计算脉冲在非线性耦合器中演化的Matlab 程序 dVSQG947i: ~;}uYJ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
,uPN\` .u8 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
p,BoiYdi % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>en\:pJn)' % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
biPj(D d [r1dgwh 8 %fid=fopen('e21.dat','w');
P1^O0) N = 128; % Number of Fourier modes (Time domain sampling points)
3e9UD N2 M1 =3000; % Total number of space steps
mFmxE v J =100; % Steps between output of space
jLn|zK T =10; % length of time windows:T*T0
$Lz!04 T0=0.1; % input pulse width
mD%IHzbn
H MN1=0; % initial value for the space output location
eV"s5X[$ dt = T/N; % time step
Y+h
?HS n = [-N/2:1:N/2-1]'; % Index
1\J9QZX0 t = n.*dt;
K >Q 6 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
qJ E_4/<^! u20=u10.*0.0; % input to waveguide 2
ux~=}{tz u1=u10; u2=u20;
49ehj1Se U1 = u1;
[X7gP4 U2 = u2; % Compute initial condition; save it in U
A
b+qLh&? ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mqbCa6>_S w=2*pi*n./T;
dL~^C I g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[?bq4u` L=4; % length of evoluation to compare with S. Trillo's paper
@hwNM#>` dz=L/M1; % space step, make sure nonlinear<0.05
5Z:T9F4 for m1 = 1:1:M1 % Start space evolution
@Z5,j) u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^<_rE- k u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
KquuM ]5S ca1 = fftshift(fft(u1)); % Take Fourier transform
yqH9*&KH{ ca2 = fftshift(fft(u2));
UW1i%u
k c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
7\N }QP0"u c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
u$FL(m4 u2 = ifft(fftshift(c2)); % Return to physical space
p
W@Yr u1 = ifft(fftshift(c1));
L)qUBp@MW if rem(m1,J) == 0 % Save output every J steps.
qHvU4v U1 = [U1 u1]; % put solutions in U array
cG&@PO]+. U2=[U2 u2];
z<%d Wz MN1=[MN1 m1];
G#ELQ/Q z1=dz*MN1'; % output location
!ST7@D end
(*kKfg4Wj end
JXH f$k hg=abs(U1').*abs(U1'); % for data write to excel
jrpki<D ha=[z1 hg]; % for data write to excel
4C )sjk?m t1=[0 t'];
8@b`a]lgrd hh=[t1' ha']; % for data write to excel file
h iv {A9a? %dlmwrite('aa',hh,'\t'); % save data in the excel format
iRx `Nx<@ figure(1)
ttls.~DG waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
- 3 S b%V\ figure(2)
&DjA?0`J waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
U2LD_-HZ ;GKL[ t I" 非线性超快脉冲耦合的数值方法的Matlab程序 O{\%{XrW Fzy kC 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。
vz)R84 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
s>W :vV@ W)'*Dcd e.^? hwl #^yOW^ % This Matlab script file solves the nonlinear Schrodinger equations
=[z P % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
WX]O1Y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
e
tL?UF$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^ cE {Uv ,N;2"$+E C=1;
JLz32 %-M M1=120, % integer for amplitude
YQyI{ M3=5000; % integer for length of coupler
[#YzU^^Ib N = 512; % Number of Fourier modes (Time domain sampling points)
YQtq?&0Ct dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
w`D$ W&3> T =40; % length of time:T*T0.
io(!z-$ dt = T/N; % time step
m#R"~ > n = [-N/2:1:N/2-1]'; % Index
.R#-u/6g( t = n.*dt;
_q}Cnp5 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'p78^4'PL w=2*pi*n./T;
^>>9? g1=-i*ww./2;
F|V KrH. g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
)wXE\$ g3=-i*ww./2;
m U P1=0;
m`):= ^nC P2=0;
8TG|frS P3=1;
s5 {B1e P=0;
zbr^ul r for m1=1:M1
cK2;)&U7 p=0.032*m1; %input amplitude
:_]0 8 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
t: oQHhO? s1=s10;
.z=%3p8+ s20=0.*s10; %input in waveguide 2
;(jL`L F s30=0.*s10; %input in waveguide 3
fJ0V|o s2=s20;
8aC=k @YE s3=s30;
V#|/\-@ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
>I<}:= %energy in waveguide 1
IOF!Ra:w p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
8 R7w$3pp\ %energy in waveguide 2
_ker,;{9C p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
` AD} 6O+x %energy in waveguide 3
'rS \9T for m3 = 1:1:M3 % Start space evolution
/Oi(5?Jn s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
; yE.R[I s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Ihr[44# s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
wnK6jMjkSf sca1 = fftshift(fft(s1)); % Take Fourier transform
ZHUW1:qs sca2 = fftshift(fft(s2));
J#F HR/zV sca3 = fftshift(fft(s3));
%#PWD7a\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
~7PiIky. sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
SS24@:"{ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Aqz $WTHW+ s3 = ifft(fftshift(sc3));
M2R krW# s2 = ifft(fftshift(sc2)); % Return to physical space
e@;'# t s1 = ifft(fftshift(sc1));
+ !" Y C end
~c]
q:pU2 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!`4i e p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2 VU N p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
8SL E*c^8 P1=[P1 p1/p10];
)f8 ;ze P2=[P2 p2/p10];
N$v_z>6Z P3=[P3 p3/p10];
"KS" [i!3j P=[P p*p];
08{^Ksg end
;DhAw 1 figure(1)
B0A y plot(P,P1, P,P2, P,P3);
fAz4>_4 E.sZjo1 转自：
http://blog.163.com/opto_wang/
