计算脉冲在非线性耦合器中演化的Matlab 程序 Y*oDO$6 g^ Yl TB % This Matlab script file solves the coupled nonlinear Schrodinger equations of
`O?T.p) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
y m,H@~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
75T_Dx(H % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p/Sbt/R Cs3^9m6;d %fid=fopen('e21.dat','w');
]va>ex$d N = 128; % Number of Fourier modes (Time domain sampling points)
/wShUR{ M1 =3000; % Total number of space steps
.R* !aK J =100; % Steps between output of space
` $LWmm# T =10; % length of time windows:T*T0
Rgy- O A T0=0.1; % input pulse width
BAj-akc f MN1=0; % initial value for the space output location
T VmH dt = T/N; % time step
INs!Ame2 n = [-N/2:1:N/2-1]'; % Index
%q ;jVj[ t = n.*dt;
h 5_G4J{1 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@H b'8F u20=u10.*0.0; % input to waveguide 2
1F8 W9b^D u1=u10; u2=u20;
&.13d q U1 = u1;
`? g`bN`Vn U2 = u2; % Compute initial condition; save it in U
}TQ{`a @ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Y}*\[}l:&x w=2*pi*n./T;
wm{3&m g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
moj ]j`P5a L=4; % length of evoluation to compare with S. Trillo's paper
g>0XxjP4 dz=L/M1; % space step, make sure nonlinear<0.05
W1Lr_z6
for m1 = 1:1:M1 % Start space evolution
BcjP+$k4_ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
dC e4u<so\ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
XKA &XpF ca1 = fftshift(fft(u1)); % Take Fourier transform
)5j;KI%t ca2 = fftshift(fft(u2));
yq-=],h c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
%=AxJp!a c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Pz#7h*;cw. u2 = ifft(fftshift(c2)); % Return to physical space
%
}|cb7l u1 = ifft(fftshift(c1));
nMfFH[I4 if rem(m1,J) == 0 % Save output every J steps.
-4rDbDsr U1 = [U1 u1]; % put solutions in U array
9//+Bh U2=[U2 u2];
`!:q;i ]} MN1=[MN1 m1];
3nZ9m z1=dz*MN1'; % output location
$mmup|;( end
9j ]sD/L5q end
unJid8Lo hg=abs(U1').*abs(U1'); % for data write to excel
.roqEasu8 ha=[z1 hg]; % for data write to excel
G&xo1K ] t1=[0 t'];
+x? #DH- hh=[t1' ha']; % for data write to excel file
4h !f/aF' %dlmwrite('aa',hh,'\t'); % save data in the excel format
4H5pr figure(1)
U t-B^x)gl waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
T u{&v'!j6 figure(2)
'bGX-C waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
$&s=68
XoL J L]+? 非线性超快脉冲耦合的数值方法的Matlab程序 E5el?=,i zl-2$}<a 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。
EV #MQM 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
Xtz-\v#0o' KIA 2"KbjG JXG" M#{ zf4Ec-) % This Matlab script file solves the nonlinear Schrodinger equations
)b<k#(i@# % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
_ rV 5E % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
F/m^?{==~* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
#j#_cImE BR^7_q4q C=1;
cYx4 ~ V^ M1=120, % integer for amplitude
HkV1sT M3=5000; % integer for length of coupler
QB:i /9 N = 512; % Number of Fourier modes (Time domain sampling points)
;!91^T l dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
nzjkX4KV T =40; % length of time:T*T0.
[S.ZJUns dt = T/N; % time step
9jN)I(^D6 n = [-N/2:1:N/2-1]'; % Index
,\ 2a=Fp t = n.*dt;
D'Z|}(d& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
,*4p?|A w=2*pi*n./T;
{7!UQrm< g1=-i*ww./2;
Am8x74? g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Eh-n g3=-i*ww./2;
c`lJu_ P1=0;
=ji1S}e~p P2=0;
5Zmw} M P3=1;
N=:5eAza P=0;
KbL V' %D for m1=1:M1
cJ M: p=0.032*m1; %input amplitude
G*S|KH s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
hS[ yNwD s1=s10;
)
\Y 7& s20=0.*s10; %input in waveguide 2
Xi ?b ]Z s30=0.*s10; %input in waveguide 3
uE[(cko s2=s20;
bifS 2>c s3=s30;
&U+ _ -Ph p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
9Rm/V5 %energy in waveguide 1
=fm]D l9h* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
)uv= S;+ %energy in waveguide 2
$Vc~/> p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
kc7lc|'z %energy in waveguide 3
=#mTfJ for m3 = 1:1:M3 % Start space evolution
]zO/A4 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
.nYUL> s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
awv De s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ZKg{0DY sca1 = fftshift(fft(s1)); % Take Fourier transform
)s1I b4C sca2 = fftshift(fft(s2));
5XuT={o sca3 = fftshift(fft(s3));
]$U xC u sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
?ER-25S sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Ku&!?m@C sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
V\V)<BARe s3 = ifft(fftshift(sc3));
K1 V#cB
WO s2 = ifft(fftshift(sc2)); % Return to physical space
9] t[J_YM s1 = ifft(fftshift(sc1));
A2}Rl%+X]6 end
"NRDNqj( p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
#fj/~[Ajv p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
qQ!1t >j+H p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
;q0uE:^ S P1=[P1 p1/p10];
b': |uu*/ P2=[P2 p2/p10];
Zo KcJA P3=[P3 p3/p10];
xEuN
P=[P p*p];
P}.7Mehf end
'0$?h9" figure(1)
)2,eFNB#n plot(P,P1, P,P2, P,P3);
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J IVr 2y8K 转自：
http://blog.163.com/opto_wang/
