计算脉冲在非线性耦合器中演化的Matlab 程序 4Wz@^7|V5 fi5x0El
% This Matlab script file solves the coupled nonlinear Schrodinger equations of
*v+xKy#M % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Nj8 `<Sl % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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1:7{k % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
K-%x] Fp= f+#^Lngo %fid=fopen('e21.dat','w');
`Sh#>
Jp N = 128; % Number of Fourier modes (Time domain sampling points)
1SddZ5 M1 =3000; % Total number of space steps
T%GdvtmS> J =100; % Steps between output of space
vM_UF{a$= T =10; % length of time windows:T*T0
QU4/hS;Ux T0=0.1; % input pulse width
wc&%icF*cr MN1=0; % initial value for the space output location
c&!EsM sU dt = T/N; % time step
8Z Y F% n = [-N/2:1:N/2-1]'; % Index
2=P.$Kx t = n.*dt;
V`F]L^m=L u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
PL;PId<9w u20=u10.*0.0; % input to waveguide 2
Ce: 2Tw u1=u10; u2=u20;
6Fp} U U1 = u1;
QWqEe|}6 U2 = u2; % Compute initial condition; save it in U
i98>=y ~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T(Q(7 w=2*pi*n./T;
mmE!!J`B g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Q-scL>IkCb L=4; % length of evoluation to compare with S. Trillo's paper
Ly e^G% { dz=L/M1; % space step, make sure nonlinear<0.05
[sx J< for m1 = 1:1:M1 % Start space evolution
A .]o&S} u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1}O&q6\"J u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
in>Os@e# ca1 = fftshift(fft(u1)); % Take Fourier transform
r]GG9si ca2 = fftshift(fft(u2));
~
Z kSYW< c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
O[9>^y\, c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
,;RAPT4 u2 = ifft(fftshift(c2)); % Return to physical space
r&$r=f< u1 = ifft(fftshift(c1));
u"WqI[IV if rem(m1,J) == 0 % Save output every J steps.
9$ ]I3k U1 = [U1 u1]; % put solutions in U array
0?x9.] U2=[U2 u2];
XTzz/.T;Z MN1=[MN1 m1];
tw<mZd2H z1=dz*MN1'; % output location
eouxNw}F1 end
= JE4C9$, end
7/ $r hg=abs(U1').*abs(U1'); % for data write to excel
adi^*7Q] ) ha=[z1 hg]; % for data write to excel
y7iHB
k"^: t1=[0 t'];
d7g3VF< j hh=[t1' ha']; % for data write to excel file
<=1 nr@L %dlmwrite('aa',hh,'\t'); % save data in the excel format
y(^hlX6gQ figure(1)
+(a}S$C waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
s{QS2 G$5 figure(2)
%Z:07|57I[ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
; M)l7f V:<NQd 非线性超快脉冲耦合的数值方法的Matlab程序 } "QV{W rMV<}C ^ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
>gj%q$@ 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
K<BS%~,I lWiC$ @ V_@r@A 0!Zp4>l\Z % This Matlab script file solves the nonlinear Schrodinger equations
U};~ff+ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
2 q4dCbJ! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
#$W bYL| % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Iu3*`H =N,ahq C=1;
5V"Fy&}: M1=120, % integer for amplitude
zB/)_AW
M3=5000; % integer for length of coupler
p3e_:5k N = 512; % Number of Fourier modes (Time domain sampling points)
3U.?Jbm-8 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
~s$
jiA1 T =40; % length of time:T*T0.
0 It[Pa qG dt = T/N; % time step
XIS.0]~ n = [-N/2:1:N/2-1]'; % Index
In3},x +$ t = n.*dt;
Cp`>dtCd ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/o/0 9K w=2*pi*n./T;
;!k{{Xndd g1=-i*ww./2;
~7kIe+V g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Kuj*U'ed7t g3=-i*ww./2;
hny(:Dj P1=0;
Rt%3\?rf P2=0;
834E
]2 P3=1;
nQ\)~MKd P=0;
NWN Pq" for m1=1:M1
o%~PWA*Qp p=0.032*m1; %input amplitude
S yf0dp3 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
H#Aar s1=s10;
bD: y u s20=0.*s10; %input in waveguide 2
vX9B^W||x s30=0.*s10; %input in waveguide 3
5O7 x4bY s2=s20;
Boi?Bt s3=s30;
|aaoi4OJ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
31FQ=(K %energy in waveguide 1
Pc{0Js5VzE p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
P%CNu %energy in waveguide 2
Vk3xWD~ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
@2Spfj_e %energy in waveguide 3
G`Ix-dADJm for m3 = 1:1:M3 % Start space evolution
/d1
B-I s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
!B Q:R(w s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
sz7|2OV" s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
D>HX1LV sca1 = fftshift(fft(s1)); % Take Fourier transform
t V]BcDp sca2 = fftshift(fft(s2));
e >FK5rz sca3 = fftshift(fft(s3));
L,KK{o|Eq sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
% w c=Mf sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
C0Oe$&
_ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
zG[GyyAQ s3 = ifft(fftshift(sc3));
N1pw*<& s2 = ifft(fftshift(sc2)); % Return to physical space
&+K:pU?[$ s1 = ifft(fftshift(sc1));
3lZ5N@z69 end
cTq}H_hC p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
0_A|K >7 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
CP%?,\ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
3ZAPcpB2 P1=[P1 p1/p10];
J7 p '_\ P2=[P2 p2/p10];
O|Z5SSlk P3=[P3 p3/p10];
< c X\|dM P=[P p*p];
u> YC4& end
(,i&pgVZ figure(1)
EWr8=@iU plot(P,P1, P,P2, P,P3);
oX;D|8 f 4ox[, 转自：
http://blog.163.com/opto_wang/
