计算脉冲在非线性耦合器中演化的Matlab 程序 .iFViVZC {'NBp0i % This Matlab script file solves the coupled nonlinear Schrodinger equations of
:^ n*V6.4 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
]k[x9,IU\y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Hi^35 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
(Ao rx #z
6DB0ni %fid=fopen('e21.dat','w');
o& ~dGG4J N = 128; % Number of Fourier modes (Time domain sampling points)
zm> >} 5R M1 =3000; % Total number of space steps
z .
'Fv7 J =100; % Steps between output of space
Us'Cs+5XcG T =10; % length of time windows:T*T0
# Mu<8`T- T0=0.1; % input pulse width
kP@H G<~ MN1=0; % initial value for the space output location
`%e|$pK dt = T/N; % time step
iC\%_5/ _ n = [-N/2:1:N/2-1]'; % Index
eNtf#Rqym t = n.*dt;
rWA6X DM7 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
IroPx#s:i u20=u10.*0.0; % input to waveguide 2
)i;un. u1=u10; u2=u20;
V\0E=M*P U1 = u1;
1I ""X]I_ U2 = u2; % Compute initial condition; save it in U
d PsLZ"I ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1B 5:s,Oyj w=2*pi*n./T;
W RF.[R" g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
58: :h. : L=4; % length of evoluation to compare with S. Trillo's paper
XIKvH-0& dz=L/M1; % space step, make sure nonlinear<0.05
=~&VdPZ for m1 = 1:1:M1 % Start space evolution
H9 U .lb u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
@OzMiN u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
= -w;z x ca1 = fftshift(fft(u1)); % Take Fourier transform
m^<p8KZ ca2 = fftshift(fft(u2));
>%u@R3PH] c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
V^WU8x c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
9YD\~v;x u2 = ifft(fftshift(c2)); % Return to physical space
P;73Hr[E# u1 = ifft(fftshift(c1));
M , `w A if rem(m1,J) == 0 % Save output every J steps.
:|rPT)yT] U1 = [U1 u1]; % put solutions in U array
nq1
'F U2=[U2 u2];
;r.EC}>m MN1=[MN1 m1];
,[* ;UR z1=dz*MN1'; % output location
)qv2)a!H end
ziiwxx_ end
\9`#]#1bx5 hg=abs(U1').*abs(U1'); % for data write to excel
E;9>ePd@ ha=[z1 hg]; % for data write to excel
lNz]H iD t1=[0 t'];
x: fW~!Xc6 hh=[t1' ha']; % for data write to excel file
YHB9mZi %dlmwrite('aa',hh,'\t'); % save data in the excel format
0OnV0 SIL figure(1)
Ab2Q
\+, waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
p $Hi[upy figure(2)
>&Y-u%}U waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
` XJm=/f ?T!)X)A# 非线性超快脉冲耦合的数值方法的Matlab程序 cG{L
jt ^nNit F
在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
6@V~0DG Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
PX2c[CDE^ uOd& XW l$XPIC~H [%pRfjM % This Matlab script file solves the nonlinear Schrodinger equations
,6{iT,~@8 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
<CZgQ\Mt % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
sI LS ey5` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[M%._ u, w!&~??&=} C=1;
Z6Fp\aI8@ M1=120, % integer for amplitude
A&"%os M3=5000; % integer for length of coupler
vUesV%9hq N = 512; % Number of Fourier modes (Time domain sampling points)
fQdK]rLj dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
-oP'4QVb T =40; % length of time:T*T0.
,R2U`EO; dt = T/N; % time step
KC#/Z2A|< n = [-N/2:1:N/2-1]'; % Index
!RH. |} t = n.*dt;
Y`B Rh9Sa ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%IY``r)j w=2*pi*n./T;
f 0>!qt g1=-i*ww./2;
m@Rtlb g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
= 0
g3=-i*ww./2;
;j%BK(5 P1=0;
C\*4q8( P2=0;
y *23$fj( P3=1;
gckI.[!b P=0;
`5~3 G2T for m1=1:M1
% $5H!!~o p=0.032*m1; %input amplitude
<RNJ >>0 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
=] C]= s1=s10;
,Lr<)p s20=0.*s10; %input in waveguide 2
04U")-\O s30=0.*s10; %input in waveguide 3
7 msAhz s2=s20;
T0z n,ej s3=s30;
;j8 )KC p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
hr GH}CU" %energy in waveguide 1
T r0 B[QF p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
$ *R/tJ. %energy in waveguide 2
TuDE@ gq( p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
GH1"xR4! %energy in waveguide 3
A:l@_*C.. for m3 = 1:1:M3 % Start space evolution
&<RpWA k{ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
kOo~%kcQ' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
9ZXlR?GA s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
~{,X3-S_H sca1 = fftshift(fft(s1)); % Take Fourier transform
$(e #aHB sca2 = fftshift(fft(s2));
mZz="ZLa: sca3 = fftshift(fft(s3));
$-}e; V Zb sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
/,=@8k!t? sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
>9e(.6&2XZ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
7\FXz'hA s3 = ifft(fftshift(sc3));
_BdE<
!r s2 = ifft(fftshift(sc2)); % Return to physical space
R218(8S s1 = ifft(fftshift(sc1));
~vlype3/EF end
1$qh`< \ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
b2b?hA'k p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
l7# yZ*<v p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
HK|ynBAo P1=[P1 p1/p10];
`Qr%+OD
P2=[P2 p2/p10];
MUfG?r\t P3=[P3 p3/p10];
2MZCw^ s> P=[P p*p];
l2N]a9bq@ end
$/!{ OU.t` figure(1)
?v> ET2wD plot(P,P1, P,P2, P,P3);
`;%]'F0` otggN:^Qw 转自：
http://blog.163.com/opto_wang/
