计算脉冲在非线性耦合器中演化的Matlab 程序 JmB7tRM8 t4)~A5s % This Matlab script file solves the coupled nonlinear Schrodinger equations of
HRO :U % % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
5Z{i't0CQ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Y$SZqW0!/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
HHa
XK )70-q yA %fid=fopen('e21.dat','w');
HJ[@;F|aU N = 128; % Number of Fourier modes (Time domain sampling points)
X%Jq9_
M1 =3000; % Total number of space steps
> #). 3 J =100; % Steps between output of space
oiYI$ql3L T =10; % length of time windows:T*T0
1~\YJEsb}d T0=0.1; % input pulse width
9:zW$Gt& MN1=0; % initial value for the space output location
eqD|3YX dt = T/N; % time step
z
zL@3/<j n = [-N/2:1:N/2-1]'; % Index
:f (UZmV$ t = n.*dt;
zr%2oFeX, u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
E
O^j,x g u20=u10.*0.0; % input to waveguide 2
~i 'Ib_%h u1=u10; u2=u20;
9[}L=n U1 = u1;
Yt79W U2 = u2; % Compute initial condition; save it in U
}$5S @, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Lqy]bnY w=2*pi*n./T;
Dz$GP A g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
o /273I L=4; % length of evoluation to compare with S. Trillo's paper
t|q@~B
: dz=L/M1; % space step, make sure nonlinear<0.05
71`)@y,Z, for m1 = 1:1:M1 % Start space evolution
jyRSe^ x u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
P)x&9OHV u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-Z )j"J ca1 = fftshift(fft(u1)); % Take Fourier transform
4PG]L`J{ ca2 = fftshift(fft(u2));
GZ.Xx c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
A?[06R5E# c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
kGm-jh u2 = ifft(fftshift(c2)); % Return to physical space
tA'O66. u1 = ifft(fftshift(c1));
Y?G9d6]Lk6 if rem(m1,J) == 0 % Save output every J steps.
Y?Ph%i2E U1 = [U1 u1]; % put solutions in U array
5, U2=[U2 u2];
?B>
{ rj MN1=[MN1 m1];
,r\ z1=dz*MN1'; % output location
x=(y end
nojJGeW% end
-0[ ?6.(s" hg=abs(U1').*abs(U1'); % for data write to excel
\q9wo*A ha=[z1 hg]; % for data write to excel
{&Kck>C' t1=[0 t'];
NzB"u+jB hh=[t1' ha']; % for data write to excel file
J`/ t;xk %dlmwrite('aa',hh,'\t'); % save data in the excel format
! h7?Ap figure(1)
bHx 09F] waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
D"kss5>w figure(2)
C+ \c(M a waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
G&qO{" Js .}'49=c 非线性超快脉冲耦合的数值方法的Matlab程序 98 dl -? /'KCW_Q 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|,YO6(L 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
z8 v] Kt & rqJ'm?>c r <Uj~S # O3Y#2lI % This Matlab script file solves the nonlinear Schrodinger equations
fyYH wG % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
>fG=(1" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
N.r8d C % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s|*0cK!K^ N|t!G^rP C=1;
ko-| hBNv M1=120, % integer for amplitude
FKhmg&+> M3=5000; % integer for length of coupler
7K"{}: N = 512; % Number of Fourier modes (Time domain sampling points)
-! d'!;
] dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
VRe7 Q0 T =40; % length of time:T*T0.
(9 g L dt = T/N; % time step
qfJi[8". n = [-N/2:1:N/2-1]'; % Index
bs_>!H1 t = n.*dt;
1< gY ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
J+hiz3N w=2*pi*n./T;
5q<cZ)v#& g1=-i*ww./2;
&<??,R14 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
uY 6]rt_#a g3=-i*ww./2;
%H)^k${ P1=0;
Vf28R,~m P2=0;
7 'T3W c P3=1;
DxuT23.
( P=0;
Uk @du7P1k for m1=1:M1
4oxAC; L p=0.032*m1; %input amplitude
Kkfz a s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
dJvT2s.t[ s1=s10;
\#)|6w- s20=0.*s10; %input in waveguide 2
"AN*2)e4 s30=0.*s10; %input in waveguide 3
<V[Qs3uo( s2=s20;
ANIx0*Yl ( s3=s30;
+pcGxje\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
V\1pn7~V %energy in waveguide 1
J d]kg,/ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
f\p#3I wwH %energy in waveguide 2
Os)jfKn2 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
4gR;,%E\TO %energy in waveguide 3
j
p"hbV for m3 = 1:1:M3 % Start space evolution
zx #HyO[a s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
exW|c~|m{A s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
G_ -8*. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
CG[2 sca1 = fftshift(fft(s1)); % Take Fourier transform
gc<w n m| sca2 = fftshift(fft(s2));
w.7p D sca3 = fftshift(fft(s3));
HB|R1<t;HB sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
!841/TR b sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
?/@ U#Qy sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
e\8|6< o[ s3 = ifft(fftshift(sc3));
j\hI, mc s2 = ifft(fftshift(sc2)); % Return to physical space
- uk}Fou s1 = ifft(fftshift(sc1));
]Rk4"i end
}}?,({T|n p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
1hTE^ \W p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
7 \0}te p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
*F:)S"3_~e P1=[P1 p1/p10];
U ;%cp P2=[P2 p2/p10];
If>bE!_BO P3=[P3 p3/p10];
Uf}u`"$F P=[P p*p];
{s7
3(B" end
"
""k}M2A figure(1)
c1 Rn1M,2k plot(P,P1, P,P2, P,P3);
i)!2DXn qr@ <'wp/ 转自：
http://blog.163.com/opto_wang/
