计算脉冲在非线性耦合器中演化的Matlab 程序 Zb134b' 9Y<#=C % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ph#tgLJ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
N?m0US u* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
yx<WSgWZ[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<6G1 1-K gt7VxZ %fid=fopen('e21.dat','w');
d)"?mD:m/M N = 128; % Number of Fourier modes (Time domain sampling points)
F|HJH"2*&q M1 =3000; % Total number of space steps
4#'(" #R J =100; % Steps between output of space
i]#+1Hf T =10; % length of time windows:T*T0
`WOYoec
T0=0.1; % input pulse width
1<< kA: d MN1=0; % initial value for the space output location
1<h >B: dt = T/N; % time step
>R2SQA o n = [-N/2:1:N/2-1]'; % Index
F5 ]C{ t = n.*dt;
\6 93 kQ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
=SAU4x jo u20=u10.*0.0; % input to waveguide 2
MCP "GZK6W u1=u10; u2=u20;
/2RajsK U1 = u1;
zA;@@)hwR U2 = u2; % Compute initial condition; save it in U
gn{=%`[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\G2B? >E; w=2*pi*n./T;
Go&D[# g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
D>!6,m2 L=4; % length of evoluation to compare with S. Trillo's paper
,\aUq|~ dz=L/M1; % space step, make sure nonlinear<0.05
@Fpb-Qd" for m1 = 1:1:M1 % Start space evolution
: ~ A%# u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
62> zt2= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Zv_jy@k ca1 = fftshift(fft(u1)); % Take Fourier transform
p<v.Q ca2 = fftshift(fft(u2));
~kCwJ<E c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
0liR c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
]O:N-Y u2 = ifft(fftshift(c2)); % Return to physical space
4TwQO$C u1 = ifft(fftshift(c1));
JN FIT;L if rem(m1,J) == 0 % Save output every J steps.
tyDY'W\] U1 = [U1 u1]; % put solutions in U array
iHp\o=# U2=[U2 u2];
nCKbgM' " MN1=[MN1 m1];
aR c ' z1=dz*MN1'; % output location
A`u$A9[ end
T`9-VX;` end
Kwhdu<6 hg=abs(U1').*abs(U1'); % for data write to excel
V
>,Z-&.% ha=[z1 hg]; % for data write to excel
o y <J6 t1=[0 t'];
a0*2) uL} hh=[t1' ha']; % for data write to excel file
SxjC wX"> %dlmwrite('aa',hh,'\t'); % save data in the excel format
~=Ncp9ej# figure(1)
#2tCV't waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
@wq#>bm figure(2)
? /JBt
/b waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
w&BGJYI `E \imL 非线性超快脉冲耦合的数值方法的Matlab程序 %k0EpJE% R1-k3;v^ 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。
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3W 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
I@l >w._. T#O??3/%$1 SLhEc g8'DoHJ* % This Matlab script file solves the nonlinear Schrodinger equations
*wV[TKaN % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
`Vq`z]} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:h:@o h_= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
#~ Q8 M*~@ oH2!5;A| C=1;
M)cGz$Q| M1=120, % integer for amplitude
zx1:`K0bi M3=5000; % integer for length of coupler
y@wF_WX2 N = 512; % Number of Fourier modes (Time domain sampling points)
Iwpbf Z dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
hFvi 5I-b T =40; % length of time:T*T0.
y5 m!*=`l` dt = T/N; % time step
<1&Ke n = [-N/2:1:N/2-1]'; % Index
o7+>G~i t = n.*dt;
j K8'T_Pah ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%q_ M iu@ w=2*pi*n./T;
x:t<ZG&Xwg g1=-i*ww./2;
*T4<& g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
MjaUdfx g3=-i*ww./2;
%McO6.M@ P1=0;
\%,&~4
! P2=0;
Oe1 t\ P3=1;
!5x
Ly6=} P=0;
"D* Wi7 for m1=1:M1
THhy ~wC". p=0.032*m1; %input amplitude
# X.+ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
S:Tm23pe s1=s10;
KIL18$3J s20=0.*s10; %input in waveguide 2
v\ZBv zd s30=0.*s10; %input in waveguide 3
?kt=z4h9( s2=s20;
h e )ulB s3=s30;
S*%iiD) p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
PdY>#Cyh %energy in waveguide 1
.F 0]6#( p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
ykq'g | %energy in waveguide 2
]Qi,j#X p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
c!&Qj %energy in waveguide 3
\Kd7dK9&] for m3 = 1:1:M3 % Start space evolution
9u wL{P& s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
S 2$5!(P s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
nR8 ]@c C s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
1a9w(X sca1 = fftshift(fft(s1)); % Take Fourier transform
za,2r^ sca2 = fftshift(fft(s2));
/~}_h O$S sca3 = fftshift(fft(s3));
{Iy7.c8S sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
~uPk sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Z|^MGyn sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2H&{1f\Bf s3 = ifft(fftshift(sc3));
gw Qvao s2 = ifft(fftshift(sc2)); % Return to physical space
qtSs)n s1 = ifft(fftshift(sc1));
kqB\xlS7k end
+0pW/4x p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
D6!t VdnVe p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
DY> <qk p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
T 2bnzI i P1=[P1 p1/p10];
5_G'68;OV P2=[P2 p2/p10];
a@|.;#FF P3=[P3 p3/p10];
bNvAyKc- P=[P p*p];
xQz #i-v end
Kp_ jy.e7& figure(1)
oofFrAaT plot(P,P1, P,P2, P,P3);
3t IYNM U\s 转自：
http://blog.163.com/opto_wang/
