计算脉冲在非线性耦合器中演化的Matlab 程序 /KL krW t4iD<{4 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
}u9#S % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_01wRsm%2 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=oBlUE % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
nU4to \q ($8< %fid=fopen('e21.dat','w');
beaSvhPU N = 128; % Number of Fourier modes (Time domain sampling points)
W#)X@Tl E M1 =3000; % Total number of space steps
gw!d [{# J =100; % Steps between output of space
cJMi`PQ; T =10; % length of time windows:T*T0
IRGcE&m T0=0.1; % input pulse width
:8K}e]!c1 MN1=0; % initial value for the space output location
y8_$YA/g dt = T/N; % time step
\TZSn1isZX n = [-N/2:1:N/2-1]'; % Index
@9eN\b%I^H t = n.*dt;
2 x>7>;> u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
U9ZuD40\ u20=u10.*0.0; % input to waveguide 2
fy]c=:EmD u1=u10; u2=u20;
2X<%BFsE U1 = u1;
|kH.o= U2 = u2; % Compute initial condition; save it in U
SJ91(K ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'W,*mf B w=2*pi*n./T;
a:8 MoH 4 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
cZJ5L>ox L=4; % length of evoluation to compare with S. Trillo's paper
[]v$QR&u#v dz=L/M1; % space step, make sure nonlinear<0.05
hq&| for m1 = 1:1:M1 % Start space evolution
lb$_$+@Vr u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
RL:B.Lv/W u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
)X ;051Q ca1 = fftshift(fft(u1)); % Take Fourier transform
N>Ih2>8t ca2 = fftshift(fft(u2));
&?1O D5 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
4Q/{l qG c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
l$1NI#& u2 = ifft(fftshift(c2)); % Return to physical space
Nc &J%a u1 = ifft(fftshift(c1));
,] :Gn5~ if rem(m1,J) == 0 % Save output every J steps.
P1 AC2<H U1 = [U1 u1]; % put solutions in U array
X;H\u6-|>6 U2=[U2 u2];
DF_wMv:>^ MN1=[MN1 m1];
N8pV[\f z1=dz*MN1'; % output location
+ %v1X&_\ end
Unv'm5/L end
#|4 G,! hg=abs(U1').*abs(U1'); % for data write to excel
d#TA20` ha=[z1 hg]; % for data write to excel
n\)1Bz t1=[0 t'];
`LNh amp hh=[t1' ha']; % for data write to excel file
CIz0Gjtx6m %dlmwrite('aa',hh,'\t'); % save data in the excel format
u7^(?"x figure(1)
~|9VVeE waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
B2oKvgw figure(2)
.dMdb7 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
{1Y @%e d&CpaOSu 非线性超快脉冲耦合的数值方法的Matlab程序 `3 i<jZMG %59uR}\ 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。
)l$}plT4 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
y+T[="W ;}iB9 Tl "!D y[J 6F!B*lr % This Matlab script file solves the nonlinear Schrodinger equations
9Q^cE\j % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
l_/(J)|a % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
FLs$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@ J&korU C+uW]]~I) C=1;
t))MZw&@ M1=120, % integer for amplitude
m0 As t<u M3=5000; % integer for length of coupler
P Wyf 3 N = 512; % Number of Fourier modes (Time domain sampling points)
! ig& 8: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
(T0M Wp 0 T =40; % length of time:T*T0.
MW6z&+Z dt = T/N; % time step
71\ 53Qr#U n = [-N/2:1:N/2-1]'; % Index
? "r=08 t = n.*dt;
iX 6>u4~( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&n
)MGg1% w=2*pi*n./T;
Go)g}# . & g1=-i*ww./2;
>>
"gb/x, g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
V0v,s^\H g3=-i*ww./2;
Kc?4q= 7q P1=0;
7M~sol[ * P2=0;
w^ut,`yW R P3=1;
Jr( =Y@Z ' P=0;
l>}f{az-T for m1=1:M1
n V7Vc; p=0.032*m1; %input amplitude
_ Lb"yug s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
#'q7 x s1=s10;
VJqk0w+ s20=0.*s10; %input in waveguide 2
oD V6[e s30=0.*s10; %input in waveguide 3
E{&MmrlL, s2=s20;
X0u,QSt' O s3=s30;
.Zczya p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
I Gcq*mR= %energy in waveguide 1
qEr?4h p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
N=BG0 t$ %energy in waveguide 2
'1:) q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
3{$7tck, %energy in waveguide 3
M/quswn1 for m3 = 1:1:M3 % Start space evolution
M&j|5UH%. s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
OQ&N] P2p s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
VFL^-tXnA^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
9Q%lS sca1 = fftshift(fft(s1)); % Take Fourier transform
>Ua'* sca2 = fftshift(fft(s2));
7Hr_ZwO/^ sca3 = fftshift(fft(s3));
u1$6:"2@5k sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
QM F sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
m+hI3@j sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
GYfOwV!zB s3 = ifft(fftshift(sc3));
]alc%(= s2 = ifft(fftshift(sc2)); % Return to physical space
b$ 7 ]cE
s1 = ifft(fftshift(sc1));
>MHlrSH2 end
FKTF?4+\U p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
N v7-6C6< p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
: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))));
-!Myw&*\V P1=[P1 p1/p10];
%hsCB
.r>| P2=[P2 p2/p10];
e4tIO P3=[P3 p3/p10];
;Z d_2CZ P=[P p*p];
b$,Hlh,^ end
}_]AQN$'G figure(1)
TC?B_;a plot(P,P1, P,P2, P,P3);
C7F Qc { sQa;l]O:NC 转自：
http://blog.163.com/opto_wang/
