计算脉冲在非线性耦合器中演化的Matlab 程序 *+ i1m `6Q u?Uu>9@Z % This Matlab script file solves the coupled nonlinear Schrodinger equations of
8mm]>u$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
ro n-v"! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`MLOf % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
o){\ qhLp 6*aU^#Hz6 %fid=fopen('e21.dat','w');
w=QlQ\ N = 128; % Number of Fourier modes (Time domain sampling points)
CyV2=o!F w M1 =3000; % Total number of space steps
X7~^D [ X J =100; % Steps between output of space
XsEo tW T =10; % length of time windows:T*T0
[ yhK4A T0=0.1; % input pulse width
K\trT!I MN1=0; % initial value for the space output location
V+$^ 4Ht dt = T/N; % time step
^\f1zg9I n = [-N/2:1:N/2-1]'; % Index
tH)fu%:p t = n.*dt;
u*S-Pji,x u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
{ aVRvZH4 u20=u10.*0.0; % input to waveguide 2
sU$<v( `" u1=u10; u2=u20;
]3\%i2NM U1 = u1;
si, )!%b U2 = u2; % Compute initial condition; save it in U
KXiStwS ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
KY'x;\0
g w=2*pi*n./T;
;Tec)Fl g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Q$*JkwPQ } L=4; % length of evoluation to compare with S. Trillo's paper
iAr]Ed"9| dz=L/M1; % space step, make sure nonlinear<0.05
)Tl]1^ for m1 = 1:1:M1 % Start space evolution
*'n L[] u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
<~Oy3#{ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
V q[4RAd^P ca1 = fftshift(fft(u1)); % Take Fourier transform
?Q[b1: ;Lm ca2 = fftshift(fft(u2));
t ch;_7? c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
S8,e `F c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Vo;0i$ u2 = ifft(fftshift(c2)); % Return to physical space
v&)G~cz u1 = ifft(fftshift(c1));
3^,p$D<T:, if rem(m1,J) == 0 % Save output every J steps.
[9;[g~;E%m U1 = [U1 u1]; % put solutions in U array
GboZ T68 U2=[U2 u2];
,ll<0Atg MN1=[MN1 m1];
ET[>kn^# z1=dz*MN1'; % output location
xdgbs-a) end
bs_< UE end
)eVn1U2*z. hg=abs(U1').*abs(U1'); % for data write to excel
0<)Ep~! ha=[z1 hg]; % for data write to excel
!DkIM}. t1=[0 t'];
%%T?LRv hh=[t1' ha']; % for data write to excel file
.3CQFbHF %dlmwrite('aa',hh,'\t'); % save data in the excel format
&U_T1-UR2 figure(1)
GO UO waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
O &
1z- figure(2)
~hb; kc3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
. ^wBv
'Y r@ c!M |m@ 非线性超快脉冲耦合的数值方法的Matlab程序 c {3P|O&. cz1 m05E 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
7po;*?Ox Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u)[i'ceQZ: 2<E@f0BVAy %F87"v~ %x8vvcO^t % This Matlab script file solves the nonlinear Schrodinger equations
q\ /xx`L % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
#!C|~= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ge ]Z5E(1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-HvJ&O.V$ K?u:-QX^ C=1;
wA o6:) M1=120, % integer for amplitude
ao"Z%#Jb~ M3=5000; % integer for length of coupler
7|k2~\@q N = 512; % Number of Fourier modes (Time domain sampling points)
bQ-n<Lx dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]Na; b T =40; % length of time:T*T0.
N>w+YFM dt = T/N; % time step
i(4.7{* n = [-N/2:1:N/2-1]'; % Index
XCT3:db t = n.*dt;
r_MP[]f|0 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
63'L58O w=2*pi*n./T;
3uL$+F g1=-i*ww./2;
y]g5S-G g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
U45-R - g3=-i*ww./2;
.M s$)1 P1=0;
@QDUz >_y P2=0;
mr,G H x P3=1;
#n+sbx5~7 P=0;
a1 x].{ for m1=1:M1
2RdpVNx\y p=0.032*m1; %input amplitude
1
J[z ![Tf s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
>:OP+Vc s1=s10;
"?6R"Vk?: s20=0.*s10; %input in waveguide 2
uT
Y G/O s30=0.*s10; %input in waveguide 3
I7C+XUQkQ s2=s20;
|M EJ)LE7 s3=s30;
9t7 e~&R p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
gX(8V*os^ %energy in waveguide 1
-| P7e p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
c^R "g)gr %energy in waveguide 2
212 =+k p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
X*a7`aL %energy in waveguide 3
%;#9lkOXWH for m3 = 1:1:M3 % Start space evolution
N6v*X+4 JH s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
#fF D|q s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
_zLEHEZ- s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
qv`:o
` sca1 = fftshift(fft(s1)); % Take Fourier transform
w$`u_P|@E: sca2 = fftshift(fft(s2));
#2+hu^Q- sca3 = fftshift(fft(s3));
n65fT+; sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
dB Hki*.u sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
HS|x sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
V/ZWyYxjLi s3 = ifft(fftshift(sc3));
9Dyw4'W.N s2 = ifft(fftshift(sc2)); % Return to physical space
R %JEx3)0m s1 = ifft(fftshift(sc1));
mG%cE(j*D end
^.M_1$- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Y5TBWcGU% p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
7N0m7 SC p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
z u1gP/ P1=[P1 p1/p10];
fVq, ? P2=[P2 p2/p10];
Koz0Xy P3=[P3 p3/p10];
! &V,+}>) P=[P p*p];
mN#&NA end
*T{KpiuP figure(1)
|\]pTA$2 plot(P,P1, P,P2, P,P3);
Lya?b 5;9.&f 转自：
http://blog.163.com/opto_wang/
