计算脉冲在非线性耦合器中演化的Matlab 程序 KPa&P:R3 `_M&zN % This Matlab script file solves the coupled nonlinear Schrodinger equations of
N'8}5Kx5 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
hle@= e/n % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Ce PI{`&, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]$A6krfh| z4(Q.0x7 %fid=fopen('e21.dat','w');
lUHpGr|U% N = 128; % Number of Fourier modes (Time domain sampling points)
1@ Rl^e y M1 =3000; % Total number of space steps
!^w}Sp J =100; % Steps between output of space
It8@Cp.dU T =10; % length of time windows:T*T0
AHTQF#U^ T0=0.1; % input pulse width
/^Zgv -n MN1=0; % initial value for the space output location
\05 n$. dt = T/N; % time step
9K#U<Q0b' n = [-N/2:1:N/2-1]'; % Index
vrXNa8,L t = n.*dt;
lLuAg ds` u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
C-VkXk u20=u10.*0.0; % input to waveguide 2
`wLMJ,@f. u1=u10; u2=u20;
5~xv"S(E} U1 = u1;
E XQ 3(:& U2 = u2; % Compute initial condition; save it in U
FdmoR; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
S{)'1J_ 0 w=2*pi*n./T;
8MCSU'uQ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
W
sDFui L=4; % length of evoluation to compare with S. Trillo's paper
9 X87" dz=L/M1; % space step, make sure nonlinear<0.05
qF4pTQf for m1 = 1:1:M1 % Start space evolution
6s&%~6J, u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
ziD+% - u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Rm=[Sj84 ca1 = fftshift(fft(u1)); % Take Fourier transform
1&JB@F9! ca2 = fftshift(fft(u2));
qISzn04 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
`xu/|})KI c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Ec|5'Kz] u2 = ifft(fftshift(c2)); % Return to physical space
__,}/|K2 u1 = ifft(fftshift(c1));
+FtL_7[v if rem(m1,J) == 0 % Save output every J steps.
qvN 5[rb U1 = [U1 u1]; % put solutions in U array
!8OUH6{2 U2=[U2 u2];
SR&'38UCe MN1=[MN1 m1];
4(}V$#^+ z1=dz*MN1'; % output location
u[1'Ap end
0D_{LBO6LU end
v/}h y$7 hg=abs(U1').*abs(U1'); % for data write to excel
h%(0| ha=[z1 hg]; % for data write to excel
jxA*Gg3cT5 t1=[0 t'];
N^By#Z hh=[t1' ha']; % for data write to excel file
>tVD[wVF0 %dlmwrite('aa',hh,'\t'); % save data in the excel format
vhu5w#]u* figure(1)
Ke,$3Yx waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Lw #vHNf6 figure(2)
Km ,:7#aV waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
/km'#f)/ }TAHVcX*p 非线性超快脉冲耦合的数值方法的Matlab程序 X4:SH> U! 73'.TReK 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
wU bLw Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[[9XqD] dFVm18 @;H1s4OZ ys$X!Ep % This Matlab script file solves the nonlinear Schrodinger equations
+UC - % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
! JVpR]lWS % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
lhhp6-r % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@mrGG F '9#h^. C=1;
z2.Z xL"* M1=120, % integer for amplitude
%.;` 0}b M3=5000; % integer for length of coupler
G/5 ]0]SO N = 512; % Number of Fourier modes (Time domain sampling points)
4GTB82V$ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
YkbZ 2J* - T =40; % length of time:T*T0.
[P?.( * dt = T/N; % time step
qT+:oMrTSm n = [-N/2:1:N/2-1]'; % Index
Um\_G@ t = n.*dt;
ImVHX~ qHJ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ia}V8 i w=2*pi*n./T;
$+.!(Js"K g1=-i*ww./2;
|Y\BI^ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
I4"U/iL51 g3=-i*ww./2;
J`4{O:{4 P1=0;
b".e6zev P2=0;
X[ up$< P3=1;
`j yBF P=0;
rq>Om MQ67 for m1=1:M1
*ioVLt,:R p=0.032*m1; %input amplitude
-v7O*xm" s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
}c~o3t(7`b s1=s10;
v&i,}p^M5 s20=0.*s10; %input in waveguide 2
4Sxt<7[f s30=0.*s10; %input in waveguide 3
5Myp#!|x : s2=s20;
51lN,VVD s3=s30;
)w 3HC($g p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
%;{R o)03 %energy in waveguide 1
5U+a{oA p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
t&99ZdE %energy in waveguide 2
!Cv:,q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
96$qH{]Ap %energy in waveguide 3
p&~= rp`E for m3 = 1:1:M3 % Start space evolution
YKT =0 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
ai,Nx:r
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
M}
{'kK s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
l
/\n7: sca1 = fftshift(fft(s1)); % Take Fourier transform
4]$$ar) sca2 = fftshift(fft(s2));
8
k%!1dyMB sca3 = fftshift(fft(s3));
9s}y*Vp sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
1-M\K^F sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
& 0*=F%Fd sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
u4UQMj|q s3 = ifft(fftshift(sc3));
{a `#O9 s2 = ifft(fftshift(sc2)); % Return to physical space
S=bdue s1 = ifft(fftshift(sc1));
) HN,A z" end
{KO +t7'Q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
') -Rv]xe p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~Uz1()ftz p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
t$W~X~// P1=[P1 p1/p10];
C_JDQByfL P2=[P2 p2/p10];
*?GV(/Q P3=[P3 p3/p10];
$WV N4fg P=[P p*p];
fq2t^c|$ end
L~])?d figure(1)
e:&(y){n( plot(P,P1, P,P2, P,P3);
pl{Pur ;i 7u9!:}Tu 转自：
http://blog.163.com/opto_wang/
