计算脉冲在非线性耦合器中演化的Matlab 程序 K& |zWpb ^;@Bz~Z % This Matlab script file solves the coupled nonlinear Schrodinger equations of
vMRKs#&8 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
=:"@YD^a4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
KAsS= ` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
r456M-~ Q ;k_q3 %fid=fopen('e21.dat','w');
82/iVm1 N = 128; % Number of Fourier modes (Time domain sampling points)
|=%$7b\C M1 =3000; % Total number of space steps
&OzJ^G\o J =100; % Steps between output of space
6@F Z,e T =10; % length of time windows:T*T0
vN4X%^:( T0=0.1; % input pulse width
R*yB); p MN1=0; % initial value for the space output location
wkm
SIN: dt = T/N; % time step
WLh_b)V| n = [-N/2:1:N/2-1]'; % Index
=u;q98r t = n.*dt;
;QE Gr|( u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
X 4/r#<Da u20=u10.*0.0; % input to waveguide 2
czZ-C +}% u1=u10; u2=u20;
Q o= U1 = u1;
;N1FP* U2 = u2; % Compute initial condition; save it in U
I"
j7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
IS=)J( 0 w=2*pi*n./T;
,*lK4 ?v g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
> XZq=q]E! L=4; % length of evoluation to compare with S. Trillo's paper
Xif`gb6` dz=L/M1; % space step, make sure nonlinear<0.05
w^p2XlQ< for m1 = 1:1:M1 % Start space evolution
%##9.Xm6l u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
5j}@Of1pd u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
ljf9L:L ca1 = fftshift(fft(u1)); % Take Fourier transform
S7SPc ca2 = fftshift(fft(u2));
x )Th2es\ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
U)l>#gf 8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
ome>Jbdhe u2 = ifft(fftshift(c2)); % Return to physical space
[X=eCHB? u1 = ifft(fftshift(c1));
oNh . Zgg if rem(m1,J) == 0 % Save output every J steps.
ePY K^D U1 = [U1 u1]; % put solutions in U array
?41| e+p U2=[U2 u2];
g,W#3b6>j MN1=[MN1 m1];
d
z\b]H] z1=dz*MN1'; % output location
}`g*pp* end
0yZw`|Zh[ end
i*; V4zh hg=abs(U1').*abs(U1'); % for data write to excel
D0]9
-h ha=[z1 hg]; % for data write to excel
$fn^i. t1=[0 t'];
$N
]P#g?Q hh=[t1' ha']; % for data write to excel file
wGxLs>|
4 %dlmwrite('aa',hh,'\t'); % save data in the excel format
; s!H figure(1)
EXi+pm waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
a & cV@~ figure(2)
rLXn35O waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
[&4y@ i'u; "ot=
非线性超快脉冲耦合的数值方法的Matlab程序 VuR BJ2D :Oj+Tc9A 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。
GkO6r'MVE 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
wb?hfe D|BN_ai9 Xg)yz~Ug g[n8N{s % This Matlab script file solves the nonlinear Schrodinger equations
IpP0|:} % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
[/k O > % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
V:+bq` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%2+]3h >g iUKj:q: C=1;
(M=Br M1=120, % integer for amplitude
2u:j6ic M3=5000; % integer for length of coupler
M#p,Z F N = 512; % Number of Fourier modes (Time domain sampling points)
zhe5i;M dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]aR4U` T =40; % length of time:T*T0.
D0P% .r"v dt = T/N; % time step
lyPXlt n = [-N/2:1:N/2-1]'; % Index
i_@RWka< t = n.*dt;
GwV FD% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%xruPWT:k w=2*pi*n./T;
vP2QAGk < g1=-i*ww./2;
P&YaJUq.u g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
izw}25SW g3=-i*ww./2;
R
pbl) P1=0;
_7 ;^od=C P2=0;
2uTa}{/% P3=1;
qw/{o:ce] P=0;
K6U>Qums for m1=1:M1
xRUYJ=|oh p=0.032*m1; %input amplitude
g}-Z]2(c# s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
D^{:UbN s1=s10;
SMFW]I2T/ s20=0.*s10; %input in waveguide 2
v3"xJN_,[p s30=0.*s10; %input in waveguide 3
NZuFxJ-` s2=s20;
M&F uXG% s3=s30;
a*hThr+$M p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
rZv+K/6*M %energy in waveguide 1
(AYS>8O& p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
/z 5lxS@# %energy in waveguide 2
abnd U,s p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
!;gke,fB %energy in waveguide 3
o;mIu#u for m3 = 1:1:M3 % Start space evolution
g@k9w{_ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
w!RH*S s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
\gkajY -? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
G= cx c_9 sca1 = fftshift(fft(s1)); % Take Fourier transform
a AM UJk sca2 = fftshift(fft(s2));
3c3Z"JV sca3 = fftshift(fft(s3));
zTB9GrU sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
E'8Bw7 Tz sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
f zO8by sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
0 l@P]_qq` s3 = ifft(fftshift(sc3));
-/%jeDKp s2 = ifft(fftshift(sc2)); % Return to physical space
`1 @ [uWl s1 = ifft(fftshift(sc1));
[u80-x< end
zIFL?8!H9{ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
~ P_kr'o p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~PnpYd<2 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
PNgMLQI6 P1=[P1 p1/p10];
\T9UbkR P2=[P2 p2/p10];
1,QZnF!.x P3=[P3 p3/p10];
e 9_+$Oo P=[P p*p];
] gksyxn3 end
Ba0D"2CgY figure(1)
kVnyX @ plot(P,P1, P,P2, P,P3);
|vz;bJG "S`wwl 转自：
http://blog.163.com/opto_wang/
