计算脉冲在非线性耦合器中演化的Matlab 程序 <x->.R_ 6i=Nk"d % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Z5[f % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
xA#'%|" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K[Ao_v2g % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
WEZ)>[Xj? ;FH_qF`.
%fid=fopen('e21.dat','w');
.4cOMi G N = 128; % Number of Fourier modes (Time domain sampling points)
B `;DAs mT M1 =3000; % Total number of space steps
a"pejW`m J =100; % Steps between output of space
bqI| wGCA" T =10; % length of time windows:T*T0
4SGF8y@WU T0=0.1; % input pulse width
)u}My Fl. MN1=0; % initial value for the space output location
O~u@J'4 dt = T/N; % time step
I/Q5Y- atg n = [-N/2:1:N/2-1]'; % Index
1v"r8=Wt t = n.*dt;
4K<T_B/ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
nd xijqw u20=u10.*0.0; % input to waveguide 2
Q!(qL[o u1=u10; u2=u20;
w @Gk# U1 = u1;
(U@uJ U2 = u2; % Compute initial condition; save it in U
*=~X1s ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
FK!UUy; w=2*pi*n./T;
DNp4U9 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
}rbsarG@ L=4; % length of evoluation to compare with S. Trillo's paper
<Q%:c4N dz=L/M1; % space step, make sure nonlinear<0.05
fNZ:l=L3): for m1 = 1:1:M1 % Start space evolution
"YQ%j+ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,Y_ [+ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
=^D{ZZw{ ca1 = fftshift(fft(u1)); % Take Fourier transform
- mPrmapb3 ca2 = fftshift(fft(u2));
g$eZT{{W c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
u*C"d1v= c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
7J$5dFV2 u2 = ifft(fftshift(c2)); % Return to physical space
o7#Mr`6H u1 = ifft(fftshift(c1));
|= U(8t if rem(m1,J) == 0 % Save output every J steps.
QnPgp(d < U1 = [U1 u1]; % put solutions in U array
@[] A&)B U2=[U2 u2];
PdNxuy MN1=[MN1 m1];
f8X /kz z1=dz*MN1'; % output location
eH y.<VX end
M!E# T-) end
/naGn@m5u hg=abs(U1').*abs(U1'); % for data write to excel
W;9J ah. ha=[z1 hg]; % for data write to excel
2xJT!lN t1=[0 t'];
Hz]
p] hh=[t1' ha']; % for data write to excel file
| Sf` Cs %dlmwrite('aa',hh,'\t'); % save data in the excel format
A[.5B i figure(1)
va_TC!{ ; waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
I-`qo7dQ_S figure(2)
-a( \(^NW waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Y
=BXV7\ *E- VS= # 非线性超快脉冲耦合的数值方法的Matlab程序 fpK` +iL,8eW 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。
Hxm CKW! 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
$={W t R raPUx _$PH iTq~ ^9G NXyuv7%5= % This Matlab script file solves the nonlinear Schrodinger equations
I$7TnM ug % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
l .wf= / % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
{=K u9\ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0Q_@2 <(%cb.^c=N C=1;
W%k0_Y/5 M1=120, % integer for amplitude
m#oZu { M3=5000; % integer for length of coupler
9ywPWT[^ N = 512; % Number of Fourier modes (Time domain sampling points)
,UD,)ZPf[ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
i%R2#F7I T =40; % length of time:T*T0.
BkTGH.4G% dt = T/N; % time step
"[LSDE"( n = [-N/2:1:N/2-1]'; % Index
8/|~E t = n.*dt;
pd rF/U+ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
UkY
`&&ic w=2*pi*n./T;
jSj
(ZU6 g1=-i*ww./2;
t/baze;V g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
%Jr6pmc g3=-i*ww./2;
]GS@ ub P1=0;
$K,6!FyBa P2=0;
FrNW@ P3=1;
Kb# }f/ P=0;
:K) =Hf2y for m1=1:M1
`[+nz
rLkO p=0.032*m1; %input amplitude
=lf&mD
_/ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
w]{NaNIeq1 s1=s10;
7 vS]O$w<4 s20=0.*s10; %input in waveguide 2
82X}@5o2 s30=0.*s10; %input in waveguide 3
2Q ,8@2w; s2=s20;
R":nG7o s3=s30;
wghz[qe p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
&!3=eVg %energy in waveguide 1
,cvLvN8 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
_faI*OY8 %energy in waveguide 2
$UZ4,S?V p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
I!)gXtJA" %energy in waveguide 3
l_!.yV{ for m3 = 1:1:M3 % Start space evolution
"}bk
*2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
up~l4]b+ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
z: aT5D s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
X^#.4:>. sca1 = fftshift(fft(s1)); % Take Fourier transform
)y7SkH| sca2 = fftshift(fft(s2));
TXi$Q%0W sca3 = fftshift(fft(s3));
C/Ig.KmXF{ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
27vLI~ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
><X!~by sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
_[SP*"
]H s3 = ifft(fftshift(sc3));
1GY[1M1^ s2 = ifft(fftshift(sc2)); % Return to physical space
Musz+<] s1 = ifft(fftshift(sc1));
d0b--v/ end
}0#cdw#gH p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
vO1P %) p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
)>ed6A1 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
=*q :R9V P1=[P1 p1/p10];
*|x2"?d-F: P2=[P2 p2/p10];
Z; @F.r P3=[P3 p3/p10];
5hE8b
{V P=[P p*p];
Y"mD)\Bw? end
a$MMp = p figure(1)
& 50Kn[ plot(P,P1, P,P2, P,P3);
C"/]X j =)%~@ 转自：
http://blog.163.com/opto_wang/
