计算脉冲在非线性耦合器中演化的Matlab 程序 95!x Tf M}5 C;E* % This Matlab script file solves the coupled nonlinear Schrodinger equations of
, Xh4(Gn#b % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_+;x 4K; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_>`0! mG % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
./g0T{& GS{9MGl %fid=fopen('e21.dat','w');
9xKFX|*$ N = 128; % Number of Fourier modes (Time domain sampling points)
cn\_;TYiJ M1 =3000; % Total number of space steps
g ]ihwm~ J =100; % Steps between output of space
e.jgV=dT- T =10; % length of time windows:T*T0
uyA9`~p=# T0=0.1; % input pulse width
NFSPw` f MN1=0; % initial value for the space output location
TRq~n7Y7C dt = T/N; % time step
8EE7mEmLH n = [-N/2:1:N/2-1]'; % Index
Ci*5E$+\ t = n.*dt;
x9ws@=[: u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
& aLR'*]6 u20=u10.*0.0; % input to waveguide 2
T5Fah#-4 u1=u10; u2=u20;
x xiLi46/ U1 = u1;
Ml3F\ fAW U2 = u2; % Compute initial condition; save it in U
ld?M ,Qd ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
OS9v. pz w=2*pi*n./T;
r"Bf@va g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
14&EdTG. L=4; % length of evoluation to compare with S. Trillo's paper
08`
@u4 dz=L/M1; % space step, make sure nonlinear<0.05
lR( &Wc\j for m1 = 1:1:M1 % Start space evolution
drZw#b u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
)5t_tPv u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
L9kP8&&KK ca1 = fftshift(fft(u1)); % Take Fourier transform
W#wM PsB ca2 = fftshift(fft(u2));
+ mcN6/ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
uJO*aA{K c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
i!HGM=f u2 = ifft(fftshift(c2)); % Return to physical space
gky_]7Av u1 = ifft(fftshift(c1));
fr?eOigbl if rem(m1,J) == 0 % Save output every J steps.
qb<gh D=j U1 = [U1 u1]; % put solutions in U array
O>Sbb2q?" U2=[U2 u2];
` WB|h)Y MN1=[MN1 m1];
Gs6 #aL}]R z1=dz*MN1'; % output location
pE< ' '` end
h>/ViB@"W| end
l}^#kHSyd hg=abs(U1').*abs(U1'); % for data write to excel
|l|]Tw ha=[z1 hg]; % for data write to excel
G](K2= t1=[0 t'];
;H= 6u hh=[t1' ha']; % for data write to excel file
xr/ k.Fz %dlmwrite('aa',hh,'\t'); % save data in the excel format
_"bx#B* figure(1)
s7e'9Bx waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
} :mI6zsNj figure(2)
^ \?9 W waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
}B- A*TI<h }rE|\ p> 非线性超快脉冲耦合的数值方法的Matlab程序 H6O\U2+ Y'5ck( 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。
i/~J0qQ 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
GN<I|mGLJK 0o]K6 b #dft-23 rA`\we) % This Matlab script file solves the nonlinear Schrodinger equations
{5udol5? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
~c^-DAgB % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
agYK aM1N % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
z!+< m < yjq
)}y,tF C=1;
9zyN8v2 M1=120, % integer for amplitude
s]iOC6v M3=5000; % integer for length of coupler
XbC8t &Q], N = 512; % Number of Fourier modes (Time domain sampling points)
M9K).P= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
DX"; v
J T =40; % length of time:T*T0.
IT (c'} dt = T/N; % time step
h 3&:"*A2 n = [-N/2:1:N/2-1]'; % Index
%\cC]<> t = n.*dt;
z aF0nov ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mSfhl(<L w=2*pi*n./T;
Lvq]SzOw g1=-i*ww./2;
A 5 X+Z g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
)ta5y7np
g3=-i*ww./2;
zmFFBf"< P1=0;
|pqpF?h5| P2=0;
cPcV[6)5K9 P3=1;
-G;1U P=0;
9pcf j x.. for m1=1:M1
".%LBs~$ p=0.032*m1; %input amplitude
=]a@ )6y s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
fn OkH s1=s10;
=!^ iiHF s20=0.*s10; %input in waveguide 2
/wE _eK. s30=0.*s10; %input in waveguide 3
s%oAsQ_y s2=s20;
\z9?rvT: s3=s30;
R3n&o%$* p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
>U<nEnB$? %energy in waveguide 1
4C%>/*%8> p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
k~f+L O %energy in waveguide 2
#sU~fq p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
h50StZ8Yr %energy in waveguide 3
8 >Z$/1Mh for m3 = 1:1:M3 % Start space evolution
aT#{t {gkA s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Vb^s 'k s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
$ud>Z;X=P s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
41o!2(e$ sca1 = fftshift(fft(s1)); % Take Fourier transform
>iH).:j sca2 = fftshift(fft(s2));
w3qf7{b sca3 = fftshift(fft(s3));
t`T\d\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
jF{gDK sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
V6MT > T sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
yH%+cm p7 s3 = ifft(fftshift(sc3));
9K46>_TyH s2 = ifft(fftshift(sc2)); % Return to physical space
C;q}3c*L s1 = ifft(fftshift(sc1));
SU
O; end
&OR v bnd6 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Q
*]`t@ q p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
5
?~-Vv31s p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
|Xm4(FN\ P1=[P1 p1/p10];
; axa ZV P2=[P2 p2/p10];
>zg8xA1zL P3=[P3 p3/p10];
&JhIn%=- P=[P p*p];
#A/J^Ko end
a^c ,=X3 figure(1)
n, jE#Z.D plot(P,P1, P,P2, P,P3);
Mc7 <[a G^rh*cb K 转自：
http://blog.163.com/opto_wang/
