计算脉冲在非线性耦合器中演化的Matlab 程序 P5^<c\Mr,Y D[ -Gzqh % This Matlab script file solves the coupled nonlinear Schrodinger equations of
9e*v&A2Y' % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
G
uLU7a % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
FV->226o% % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
i `}nv, N-O"y3W} %fid=fopen('e21.dat','w');
&n)=OConge N = 128; % Number of Fourier modes (Time domain sampling points)
L)`SNN\ipR M1 =3000; % Total number of space steps
8qY\T0 J =100; % Steps between output of space
Z* Fxr;)d T =10; % length of time windows:T*T0
A/zZ%h T0=0.1; % input pulse width
/ .ddx< MN1=0; % initial value for the space output location
LyB &u( ) dt = T/N; % time step
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2
n = [-N/2:1:N/2-1]'; % Index
DiLZ5^`] t = n.*dt;
d?uN6 JH9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
sD[G?X u20=u10.*0.0; % input to waveguide 2
YA vO V-L u1=u10; u2=u20;
U)n+j}vi U1 = u1;
:QV-! U2 = u2; % Compute initial condition; save it in U
Z+*t=?L,,G ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
C;C= g1I} w=2*pi*n./T;
T3W? -, g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
/Dl{I7W L=4; % length of evoluation to compare with S. Trillo's paper
~RRp5x _ dz=L/M1; % space step, make sure nonlinear<0.05
)Zcw G(o0 for m1 = 1:1:M1 % Start space evolution
vl{G;[6 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1D6F
WYV8 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
. (7 end< ca1 = fftshift(fft(u1)); % Take Fourier transform
ph;ds+b ca2 = fftshift(fft(u2));
X_6h8 n}i c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
- 9Ll'fbq c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
l".LtUf- u2 = ifft(fftshift(c2)); % Return to physical space
CQ`$' oy?W u1 = ifft(fftshift(c1));
X{j` H\'L if rem(m1,J) == 0 % Save output every J steps.
?IWLH-fkP U1 = [U1 u1]; % put solutions in U array
=/J{>S>(i U2=[U2 u2];
nF8|*}w MN1=[MN1 m1];
;6T >p z1=dz*MN1'; % output location
iIe \m V end
VX!UT=; end
gW[(gf.oo hg=abs(U1').*abs(U1'); % for data write to excel
2th> +M~A ha=[z1 hg]; % for data write to excel
Z?7XuELKV t1=[0 t'];
p%8v+9+h2 hh=[t1' ha']; % for data write to excel file
= % O @%v %dlmwrite('aa',hh,'\t'); % save data in the excel format
+ ~6Nq(kV figure(1)
3j]P\T waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
oY#62&wk4 figure(2)
Aw38T w waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
yMQZulCWE ]W-7 U_ 非线性超快脉冲耦合的数值方法的Matlab程序 %SHjJCS3 *Z+8L*k97 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。
Z uh!{_x; 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
a2{ nrGD P2q'P& [HV>4,,3" a<W[???m/M % This Matlab script file solves the nonlinear Schrodinger equations
o
IUjd % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
5L'bF2SI % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
jP]I>Tq % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
X/5\L.g2 | m^qA](M C=1;
WxN@& g( M1=120, % integer for amplitude
AS}
FRNIVx M3=5000; % integer for length of coupler
^sWsP` DV N = 512; % Number of Fourier modes (Time domain sampling points)
yK $.wd 2, dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
9vAY|b^ T =40; % length of time:T*T0.
W'
DpI7 dt = T/N; % time step
_* xjG \! n = [-N/2:1:N/2-1]'; % Index
Y55Yo5<j/+ t = n.*dt;
lcv&/ A ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
F|eKt/> e w=2*pi*n./T;
\Kx@?, g1=-i*ww./2;
P Wwz<AI+ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
t3~ZGOn g3=-i*ww./2;
O[N}@%HMW
P1=0;
44uM:; P2=0;
`30og]F0YJ P3=1;
rj.] M6# P=0;
f`8]4ms" for m1=1:M1
[@l:C\2 p=0.032*m1; %input amplitude
+}XFkH ~ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1@ e22\ s1=s10;
sd@JQ%O s20=0.*s10; %input in waveguide 2
k63]Qf=5?N s30=0.*s10; %input in waveguide 3
Q :
H`TSR] s2=s20;
y?ps+ce93 s3=s30;
F~NmLm p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
}`O_ %energy in waveguide 1
\m>m E/N p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
r[>=iim %energy in waveguide 2
m.F \Mn p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Rmq8lU %energy in waveguide 3
v4?qI >/ for m3 = 1:1:M3 % Start space evolution
q'07 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
.,)C^hs@ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Ur`jmB s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
F __(iX xC sca1 = fftshift(fft(s1)); % Take Fourier transform
Fq]ht* sca2 = fftshift(fft(s2));
'nK(cKDIG sca3 = fftshift(fft(s3));
ICJ p- sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
g UfLw sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
/[[_}\xI% sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
d"E@e21 s3 = ifft(fftshift(sc3));
i2a"" zac s2 = ifft(fftshift(sc2)); % Return to physical space
#cN0ciCT' s1 = ifft(fftshift(sc1));
F,t
,Ja end
)1P Z# p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
sH//*y p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
l!U_ 7)s/ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
2wHvHH! P1=[P1 p1/p10];
#].n0[ P2=[P2 p2/p10];
^ -s'Ad3 P3=[P3 p3/p10];
Im
NTk P=[P p*p];
*, /ADtL end
FME&v Uh/ figure(1)
{uurM` f}: plot(P,P1, P,P2, P,P3);
`/zx2Tkk lJ+05\ pE 转自：
http://blog.163.com/opto_wang/
