计算脉冲在非线性耦合器中演化的Matlab 程序 !`Le`c P> |Ef~j % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Sq<3Rw % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_'&k#Q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0Qt~K#mr/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
y`({ .L TWtC-w I; %fid=fopen('e21.dat','w');
D_Guc8* N = 128; % Number of Fourier modes (Time domain sampling points)
#o~[ 1K+Yq M1 =3000; % Total number of space steps
h: _NA J =100; % Steps between output of space
Mg+4huT T =10; % length of time windows:T*T0
u9BjgK(M T0=0.1; % input pulse width
;>5, MN1=0; % initial value for the space output location
lel Mt= dt = T/N; % time step
c+H)ed> n = [-N/2:1:N/2-1]'; % Index
1}`2\3, t = n.*dt;
ssPI$IRg! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
H)\4=^ u20=u10.*0.0; % input to waveguide 2
s88y{o u1=u10; u2=u20;
s_TD4~
$ U1 = u1;
NfOp=X?Y U2 = u2; % Compute initial condition; save it in U
)]3L/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ve6x / PD w=2*pi*n./T;
E3bwy K!s g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
]uAS+ shQ& L=4; % length of evoluation to compare with S. Trillo's paper
<;aJ#qT dz=L/M1; % space step, make sure nonlinear<0.05
)}q uw"H for m1 = 1:1:M1 % Start space evolution
#sS9vv7i u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
6vF/e#}, u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
v O PMgEI ca1 = fftshift(fft(u1)); % Take Fourier transform
n? }5 ! ca2 = fftshift(fft(u2));
eJW[ ] ! c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
*l:&f_ngV c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Fk aXA.JE u2 = ifft(fftshift(c2)); % Return to physical space
UP?D@ogl< u1 = ifft(fftshift(c1));
tR5tPPw if rem(m1,J) == 0 % Save output every J steps.
6 A.P6DW U1 = [U1 u1]; % put solutions in U array
>r=6A
U2=[U2 u2];
J+lGh9G MN1=[MN1 m1];
z$66\/V'] z1=dz*MN1'; % output location
T30Zk *V end
^g[J*{+!W end
svqvG7 hg=abs(U1').*abs(U1'); % for data write to excel
Nkx0CG* ha=[z1 hg]; % for data write to excel
i0iez9B
t1=[0 t'];
I.-v?1>, hh=[t1' ha']; % for data write to excel file
v[sm QO %dlmwrite('aa',hh,'\t'); % save data in the excel format
Ajg\aof0{ figure(1)
<$Z tik1 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
(2d3 jQN` figure(2)
1g~y]iQ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
#>XeR>T <>n9'i1 非线性超快脉冲耦合的数值方法的Matlab程序 <&6u]uKrW v iJJ
e'\2 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。
BW>5?0E[4( 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
9{$8\E9*nd Hg aZbb>' /,LfA2^_j{ ;$z7[+M % This Matlab script file solves the nonlinear Schrodinger equations
l0:5q?g % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
x^X$M$o,l % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Hsgy'X%om % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3(C :X1 (![t_r0 C=1;
bs
BZ E M1=120, % integer for amplitude
bQ"N
;d)e M3=5000; % integer for length of coupler
K?[) E3 N = 512; % Number of Fourier modes (Time domain sampling points)
6{8/P'@/Zz dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
-p] >Be+^x T =40; % length of time:T*T0.
%<AS?Ry dt = T/N; % time step
hF.6}28U1 n = [-N/2:1:N/2-1]'; % Index
r ^ Y~mq t = n.*dt;
$o"g73`3 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
JtFiFa CxY w=2*pi*n./T;
nP OO3!<{ g1=-i*ww./2;
+aj^Cs1$ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
rFfy#e g3=-i*ww./2;
0E1=W 6UZ P1=0;
Z}+ yI, P2=0;
[Y$V\h=V P3=1;
Z(`r -}f I P=0;
@/ k x
er for m1=1:M1
f1J %]g! p=0.032*m1; %input amplitude
_Z.cMYN s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
;iQp7aW{$ s1=s10;
GG+5/hU s20=0.*s10; %input in waveguide 2
Z\' wm' s30=0.*s10; %input in waveguide 3
{>h97}P s2=s20;
}PZ= `w*O s3=s30;
'W(xgOP1 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
!UcOl0"6 %energy in waveguide 1
Hd374U<8]T p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
rREzM)GA %energy in waveguide 2
<sc\EK p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
nP ;;MX:B %energy in waveguide 3
-X8eabb for m3 = 1:1:M3 % Start space evolution
LipxAE?O s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
s1 =+:: s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
`kPc!I7Y s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
\K }aQKB/j sca1 = fftshift(fft(s1)); % Take Fourier transform
SOj`Y|6^: sca2 = fftshift(fft(s2));
Wcn[gn< sca3 = fftshift(fft(s3));
3S ;N(A4 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
:".w{0l@ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
+Vy_9I(4Z sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
:XYy7x z< s3 = ifft(fftshift(sc3));
1eD.:_t4 s2 = ifft(fftshift(sc2)); % Return to physical space
/PW&$P1.]" s1 = ifft(fftshift(sc1));
S =PJhAF end
6c & Y p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
:Eo8v$W\RB p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
V7@
{ D p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
R04J3D| P1=[P1 p1/p10];
/WYh[XKe P2=[P2 p2/p10];
Q;wB{vr$ P3=[P3 p3/p10];
!+KhFC&Py P=[P p*p];
f'_M 0x end
anC+r(jjg9 figure(1)
Dft%ip2 plot(P,P1, P,P2, P,P3);
;RHNRVP !.-.#<<_a 转自：
http://blog.163.com/opto_wang/
