计算脉冲在非线性耦合器中演化的Matlab 程序 7 Caap/L: 7R`ZTfD % This Matlab script file solves the coupled nonlinear Schrodinger equations of
au}0PnA; % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
E,?aBRxy % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;< )-*?m9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Gt%? [ tlxjs]{0E %fid=fopen('e21.dat','w');
8RT0&[ N = 128; % Number of Fourier modes (Time domain sampling points)
OsSiBb,W79 M1 =3000; % Total number of space steps
waq_ d. J =100; % Steps between output of space
x 3co? T =10; % length of time windows:T*T0
%>:)4A T0=0.1; % input pulse width
2uR4~XjF MN1=0; % initial value for the space output location
)xy{[ K|M( dt = T/N; % time step
y?4=u,{C n = [-N/2:1:N/2-1]'; % Index
<W|{)U?p t = n.*dt;
F4{. 7BT u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
J3S byI!T u20=u10.*0.0; % input to waveguide 2
@ DKl<F u1=u10; u2=u20;
ph'SS=!. U1 = u1;
k.R/ X U2 = u2; % Compute initial condition; save it in U
MJR\ g3 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"&o@%){] w=2*pi*n./T;
5<8>G?Y g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1ZW'PXUZ L=4; % length of evoluation to compare with S. Trillo's paper
C baAnm1 dz=L/M1; % space step, make sure nonlinear<0.05
^
J@i7 FOb for m1 = 1:1:M1 % Start space evolution
90696v. u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
"1 TM u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
I :)#U[tn0 ca1 = fftshift(fft(u1)); % Take Fourier transform
<; Z~ vZ] ca2 = fftshift(fft(u2));
` Z V'7| c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
L#MxB|fcr c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
g#nsA(_L u2 = ifft(fftshift(c2)); % Return to physical space
q$*_C kT u1 = ifft(fftshift(c1));
3'uES4 +r if rem(m1,J) == 0 % Save output every J steps.
{YLJKu!M U1 = [U1 u1]; % put solutions in U array
SL 5DWZ U2=[U2 u2];
KEB>}_[ MN1=[MN1 m1];
{$=%5 z1=dz*MN1'; % output location
uXa}<=O end
T $]L 5 end
eb woMG,B- hg=abs(U1').*abs(U1'); % for data write to excel
! r\ktX ha=[z1 hg]; % for data write to excel
APm[)vw#f t1=[0 t'];
J3E: r_+ hh=[t1' ha']; % for data write to excel file
` ,=p\g|D %dlmwrite('aa',hh,'\t'); % save data in the excel format
l zkn B figure(1)
Mo
r-$a8 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
j?ubh{Izm figure(2)
Ek p
0.c8: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
> (J!8*7 f3|=T8"t 非线性超快脉冲耦合的数值方法的Matlab程序 {%}6 d~Bg I 9&<:` 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。
!H .lVA 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
;] o^u.PC \:28z td$Jx}'A NT:>.~ah@& % This Matlab script file solves the nonlinear Schrodinger equations
ozwqK oE % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
.b)(_* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5WG@ ;K% % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0t yU%z{RV d u )G)~ C=1;
QNBzc {XB M1=120, % integer for amplitude
0$uS)J\;K M3=5000; % integer for length of coupler
O/@ [VPf N = 512; % Number of Fourier modes (Time domain sampling points)
@3D%i#2o&[ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
.v8=zi:7Y T =40; % length of time:T*T0.
v 65r@)\` dt = T/N; % time step
l8l i@K n = [-N/2:1:N/2-1]'; % Index
~<R~ Q:T t = n.*dt;
5<
nK.i, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
5n#&Hjb*F0 w=2*pi*n./T;
8\_,Y
ji g1=-i*ww./2;
"FD~XSRL g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
{(Z1JoSl g3=-i*ww./2;
KwyXM9h6= P1=0;
NE nP3A P2=0;
AIo;\35 P3=1;
3P>@ : P=0;
{$.{VE+v5 for m1=1:M1
m8` A~ p=0.032*m1; %input amplitude
0$
EJ4 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
94/}@<d-= s1=s10;
?!vW&KJZx s20=0.*s10; %input in waveguide 2
XRin~wz|S s30=0.*s10; %input in waveguide 3
HX[#tT |m~ s2=s20;
?RyvM_(N6 s3=s30;
Vt>E\{@[t p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
VW/1[?HG5 %energy in waveguide 1
93,ExgFt p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
CiF bk&-g %energy in waveguide 2
JJO"\^,;~ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
A O]e^Q %energy in waveguide 3
5lbh
"m= for m3 = 1:1:M3 % Start space evolution
zE{zX@ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
KcE=m\ h s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
<9vkiEo s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
'ZZ/:MvQa sca1 = fftshift(fft(s1)); % Take Fourier transform
PV Q%y sca2 = fftshift(fft(s2));
W3kilhZ sca3 = fftshift(fft(s3));
8'62[e|=7[ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
ujBADDwOg) sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
iBt5aUt sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
R/7l2 * s3 = ifft(fftshift(sc3));
co|0s+%PBq s2 = ifft(fftshift(sc2)); % Return to physical space
*QJ /DC$ s1 = ifft(fftshift(sc1));
)L Ul? end
&aU+6'+QXB p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
v%w]Q B p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
,'}ZcN2) p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9EW 7,m{A P1=[P1 p1/p10];
9`{cX P2=[P2 p2/p10];
CJ >=odK[ P3=[P3 p3/p10];
G})mw P=[P p*p];
UgJHS l end
t!$/r]XM h figure(1)
ah.Kb(d: plot(P,P1, P,P2, P,P3);
J/ ~]A1fP6 BH1To&ol 转自：
http://blog.163.com/opto_wang/
