计算脉冲在非线性耦合器中演化的Matlab 程序 iN0'/)ar BVus3Y5IJQ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
]sP % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
%ib7)8Ki0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
XN \rq= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
rkdA4'66w ]TtID4qL %fid=fopen('e21.dat','w');
y=
8SD7P' N = 128; % Number of Fourier modes (Time domain sampling points)
Fwvc+ a M1 =3000; % Total number of space steps
>@a7Zzl0H J =100; % Steps between output of space
T^$`Z. T =10; % length of time windows:T*T0
Wi\k&V.mE T0=0.1; % input pulse width
\ j.l1O MN1=0; % initial value for the space output location
>lJTS t5{ dt = T/N; % time step
K0I.3| 6C n = [-N/2:1:N/2-1]'; % Index
f\R TO63|O t = n.*dt;
d mT ZEO u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
?-0, x|ul u20=u10.*0.0; % input to waveguide 2
96; gzG@1! u1=u10; u2=u20;
Cd6th
F) U1 = u1;
@S5HMJ2= U2 = u2; % Compute initial condition; save it in U
#l9sQ-1Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Bw+ ?MdS w=2*pi*n./T;
tU!Yg "4Q g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
jWvi% I qi L=4; % length of evoluation to compare with S. Trillo's paper
vw a*'C dz=L/M1; % space step, make sure nonlinear<0.05
G%!i="/9 for m1 = 1:1:M1 % Start space evolution
nLANW Qk9 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1BP/,d |+ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
U ){4W0 ca1 = fftshift(fft(u1)); % Take Fourier transform
[P }mDX ca2 = fftshift(fft(u2));
DV>;sCMJ % c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
H _| re c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
$|[N3 u2 = ifft(fftshift(c2)); % Return to physical space
B
o%Sl u1 = ifft(fftshift(c1));
b53s@7/mq if rem(m1,J) == 0 % Save output every J steps.
w~=xO_% U1 = [U1 u1]; % put solutions in U array
|S<!' rY U2=[U2 u2];
3'0Jn6( MN1=[MN1 m1];
Fs =)*6}& z1=dz*MN1'; % output location
\W= Z`w3 end
x] R0zol end
%z.d;[Hs hg=abs(U1').*abs(U1'); % for data write to excel
P)Oe?z;G? ha=[z1 hg]; % for data write to excel
]HXHz(?;F t1=[0 t'];
+o0yx U
7t hh=[t1' ha']; % for data write to excel file
TnKOr~ @* %dlmwrite('aa',hh,'\t'); % save data in the excel format
cBOt=vg,5 figure(1)
Be^"sC waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
E]a ;Ydf~ figure(2)
xwHE,ykE waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
@~5Fcfmm $ S 2
/* 非线性超快脉冲耦合的数值方法的Matlab程序 A9J{>f
0G Q8} r 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。
-Q BM^L 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
LN5q_ZvR nYv keT d@b2XCh< K Are0Nj&? % This Matlab script file solves the nonlinear Schrodinger equations
&%(SkL_] % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
XgeUS;qtta % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
hKnV=Ha( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7*W O9R/ tuY= )? C=1;
ip*^eS^ M1=120, % integer for amplitude
Y~#F\ v M3=5000; % integer for length of coupler
^'+#BPo9@ N = 512; % Number of Fourier modes (Time domain sampling points)
DPmY_[OAE dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
#~qza ETv, T =40; % length of time:T*T0.
I1K %n'D dt = T/N; % time step
)! G 10 n = [-N/2:1:N/2-1]'; % Index
WOeLn[ t = n.*dt;
J'WOqAnPZ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
P"@^BQ4 w=2*pi*n./T;
Z}SqiT g1=-i*ww./2;
X_Pbbx_j g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
WZTv g3=-i*ww./2;
G_ ~qk/7mF P1=0;
lKqFuLHwF P2=0;
YZ<5-C P3=1;
x[+bLlb P=0;
~~t >; for m1=1:M1
xnw' &E p=0.032*m1; %input amplitude
{aK3'-7 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
\DD4=XGA s1=s10;
:RBeq,QaO s20=0.*s10; %input in waveguide 2
43rV> W, s30=0.*s10; %input in waveguide 3
I\[z(CHg @ s2=s20;
EW `WFBjj s3=s30;
aJ1{9 5ea p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
KO" +"1 . %energy in waveguide 1
hm<:\(q p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Nm%#rZrN~Q %energy in waveguide 2
+-5YmN' p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
+ k F%>F] %energy in waveguide 3
y T&#k 1 for m3 = 1:1:M3 % Start space evolution
%ca` v;]. s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
LA/Qm/T s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
8"V1h72vcW s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
7lwFxP5QT sca1 = fftshift(fft(s1)); % Take Fourier transform
Jv]$@># sca2 = fftshift(fft(s2));
N6%L4v8-}X sca3 = fftshift(fft(s3));
^L.' At sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
A.$P1zwC sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
%):pfM;b sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
dAM]ZR< s3 = ifft(fftshift(sc3));
sEL0h4 s2 = ifft(fftshift(sc2)); % Return to physical space
'coY`B; 8 s1 = ifft(fftshift(sc1));
Y^ 8'P /A end
"Rtt~["% p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
:j/sTO= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
jL'R4z p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
;U y}( P1=[P1 p1/p10];
'S&Zq: P2=[P2 p2/p10];
:6o|6MC! P3=[P3 p3/p10];
z;N`jqo P=[P p*p];
8 ~Pdr]5 end
6C
?,V3Z figure(1)
(eHTXk*V` plot(P,P1, P,P2, P,P3);
h 1f 05 {yd(n_PqY 转自：
http://blog.163.com/opto_wang/
