计算脉冲在非线性耦合器中演化的Matlab 程序 xO'xZ%cUI aaesgF % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Jd/XEs?<q % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
]=0$-ImQ@x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&0@AM_b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.?-]+ -J?` je~gk6}Y %fid=fopen('e21.dat','w');
7.1FRxS N = 128; % Number of Fourier modes (Time domain sampling points)
u=!n9W~" M1 =3000; % Total number of space steps
VWE`wan< J =100; % Steps between output of space
qu0dWgK T =10; % length of time windows:T*T0
uF\f>E)/N% T0=0.1; % input pulse width
% KmhR2v MN1=0; % initial value for the space output location
UNKXfe(X9 dt = T/N; % time step
5B+I\f& n = [-N/2:1:N/2-1]'; % Index
n%:& N t = n.*dt;
#jR1ti)p u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
{( qH8 A u20=u10.*0.0; % input to waveguide 2
TY *q[AWG u1=u10; u2=u20;
/7XVr"R U1 = u1;
}Fgp*x-G U2 = u2; % Compute initial condition; save it in U
eWAgYe2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$iAd)2LT w=2*pi*n./T;
Ewczq1%l: g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1c03<(FCd L=4; % length of evoluation to compare with S. Trillo's paper
+h? z7ZY^ dz=L/M1; % space step, make sure nonlinear<0.05
"+KAYsVtU for m1 = 1:1:M1 % Start space evolution
5QJ FNE u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
#_[W*-|L u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
sD`OHV: ca1 = fftshift(fft(u1)); % Take Fourier transform
)1S"D~j- ca2 = fftshift(fft(u2));
q| 7$@H^* c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&IgH]?t c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
$79-)4;z4 u2 = ifft(fftshift(c2)); % Return to physical space
qx\P(dOUf u1 = ifft(fftshift(c1));
}=Ju C+#~n if rem(m1,J) == 0 % Save output every J steps.
B#;0 { U1 = [U1 u1]; % put solutions in U array
d<B=p&~ U2=[U2 u2];
G .k\N(l MN1=[MN1 m1];
Z:s:NvFX z1=dz*MN1'; % output location
WL/9r
*jW end
b_j8g{/9 end
|F^h >^
x hg=abs(U1').*abs(U1'); % for data write to excel
GjvTYg~ ha=[z1 hg]; % for data write to excel
/0I=?+QSo t1=[0 t'];
/N82h`\n hh=[t1' ha']; % for data write to excel file
AT]Ty %dlmwrite('aa',hh,'\t'); % save data in the excel format
iKN800^u figure(1)
@&M$oI$4* waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
>n^[-SWJCT figure(2)
$y&1.caMa waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
-$m?ShDd hz _F^gF 非线性超快脉冲耦合的数值方法的Matlab程序 $*i"rl JC 5!)_" u3 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
bZsg7[: C Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-6u#:pVpU bkfk9P SR\F2@u 9K` uGu % This Matlab script file solves the nonlinear Schrodinger equations
ngHPOI16 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Nt#a_ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>E3 lY/[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[r5 k8TB1 SQd`xbIuL C=1;
86,$ I+ M1=120, % integer for amplitude
Z6 vm!#\ M3=5000; % integer for length of coupler
pe1 _E
KU N = 512; % Number of Fourier modes (Time domain sampling points)
N>}2&'I dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
h*GU7<F:a T =40; % length of time:T*T0.
$"&U%3 dt = T/N; % time step
dE CH/vJ^ n = [-N/2:1:N/2-1]'; % Index
|r=.}9
- t = n.*dt;
9&`e jeD ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
^."HD ( w=2*pi*n./T;
pD>^Dfd g1=-i*ww./2;
d@72z r g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
/o_h'l|PS g3=-i*ww./2;
MjHjL~ Tg P1=0;
dnP3{!"b P2=0;
].eY]o}= P3=1;
Xqac$%[3 P=0;
8>|@O<2\ for m1=1:M1
=_L p=0.032*m1; %input amplitude
q;V1fogqI) s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
S3k>34_%9 s1=s10;
'Na/AcRdg s20=0.*s10; %input in waveguide 2
!B3lsXLSY s30=0.*s10; %input in waveguide 3
> xt*( j&} s2=s20;
p3NTI /- s3=s30;
Dy[
YL p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Xkv+"F=- %energy in waveguide 1
6/#5TdJA p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Q4;br ?2H %energy in waveguide 2
Mwdw7MZ"S p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
[n_H9$ %energy in waveguide 3
-~HlME *~f for m3 = 1:1:M3 % Start space evolution
?Ze3t5Ll s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
PUN.nt s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
'd" \h# s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
QJG]z'c+ sca1 = fftshift(fft(s1)); % Take Fourier transform
j{nkus2 sca2 = fftshift(fft(s2));
@Yq! sca3 = fftshift(fft(s3));
_5nQe
! sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
A_t<SG5
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
pP'-}% sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
I k#>6 s3 = ifft(fftshift(sc3));
_]=` F
l s2 = ifft(fftshift(sc2)); % Return to physical space
a`w)awb s1 = ifft(fftshift(sc1));
Te {L@sj end
bz~-uHC p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
QsmG(1= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
iDO~G($C p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]'aG oR P1=[P1 p1/p10];
b'N"?W^YQ P2=[P2 p2/p10];
,
"zS
pN P3=[P3 p3/p10];
FVsNOU P=[P p*p];
B(MO!GNg= end
Dz&4za+{ figure(1)
ubhem(p# plot(P,P1, P,P2, P,P3);
'FBvAk6 )N-+, Ms 转自：
http://blog.163.com/opto_wang/
