计算脉冲在非线性耦合器中演化的Matlab 程序 aFnel8 R;< q<i_l % This Matlab script file solves the coupled nonlinear Schrodinger equations of
^hIdmTf6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
W XQ @kQD % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
u^Q`xd1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8u[_t.y4m kK? SG3 %fid=fopen('e21.dat','w');
KgL!~J N = 128; % Number of Fourier modes (Time domain sampling points)
[YDSS/ M1 =3000; % Total number of space steps
6D;N.wDZ J =100; % Steps between output of space
V b0T)C T =10; % length of time windows:T*T0
]fyfL|(; T0=0.1; % input pulse width
^b8~X [1J_ MN1=0; % initial value for the space output location
8 x{Owj:Q dt = T/N; % time step
IG^@ VQ% n = [-N/2:1:N/2-1]'; % Index
P?0X az t = n.*dt;
]E`<8hRB u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
&2 tfj(ms u20=u10.*0.0; % input to waveguide 2
a|ufm^ F u1=u10; u2=u20;
1!#N-^qk U1 = u1;
U+S=MP
}: U2 = u2; % Compute initial condition; save it in U
S6~y!J6Ok4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
cn'> dz 3v w=2*pi*n./T;
+,Eam6g{ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
v3-/ [-XB: L=4; % length of evoluation to compare with S. Trillo's paper
DH(<{ #u dz=L/M1; % space step, make sure nonlinear<0.05
2dn ^K3 for m1 = 1:1:M1 % Start space evolution
_#8hgwf> u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
2b"*~O; u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
78& |^sq ca1 = fftshift(fft(u1)); % Take Fourier transform
z0 "DbZ;d ca2 = fftshift(fft(u2));
8D*7{Q c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
l]*RiK2AC c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
)x.% PUA u2 = ifft(fftshift(c2)); % Return to physical space
n
Bu!2c u1 = ifft(fftshift(c1));
f|d~=\0y if rem(m1,J) == 0 % Save output every J steps.
+3v)@18B1 U1 = [U1 u1]; % put solutions in U array
u$nzpw0=H U2=[U2 u2];
y=3 dGOFB MN1=[MN1 m1];
_7c3=f83 z1=dz*MN1'; % output location
h@,ja end
@C;1e 7 end
JF=R$! 5 hg=abs(U1').*abs(U1'); % for data write to excel
:qzg?\( ha=[z1 hg]; % for data write to excel
@r"\bBi t1=[0 t'];
!>`Q]M` hh=[t1' ha']; % for data write to excel file
bLc5$U$!I %dlmwrite('aa',hh,'\t'); % save data in the excel format
|XyX%5p* figure(1)
FYAEM!dyy waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
6= ?0&Bx& figure(2)
]!hjKu" waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
WogUILB #C S>_qe.{ 非线性超快脉冲耦合的数值方法的Matlab程序 M 8},RR@{ k8gH#ENNK 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。
vq$6e*A Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%cF`x_h[j &Vl no* EC+t-:a] OSu&vFKz % This Matlab script file solves the nonlinear Schrodinger equations
z/7q#~J, % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
bt}8ymcG % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
so-5% S % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
PRh C1# {oQs*`=l> C=1;
pbMANZU[ M1=120, % integer for amplitude
_>gz& M3=5000; % integer for length of coupler
3.&BhLT N = 512; % Number of Fourier modes (Time domain sampling points)
6)INr,d dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
pc`P;Eui T =40; % length of time:T*T0.
) nm+_U dt = T/N; % time step
JPI%{@Qc^ n = [-N/2:1:N/2-1]'; % Index
L8 P0bNi t = n.*dt;
EP >u% ]# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
k+QGvgP[4@ w=2*pi*n./T;
`z!AjAT-G g1=-i*ww./2;
FXCBX:LnvU g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
F^d J{<yX g3=-i*ww./2;
[4Q;(67 P1=0;
%
km <+F=~ P2=0;
+M j 6.X P3=1;
'6N)sqTR P=0;
-]3 K#M)s for m1=1:M1
E$"NOR p=0.032*m1; %input amplitude
Fa("Gok[ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
?2@^O=I s1=s10;
SioeIXU s20=0.*s10; %input in waveguide 2
Tm %5:/<8 s30=0.*s10; %input in waveguide 3
?:R ]p2 ID s2=s20;
]E9iaq6Z s3=s30;
cU;Bm}U p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
I;4quFBlMu %energy in waveguide 1
!LK xZ" p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
E\iK_'# %energy in waveguide 2
-}7$;QK&a p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
jCqz^5=$ %energy in waveguide 3
*HrEh; 3^J for m3 = 1:1:M3 % Start space evolution
1]xmOx[mb s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
^ :VH?I= s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
I ~7iIUD s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
pGie!2T E sca1 = fftshift(fft(s1)); % Take Fourier transform
1AJ6NBC&c sca2 = fftshift(fft(s2));
;4 O[/;i sca3 = fftshift(fft(s3));
- %fQr5 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
WwmYJl0 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
yP58H{hQM8 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
/^=1]+_! s3 = ifft(fftshift(sc3));
IMM;LC%rD9 s2 = ifft(fftshift(sc2)); % Return to physical space
,_V V;P s1 = ifft(fftshift(sc1));
@e YpARF end
a`wjZ"}'[ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Xi="gxp$% p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
D||0c"E p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
(cj9xROx P1=[P1 p1/p10];
0|e [o" P2=[P2 p2/p10];
+n1!xv] P3=[P3 p3/p10];
>LBA0ynh
{ P=[P p*p];
*7Vb([x4; end
J v} figure(1)
[8QK @5[ plot(P,P1, P,P2, P,P3);
hjL;B 'IL VMah3T! 转自：
http://blog.163.com/opto_wang/
