计算脉冲在非线性耦合器中演化的Matlab 程序
6H'HxB4 /tUy3myJ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
IKi5 v~bE % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
-=(!g&0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Kw#i),M % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%*\es7m} z@w Mc
EH %fid=fopen('e21.dat','w');
mQY_`&Jq N = 128; % Number of Fourier modes (Time domain sampling points)
$jg *pmR- M1 =3000; % Total number of space steps
f"St&q>[s J =100; % Steps between output of space
n/h,Lr)Z T =10; % length of time windows:T*T0
SCz(5[MZJ T0=0.1; % input pulse width
ca>Z7qT! MN1=0; % initial value for the space output location
&\Amn?Iq dt = T/N; % time step
z(H^..<!5 n = [-N/2:1:N/2-1]'; % Index
~ {Mn{ t = n.*dt;
N&M~0iw u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
?2oHZ%G u20=u10.*0.0; % input to waveguide 2
.B\ 5OI,] u1=u10; u2=u20;
$H-!j%hV U1 = u1;
[/X4"D-uOK U2 = u2; % Compute initial condition; save it in U
SXy=<%ed ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
AW,53\ 0 w=2*pi*n./T;
6qaulwV4t g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
3JVK L=4; % length of evoluation to compare with S. Trillo's paper
>ss/D^YS dz=L/M1; % space step, make sure nonlinear<0.05
:duo#w"K for m1 = 1:1:M1 % Start space evolution
R%'^ gFk 8 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
HB7;0yt`: u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
]Oif|k`{ ca1 = fftshift(fft(u1)); % Take Fourier transform
}oNhl^JC ca2 = fftshift(fft(u2));
2/0v B> c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
L>YU,I\o c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
3Oi
nK[' u2 = ifft(fftshift(c2)); % Return to physical space
qv@$ZL R u1 = ifft(fftshift(c1));
m o:D9 if rem(m1,J) == 0 % Save output every J steps.
lg b?)= U1 = [U1 u1]; % put solutions in U array
Rb{U+/gq U2=[U2 u2];
Q*b]_0 Rb MN1=[MN1 m1];
M6 }3wM*4 z1=dz*MN1'; % output location
'CN|'W)g7 end
WAS U0 end
Oj^,m .R hg=abs(U1').*abs(U1'); % for data write to excel
^6_Cc ha=[z1 hg]; % for data write to excel
7bV{Q355P t1=[0 t'];
M-giR:, hh=[t1' ha']; % for data write to excel file
67VT\f %dlmwrite('aa',hh,'\t'); % save data in the excel format
iURk=*Z= figure(1)
fF V!)Zj waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
) lZp9O figure(2)
Lg+G; W waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
<NuUW9+ oDU ;E 非线性超快脉冲耦合的数值方法的Matlab程序 B}&x aY u6bXv( 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。
!H}vu]R 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
nTz6LVF <Ce2r"U1e <0PT"ij yd?x= | % This Matlab script file solves the nonlinear Schrodinger equations
-Q
U^c2 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
k+DR]icv % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
I:d[Q
s % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:.4 5u}[ PgRDKygE C=1;
INyk3 `FT M1=120, % integer for amplitude
7 %{ | M3=5000; % integer for length of coupler
T9879[ZU\ N = 512; % Number of Fourier modes (Time domain sampling points)
[mPjP%{=@ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
14"J d\M8 T =40; % length of time:T*T0.
?|ZTaX6A dt = T/N; % time step
#Z<a
n = [-N/2:1:N/2-1]'; % Index
#2EI\E&$ t = n.*dt;
`8Lo { P ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]Ty isaT w=2*pi*n./T;
.({smN,B g1=-i*ww./2;
Ey4z.s'-l g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
P'O#I}Dmw< g3=-i*ww./2;
= hN
!;7 G P1=0;
Qx'`PNU9\ P2=0;
C(K; zo*S( P3=1;
xQ'2BAEa P=0;
P:N1 #| g for m1=1:M1
HuV J\%. p=0.032*m1; %input amplitude
{pHM}, WJ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
U_{Ux 2 s1=s10;
MG{YrX) oi s20=0.*s10; %input in waveguide 2
EV NY*&p s30=0.*s10; %input in waveguide 3
+r<0zh,n. s2=s20;
V} zEK0n(6 s3=s30;
D2,z)O%VK p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
I'@Ydt2 %energy in waveguide 1
jr`Es s p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
6 HlePTf8 %energy in waveguide 2
Usta0Ag p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
b ? j< BvQ %energy in waveguide 3
?Oc{bF7 for m3 = 1:1:M3 % Start space evolution
3dDX8M? s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
0]jA<vLR s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
o #hjvg s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Y!T
%cTK)a sca1 = fftshift(fft(s1)); % Take Fourier transform
nQ/E5y
sca2 = fftshift(fft(s2));
shM SN]S_x sca3 = fftshift(fft(s3));
!Lh^oPT"I sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
@ G4X sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
eBJUv]o % sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
;-Jb1"5 s3 = ifft(fftshift(sc3));
:hI@AA>g s2 = ifft(fftshift(sc2)); % Return to physical space
&wB\ ~Ie- s1 = ifft(fftshift(sc1));
1\r|g2Z
: end
%/rMg "f: p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
K_ ci_g": p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
MW+b;0U`# p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
x rN
&N_K# P1=[P1 p1/p10];
''kS*3 P2=[P2 p2/p10];
41_SRh7N P3=[P3 p3/p10];
RAp=s P=[P p*p];
EFc-foN end
1DA1N<' figure(1)
":nQgV\ 9 plot(P,P1, P,P2, P,P3);
<u=4*:QE m B\C?=_ 转自：
http://blog.163.com/opto_wang/
