计算脉冲在非线性耦合器中演化的Matlab 程序 B}N1}i+
hF5(1s}e$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
/9?yw! % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
(!9+QXb' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&=wvlI52` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
SPtx_+ Q)S I(Vg %fid=fopen('e21.dat','w');
pLMaXX~4_ N = 128; % Number of Fourier modes (Time domain sampling points)
YuoIhT M1 =3000; % Total number of space steps
"@Qg]#]JH J =100; % Steps between output of space
jQ-2SA O T =10; % length of time windows:T*T0
$A T kCO T0=0.1; % input pulse width
h)z2#qfc MN1=0; % initial value for the space output location
,!P} Y[| dt = T/N; % time step
b]N&4t n = [-N/2:1:N/2-1]'; % Index
Qp>Z&LvC5 t = n.*dt;
ylQ9Su>o u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
FRayB VHL u20=u10.*0.0; % input to waveguide 2
S{,|Fa^PPO u1=u10; u2=u20;
9A9T'g)Du U1 = u1;
Nc? '} , U2 = u2; % Compute initial condition; save it in U
4"\%/kG ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
iMQ0Sq-%1 w=2*pi*n./T;
ciF qj3JS g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
{~ XnmBs L=4; % length of evoluation to compare with S. Trillo's paper
@eq.&{& dz=L/M1; % space step, make sure nonlinear<0.05
pfFHuS~ for m1 = 1:1:M1 % Start space evolution
3kVN[0 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
4Of kagg u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
C3(h j ca1 = fftshift(fft(u1)); % Take Fourier transform
\(r$f!` ca2 = fftshift(fft(u2));
.s KfwcYu4 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
r^ABu_u(`I c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
|n~,{= u2 = ifft(fftshift(c2)); % Return to physical space
6r`Xi& u1 = ifft(fftshift(c1));
o1 uM( if rem(m1,J) == 0 % Save output every J steps.
s3 VD6xi7 U1 = [U1 u1]; % put solutions in U array
buhbUmQ2 U2=[U2 u2];
Tf('iZ2+ MN1=[MN1 m1];
`O0y8 z1=dz*MN1'; % output location
Ns5P,[pBOZ end
F e.90) end
aDu[iaZ hg=abs(U1').*abs(U1'); % for data write to excel
dAy\IfZX= ha=[z1 hg]; % for data write to excel
L<6nM
;d t1=[0 t'];
Z_[L5B]Gwd hh=[t1' ha']; % for data write to excel file
js% n]$N %dlmwrite('aa',hh,'\t'); % save data in the excel format
J5 Ti@(G5V figure(1)
[\ &2& waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
d$Y_vX< figure(2)
(B! DBnq waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Qraa0]56 Np/vPaAk 非线性超快脉冲耦合的数值方法的Matlab程序 F@zTz54t SIc~cZ!Yu 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
ImbA2Gcs Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vJS}_j]_@ \r [@A3O m) Wq *&,o XWq"_$&LF % This Matlab script file solves the nonlinear Schrodinger equations
U]g9t<jD % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
gAf4 w q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@jrxbo;5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@a,=ApS" :[0 )Uu{ C=1;
RL fQT_V M1=120, % integer for amplitude
^ dE[ ; M3=5000; % integer for length of coupler
k;)mc+ ~+ N = 512; % Number of Fourier modes (Time domain sampling points)
h0I5zQZm dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Bx6,U4o* T =40; % length of time:T*T0.
*B9xL[} dt = T/N; % time step
'( g;nU< n = [-N/2:1:N/2-1]'; % Index
OXn-!J90P t = n.*dt;
hTmJ
~m'J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
yB 'C9wEH w=2*pi*n./T;
;'
H\s g1=-i*ww./2;
u7j,Vc' ~ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
F/3L^k] g3=-i*ww./2;
}Z< Sca7 P1=0;
NytodVZ'3 P2=0;
dczSW ]% P3=1;
PZlPC#E- P=0;
# s7e/GdKb for m1=1:M1
v>N*f~n p=0.032*m1; %input amplitude
1b 2 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
g:GywX W s1=s10;
uh \Tf5 s20=0.*s10; %input in waveguide 2
23 #JmR s30=0.*s10; %input in waveguide 3
<K,X5ctM} s2=s20;
WNKg>$M s3=s30;
w.#z>4#3- p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
k 8%@PC$ %energy in waveguide 1
Sw5:T p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
F^S]7{ %energy in waveguide 2
.k
+>T*c{ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
pS}IU{#; %energy in waveguide 3
"S*@._ for m3 = 1:1:M3 % Start space evolution
{J,4g:4G s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
%r*,m3d s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
KWAd~8,mk s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
2)T;N`tNw sca1 = fftshift(fft(s1)); % Take Fourier transform
nwC*w`4 sca2 = fftshift(fft(s2));
`AvK=] sca3 = fftshift(fft(s3));
A|YgA66M sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
V>GJO (9 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
5SmJ'zFO sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
foL4s;2 s3 = ifft(fftshift(sc3));
h w*u. 46 s2 = ifft(fftshift(sc2)); % Return to physical space
z%iPk'^ s1 = ifft(fftshift(sc1));
rm$d v%q end
lNt xM"G& p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
5h0Hk<N p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
/e*fsQ>M: p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
kqxq'Aq)d P1=[P1 p1/p10];
iA[o;D# P2=[P2 p2/p10];
67Qu<9} <- P3=[P3 p3/p10];
8#- Nx]VM P=[P p*p];
c 3o3i end
jb{9W7;RL figure(1)
_ qwf3Q@ plot(P,P1, P,P2, P,P3);
+v:] #1
-$I30.# 转自：
http://blog.163.com/opto_wang/
