计算脉冲在非线性耦合器中演化的Matlab 程序 )r?}P1J7 [85spub&} % This Matlab script file solves the coupled nonlinear Schrodinger equations of
O/(`S<iip % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
q9K)Xk$LF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Wis ~$" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
net@j#}j- a.\:T,cP> %fid=fopen('e21.dat','w');
G_8R K,H. N = 128; % Number of Fourier modes (Time domain sampling points)
< NY^M! M1 =3000; % Total number of space steps
!*&V - 4 J =100; % Steps between output of space
SHxNr(wJ<Q T =10; % length of time windows:T*T0
Lg+Ac5 y}` T0=0.1; % input pulse width
1-uxC^u?|# MN1=0; % initial value for the space output location
pU}(@oy dt = T/N; % time step
7F7 {)L n = [-N/2:1:N/2-1]'; % Index
s c,Hq\$& t = n.*dt;
i uW[`ou X u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Rok7n1gW u20=u10.*0.0; % input to waveguide 2
U}[d_f u1=u10; u2=u20;
?3,:-"(@p U1 = u1;
| j`@eF/" U2 = u2; % Compute initial condition; save it in U
HWrO"b*tO ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ZU4nc 3__ w=2*pi*n./T;
YlQ=5u^+ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
{4}yKjW%z L=4; % length of evoluation to compare with S. Trillo's paper
/Iy]DU8 dz=L/M1; % space step, make sure nonlinear<0.05
IMFDM."s for m1 = 1:1:M1 % Start space evolution
bo>*fNqAIy u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
65P0,b6"OT u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
DJ k /{Z: ca1 = fftshift(fft(u1)); % Take Fourier transform
~H_/zK 6e ca2 = fftshift(fft(u2));
2WL|wwA c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
)9G[dDeC c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
%N6A+ 5H u2 = ifft(fftshift(c2)); % Return to physical space
k Z
.gO u1 = ifft(fftshift(c1));
l/ GGC nO/ if rem(m1,J) == 0 % Save output every J steps.
, kGc]{'W U1 = [U1 u1]; % put solutions in U array
jD]~ AwRJ U2=[U2 u2];
E0=)HTtS MN1=[MN1 m1];
<?6|.\ & z1=dz*MN1'; % output location
wu!59pL end
iN\4gQ! end
34O
`@j0-3 hg=abs(U1').*abs(U1'); % for data write to excel
6 7.+
.2 ha=[z1 hg]; % for data write to excel
8 +/rlHp t1=[0 t'];
x,+{9 hh=[t1' ha']; % for data write to excel file
~ "H,/m%2o %dlmwrite('aa',hh,'\t'); % save data in the excel format
_ QI\ figure(1)
BLdvyVFx waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
l"T44CL; figure(2)
'RR~7h waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
(O?.)jEW(. W ]1)zO 非线性超快脉冲耦合的数值方法的Matlab程序 . B9iLI Jb@V}Ul$ 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。
X*XZb F"= 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
.Wj;% | Q#X8u-~ o Q 2Fj j NjScc%@y % This Matlab script file solves the nonlinear Schrodinger equations
,/%=su x % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
+b<FO+E_ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;>yxNGV` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
gIa+5\qYY HxV=F66"
C=1;
=E 4LRKn M1=120, % integer for amplitude
g" DG]/ev M3=5000; % integer for length of coupler
a=9:[ N = 512; % Number of Fourier modes (Time domain sampling points)
ay
;S4c/_ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
gMmaK0uhS T =40; % length of time:T*T0.
!4R WYMV " dt = T/N; % time step
SI-q C n = [-N/2:1:N/2-1]'; % Index
5h-SCB>P t = n.*dt;
m bxZL<ua ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ci.+pF w=2*pi*n./T;
z uad~%D<I g1=-i*ww./2;
9G#n 0&wRJ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ColV8oVnU g3=-i*ww./2;
4y?n
[/M/ P1=0;
b9J_1Gl] P2=0;
1>_8d"<Gd P3=1;
,{u
yG: P=0;
Oi'5ytsES for m1=1:M1
y<|7z9 9L p=0.032*m1; %input amplitude
3vN_p$ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
VU(v3^1" s1=s10;
}<v@0 1 s20=0.*s10; %input in waveguide 2
Ys!8 2M$g s30=0.*s10; %input in waveguide 3
uM IIYS s2=s20;
eK?MKe s3=s30;
(Aao Ca [ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
EzM
?Nft %energy in waveguide 1
uK"=i8rs4 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
v \gLWq' %energy in waveguide 2
l'-Bu( p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
{ OkV %Q< %energy in waveguide 3
*xxx:*6rk; for m3 = 1:1:M3 % Start space evolution
Q:G4Z9Kt s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
k W Ml s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|&+ o^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
D rUO- sca1 = fftshift(fft(s1)); % Take Fourier transform
&tLgG4pd sca2 = fftshift(fft(s2));
d9f C<Tp sca3 = fftshift(fft(s3));
y| i,| sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
{ M4gF8(M sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
mP~QWx![N sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
JxdDC^> 0 s3 = ifft(fftshift(sc3));
~S"+S/z/k s2 = ifft(fftshift(sc2)); % Return to physical space
#4Rx]zW^% s1 = ifft(fftshift(sc1));
BDW^7[n end
X;
\+<LE p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
y1eW pPJa p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
r[`9uVT/ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
)hn6sXo+ P1=[P1 p1/p10];
*e Tq VG. P2=[P2 p2/p10];
D09Sg%w P3=[P3 p3/p10];
~ ?Qe? hB P=[P p*p];
jjB~ G^n end
OhQgF figure(1)
n`?aC|P2s plot(P,P1, P,P2, P,P3);
gZ3u=uME ah4N|zJ>v 转自：
http://blog.163.com/opto_wang/
