计算脉冲在非线性耦合器中演化的Matlab 程序 EWr8=@iU App9um3: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
S<-e/`p=H % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
gbl`_t/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\["'%8[:gR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"IvFkS=*Q 7e`ylnP! %fid=fopen('e21.dat','w');
{dbPMx N = 128; % Number of Fourier modes (Time domain sampling points)
^xpiNP!?a M1 =3000; % Total number of space steps
G(;C~kHX J =100; % Steps between output of space
>=WlrmI T =10; % length of time windows:T*T0
tlz+ !> T0=0.1; % input pulse width
z-Ndv;: MN1=0; % initial value for the space output location
X=W.{? dt = T/N; % time step
v&8%t 7| n = [-N/2:1:N/2-1]'; % Index
5 wT
e? t = n.*dt;
Oh|KbM*vS u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
TsvF~Gdp u20=u10.*0.0; % input to waveguide 2
&2,0?ra2& u1=u10; u2=u20;
HqZ 3] U1 = u1;
;:Yz7<>Y, U2 = u2; % Compute initial condition; save it in U
qkLp8/G>pO ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ISbhC!59 w=2*pi*n./T;
Hl 3%+f g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
I|SQhbi L=4; % length of evoluation to compare with S. Trillo's paper
_UqE
-+& dz=L/M1; % space step, make sure nonlinear<0.05
E76#xsyhF for m1 = 1:1:M1 % Start space evolution
S
6|# 9C& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
IGtpL[. ;/ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_@gd9Fi7J ca1 = fftshift(fft(u1)); % Take Fourier transform
B F,8[|%# ca2 = fftshift(fft(u2));
-%g$~MZ?' c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
DUAI c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
A\1X- Mm u2 = ifft(fftshift(c2)); % Return to physical space
):c)$$dn u1 = ifft(fftshift(c1));
Hkv4 ^| if rem(m1,J) == 0 % Save output every J steps.
/3!c
;( U1 = [U1 u1]; % put solutions in U array
WcG}9)9 U2=[U2 u2];
@ rV|7% u MN1=[MN1 m1];
k|Syw A Tr z1=dz*MN1'; % output location
n;F/}:c_a end
EV$$wrohQ` end
A0@E^bG hg=abs(U1').*abs(U1'); % for data write to excel
4dgo*9 ha=[z1 hg]; % for data write to excel
1c%ee$Q t1=[0 t'];
3om_Z /k hh=[t1' ha']; % for data write to excel file
k\NwH?ppu %dlmwrite('aa',hh,'\t'); % save data in the excel format
u@{z
xYn figure(1)
FD+y?UF waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
y;r{0lTB figure(2)
mk' $ |2O waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
A.%MrgOOX :|V`QM 非线性超快脉冲耦合的数值方法的Matlab程序 t
5{Y' u5 1%~ 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。
d`g)(* 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
3R=R k TJhzyJ"t n$03 ##pf BS@x&DB % This Matlab script file solves the nonlinear Schrodinger equations
{j!jm5 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
YWXY 4*G % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Pcs62aE % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&l0-0 T> Q~y) V C=1;
l[ P VWM M1=120, % integer for amplitude
B'kV.3t M3=5000; % integer for length of coupler
ylo /]pVs N = 512; % Number of Fourier modes (Time domain sampling points)
c2,;t)%@ E dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
K*]^0 T =40; % length of time:T*T0.
\H -,^[G3 dt = T/N; % time step
Ol @ssm n = [-N/2:1:N/2-1]'; % Index
MB:VACCr t = n.*dt;
VOY#Y*)g ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`-J$7)d@ w=2*pi*n./T;
^G*zFqa+` g1=-i*ww./2;
itpljh g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
G8Qo]E9-/ g3=-i*ww./2;
@8 ;0p P1=0;
"+@>!U P2=0;
8e:\T.)M P3=1;
uh8+Y%V
p P=0;
.R<Ke\y/ for m1=1:M1
(0c L!
N;; p=0.032*m1; %input amplitude
=ll{M{0Q]! s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
5Y W.s s1=s10;
|LwW/>I s20=0.*s10; %input in waveguide 2
jb5nL`(j$ s30=0.*s10; %input in waveguide 3
S7A[HG; s2=s20;
sgRD]SF s3=s30;
TSp;Vr OP p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
P_Bhec|#fT %energy in waveguide 1
YcQ3 :i p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
/;K?Y#mf~j %energy in waveguide 2
?u)[xEx6}+ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
2!y %nkO* %energy in waveguide 3
yE80 *C~d for m3 = 1:1:M3 % Start space evolution
>e4w8Svcy s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
eLd7|*| s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
M10u? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
[|NgrU_. sca1 = fftshift(fft(s1)); % Take Fourier transform
cfg_xrW0^ sca2 = fftshift(fft(s2));
\B$Q%\- PX sca3 = fftshift(fft(s3));
-T 5$l sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
j. m(Z} sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
HJh9 <I sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
! 54(K6a[ s3 = ifft(fftshift(sc3));
>d{O1by=d9 s2 = ifft(fftshift(sc2)); % Return to physical space
#G/
_FRo` s1 = ifft(fftshift(sc1));
L+b"d3!G&% end
?d?
cD p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
|iJ+e -_R p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
_s&sA2r< p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
!FhiTh:GCh P1=[P1 p1/p10];
,Z"l3~0\ P2=[P2 p2/p10];
[p%OIqC`pB P3=[P3 p3/p10];
G3.MS7 J P=[P p*p];
ti)4J2c,8 end
T 5jZd@VT, figure(1)
HxgH* IMs plot(P,P1, P,P2, P,P3);
3XeCaq'N -54 转自：
http://blog.163.com/opto_wang/
