计算脉冲在非线性耦合器中演化的Matlab 程序 |~#A ?mK- zhbSi w % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#;5Q d' % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
$|@pY| f % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
?:&2iW7z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_s<s14+od V(:wYk?ZR %fid=fopen('e21.dat','w');
u'k+t`V& N = 128; % Number of Fourier modes (Time domain sampling points)
vz|(KN[ M1 =3000; % Total number of space steps
A6J:!sY4A J =100; % Steps between output of space
^vTx%F T =10; % length of time windows:T*T0
1GIBqs~- T0=0.1; % input pulse width
2h#.:!/SMw MN1=0; % initial value for the space output location
G
B,O dt = T/N; % time step
,CN (;z) n = [-N/2:1:N/2-1]'; % Index
@!j6 y (@ t = n.*dt;
H:OpS-b u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
C <(qk _ u20=u10.*0.0; % input to waveguide 2
W /*?y & u1=u10; u2=u20;
f mJK+ U1 = u1;
w{u,YM(Q U2 = u2; % Compute initial condition; save it in U
:R3iLy ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
kr@!j@j$ w=2*pi*n./T;
+v'2s@e`
# g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
F FcIOn L=4; % length of evoluation to compare with S. Trillo's paper
h_\(
$" dz=L/M1; % space step, make sure nonlinear<0.05
5 UOqS#"0 for m1 = 1:1:M1 % Start space evolution
)v*k\:Hw u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
s diWQ v u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
'U*#7 1S ca1 = fftshift(fft(u1)); % Take Fourier transform
_ker,;{9C ca2 = fftshift(fft(u2));
` AD} 6O+x c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
'rS \9T c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
7+}WU 4 u2 = ifft(fftshift(c2)); % Return to physical space
G mE`YW u1 = ifft(fftshift(c1));
Ihr[44# if rem(m1,J) == 0 % Save output every J steps.
wnK6jMjkSf U1 = [U1 u1]; % put solutions in U array
ZHUW1:qs U2=[U2 u2];
J#F HR/zV MN1=[MN1 m1];
%#PWD7a\ z1=dz*MN1'; % output location
/hmDeP o} end
bfEH>pQ> # end
tN_=&|{WE4 hg=abs(U1').*abs(U1'); % for data write to excel
AAW] Y#UwW ha=[z1 hg]; % for data write to excel
= =gL!e{ t1=[0 t'];
T31F8K3x hh=[t1' ha']; % for data write to excel file
@GGQ13Cj( %dlmwrite('aa',hh,'\t'); % save data in the excel format
S8+l!$7 figure(1)
Hz[1c4)'F waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
9<i M2(IW{ figure(2)
Q[aF"5h% waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
%'=2Jy6h ssS"X@VZ
\ 非线性超快脉冲耦合的数值方法的Matlab程序 mPqK k UZmUYSu; 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。
#_`p
0wY 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
jUl_ToX 6J#R1.h jJNl{nyq O!hp=`B,jf % This Matlab script file solves the nonlinear Schrodinger equations
n/ :#: % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
{Rb;1 eYj % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
FGie*t % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|Kjfh};-C 4}t&yu<P> C=1;
FV7'3fIa M1=120, % integer for amplitude
$T:;Kc W) M3=5000; % integer for length of coupler
H3vnc\d~ N = 512; % Number of Fourier modes (Time domain sampling points)
NS""][# dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
iOCs% J T =40; % length of time:T*T0.
+- SO}P dt = T/N; % time step
;($xAAR n = [-N/2:1:N/2-1]'; % Index
PhV/WjCZ t = n.*dt;
S.`hl/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
;&f(7 Q+T_ w=2*pi*n./T;
e6H}L:; g1=-i*ww./2;
~%
t'}JDZ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
M;'GnGFf g3=-i*ww./2;
|,S]EHIy P1=0;
@%*@Rar P2=0;
EAm31v C P3=1;
X2 ;72 P=0;
i `p1e5$ for m1=1:M1
@Q{:m)\ p=0.032*m1; %input amplitude
m8x?`Gw~jw s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Nu3IYS5& s1=s10;
[{ #T N s20=0.*s10; %input in waveguide 2
f%1\1_^g s30=0.*s10; %input in waveguide 3
Anpp`>} N s2=s20;
trjeGSt& s3=s30;
:w
Y%= p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Z%LS{o~LK. %energy in waveguide 1
5D?{dA:Rq p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
]Ol
w6W?% %energy in waveguide 2
+t1+1 Zv p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
,' t&L] %energy in waveguide 3
bG* l_ for m3 = 1:1:M3 % Start space evolution
"X._:||8
s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
d2US~.;>l s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
J#4pA{0 1w s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
\fSruhD sca1 = fftshift(fft(s1)); % Take Fourier transform
$!!y v'K sca2 = fftshift(fft(s2));
]\>MDH sca3 = fftshift(fft(s3));
!>!jLZ0 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
; 14Q@yrZ0 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
-:F r($^ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
i$}G[v<4 s3 = ifft(fftshift(sc3));
7<(U`9W/q s2 = ifft(fftshift(sc2)); % Return to physical space
#K$0%0=M s1 = ifft(fftshift(sc1));
q o-|.I end
TNeL%s?B3 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
4T"L#o1 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
$Jn.rX0}$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Y#-c<o}f P1=[P1 p1/p10];
vl}}h%BC P2=[P2 p2/p10];
`WxGU P3=[P3 p3/p10];
tj8o6N# P=[P p*p];
F.(e}EMyNh end
1cMdoQ figure(1)
yg m6(+ plot(P,P1, P,P2, P,P3);
PR(KDwsT&l }TuMMO4+ 转自：
http://blog.163.com/opto_wang/
