计算脉冲在非线性耦合器中演化的Matlab 程序 #|PPkg%v< J#.f%VJ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
C n"_x % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
1.9bU/X % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
WC T mf8f % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"Jahc.I 8H'ybfed %fid=fopen('e21.dat','w');
w"`Zf7a{/ N = 128; % Number of Fourier modes (Time domain sampling points)
mXY G ^} M1 =3000; % Total number of space steps
FR9w0{o J =100; % Steps between output of space
=oE(ur T =10; % length of time windows:T*T0
p<
Y-b,& T0=0.1; % input pulse width
Ux,?\Vd MN1=0; % initial value for the space output location
eOoqH$
i dt = T/N; % time step
U[0x\~[$K n = [-N/2:1:N/2-1]'; % Index
^4b;rLfk@ t = n.*dt;
6i+<0b}!/ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Y #,&Tu u20=u10.*0.0; % input to waveguide 2
z @g%9 |U u1=u10; u2=u20;
(ZPl~ZO U1 = u1;
<ni_78 U2 = u2; % Compute initial condition; save it in U
0OXl `V`w ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/ Nc)bF%gX w=2*pi*n./T;
0BwxPD#6bv g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
#<LJns\t
L=4; % length of evoluation to compare with S. Trillo's paper
)/t&a$[ dz=L/M1; % space step, make sure nonlinear<0.05
ZveNe~D7C for m1 = 1:1:M1 % Start space evolution
bm*.*A] u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
{q/;G!ON.S u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
e# U@n
j6 ca1 = fftshift(fft(u1)); % Take Fourier transform
r|63T%q! ca2 = fftshift(fft(u2));
4s e6+oJe c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
gSa !zQN6 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
A`- -*$ 8\ u2 = ifft(fftshift(c2)); % Return to physical space
w%?Zb[!& u1 = ifft(fftshift(c1));
V3%
>TNp if rem(m1,J) == 0 % Save output every J steps.
CnpQdI U1 = [U1 u1]; % put solutions in U array
{wDq*va U2=[U2 u2];
*@ { MN1=[MN1 m1];
qeW.~B!B z1=dz*MN1'; % output location
y6dQ4Whv& end
rB|1<jR end
=@nE :uto] hg=abs(U1').*abs(U1'); % for data write to excel
J-|&[-Z
ha=[z1 hg]; % for data write to excel
)oALB vX t1=[0 t'];
O14\_eAu6 hh=[t1' ha']; % for data write to excel file
cL<,]%SkE %dlmwrite('aa',hh,'\t'); % save data in the excel format
bv;. 6C(T< figure(1)
~?4 BP%g-y waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
W
]$/qyc&J figure(2)
qSDn 0^y waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
S"VO@)d **\?-*c=U 非线性超快脉冲耦合的数值方法的Matlab程序 &mW7FR'( S
n<X 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。
Bq ;GO 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
+1a 3^A\ QH,Fw$1 1:iB1Tc lP < -mhz`^ % This Matlab script file solves the nonlinear Schrodinger equations
?@z/#3b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
!PA ><F % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!>"fDz<w` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
jo?[M o[1#)& C=1;
Q 5hOVD% M1=120, % integer for amplitude
Z4X, D`s M3=5000; % integer for length of coupler
GKbbwT0T| N = 512; % Number of Fourier modes (Time domain sampling points)
fLpWTkr0 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
h56Kmx xk T =40; % length of time:T*T0.
kS35X)- dt = T/N; % time step
k dWU z( n = [-N/2:1:N/2-1]'; % Index
#1C]ZV] B t = n.*dt;
w=CzPNRHH! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
U {Knjo S w=2*pi*n./T;
1{ 5t. g1=-i*ww./2;
eh%{BXW[p g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
&qK:LHhj g3=-i*ww./2;
u|Oc+qA( P1=0;
n!.=05OtX P2=0;
c3Gy1#f:#2 P3=1;
%Oo
f/q P=0;
D^2lb "3 for m1=1:M1
6uv~.-T<l p=0.032*m1; %input amplitude
IBvn
q8\ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3;FV^V' s1=s10;
SuB 8mPn s20=0.*s10; %input in waveguide 2
ZPY&q&R s30=0.*s10; %input in waveguide 3
]kXW eY < s2=s20;
C=|8C70[%N s3=s30;
]=%6n@z' p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
#s81 k@#X %energy in waveguide 1
_g
fmo p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
o
^ \+Ua %energy in waveguide 2
Q-!gO p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
+zd /< %energy in waveguide 3
qp)Wt6 k? for m3 = 1:1:M3 % Start space evolution
)#8g<]q s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
O_ZYm{T[7 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
r{t6Vv2J s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
zd) QCq sca1 = fftshift(fft(s1)); % Take Fourier transform
K,JK9)T sca2 = fftshift(fft(s2));
\gkhSL q sca3 = fftshift(fft(s3));
6D[]Jf,9 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
w[\rS`J sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
BdiV sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
lz ::6} s3 = ifft(fftshift(sc3));
^a`3)WBv8 s2 = ifft(fftshift(sc2)); % Return to physical space
-C i&h s1 = ifft(fftshift(sc1));
fN&uat 7 end
AD^I1 ]2f p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
'e' p`* p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
GB^ `A p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
P $0c{B4I P1=[P1 p1/p10];
;x 2o|#`b P2=[P2 p2/p10];
YvcV801Go P3=[P3 p3/p10];
F8 1EZ/ P=[P p*p];
R|'W#"{@ end
$.kJBRgV* figure(1)
K6
>\4'q plot(P,P1, P,P2, P,P3);
8Z_ 4%vUBg 0^dYu /i5 转自：
http://blog.163.com/opto_wang/
