1)); % Take Fourier transform
"m^whHj sca2 = fftshift(fft(s2));
*ml& }9 sca3 = fftshift(fft(s3));
lNV%R( sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
F^i v1b sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
>AcpJ|V sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
N_jCx* .G s3 = ifft(fftshift(sc3));
}@Mx@ S s2 = ifft(fftshift(sc2)); % Return to physical space
~'/I[y4t s1 = ifft(fftshift(sc1));
;1Kxqp z_i end
i*16k dI. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
5gpqN)|)[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
F">>,Oc)U" p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
.HTX7mA3 P1=[P1 p1/p10];
t(SSr M] P2=[P2 p2/p10];
#A|~s;s>N P3=[P3 p3/p10];
C #]% P=[P p*p];
xJ"CAg|B end
-"L)<J@gQ? figure(1)
?L|Jc_E plot(P,P1, P,P2, P,P3);
\-c 8/= B"O5P> 转自：
http://blog.163.com/opto_wang/
