计算脉冲在非线性耦合器中演化的Matlab 程序 ;HO= @*( (1(q % This Matlab script file solves the coupled nonlinear Schrodinger equations of
oa p4rHk} % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
)Ql%r?(F+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%>{0yEC % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
x s|FE3:a NC(~l %fid=fopen('e21.dat','w');
aqk!T%fg N = 128; % Number of Fourier modes (Time domain sampling points)
(O 3 nL. M1 =3000; % Total number of space steps
x7[BK_SY J =100; % Steps between output of space
eeB{c.# T =10; % length of time windows:T*T0
tG a8W T0=0.1; % input pulse width
zK@@p+n_#. MN1=0; % initial value for the space output location
3
Za} b| dt = T/N; % time step
h2d (?vOT n = [-N/2:1:N/2-1]'; % Index
o>pJPV t = n.*dt;
ZD{LXJ{Vm u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
$xN|5;+ u20=u10.*0.0; % input to waveguide 2
fE
mr^ R u1=u10; u2=u20;
/k3:']G, s U1 = u1;
wf<M)Rs| U2 = u2; % Compute initial condition; save it in U
.?$gpM?i ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<)D$51 &0 w=2*pi*n./T;
H/M@t\$Dc g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ew4U)2J+ L=4; % length of evoluation to compare with S. Trillo's paper
H4+i.*T # dz=L/M1; % space step, make sure nonlinear<0.05
6=Otq=WH for m1 = 1:1:M1 % Start space evolution
S)@j6(HC4 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
C,4 e"yynb u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
3^yK!-Wp( ca1 = fftshift(fft(u1)); % Take Fourier transform
WH^%:4 ca2 = fftshift(fft(u2));
8Zd]wY O c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
+
{'.7# c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
>^3i|PB u2 = ifft(fftshift(c2)); % Return to physical space
VI *$em O0 u1 = ifft(fftshift(c1));
qIT@g"%}t if rem(m1,J) == 0 % Save output every J steps.
7@W>E;go U1 = [U1 u1]; % put solutions in U array
(#c:b U2=[U2 u2];
vnuN6M{ MN1=[MN1 m1];
EfT=? z1=dz*MN1'; % output location
dSHDWu& end
5Gm_\kd end
1?l1:}^ L hg=abs(U1').*abs(U1'); % for data write to excel
ZbKg~jdF ha=[z1 hg]; % for data write to excel
]7A'7p $Y t1=[0 t'];
\s\?l(ooq" hh=[t1' ha']; % for data write to excel file
;!Fn1|) %dlmwrite('aa',hh,'\t'); % save data in the excel format
5|)W. *Q figure(1)
=Dj#gV waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
4CTi]E=H{ figure(2)
GTHt'[t@; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
=?8@#]G+ ]6j{@z?{ 非线性超快脉冲耦合的数值方法的Matlab程序 w,D+j74e$ Zv {'MIv&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。
1_G^w
qk 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
~wdGd+ez (/$^uWj }x ,S% M- {{!-Gr % This Matlab script file solves the nonlinear Schrodinger equations
:Zlwy -[ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Q/Rqa5LI: % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1xvu<|F % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
uXiN~j &Be |I=T @1_D C=1;
gRzxLf`K M1=120, % integer for amplitude
t6t! t* jO M3=5000; % integer for length of coupler
DHRlWQox N = 512; % Number of Fourier modes (Time domain sampling points)
&7s.` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
l U] nd[x T =40; % length of time:T*T0.
4<v&S2Yq dt = T/N; % time step
x?<FJ"8"k n = [-N/2:1:N/2-1]'; % Index
Vjp y~iP4B t = n.*dt;
|uJ%5y# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
~V6D < w=2*pi*n./T;
"J1
4C9u
g1=-i*ww./2;
1\.pMHv/ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
w32y3~ g3=-i*ww./2;
~VB1OLgv#. P1=0;
1Z&(6cDY8M P2=0;
: rVnc =k P3=1;
\{D"
!e P=0;
, ]D,P for m1=1:M1
QZ8I V> p=0.032*m1; %input amplitude
xyxy` qR A s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
_"{Xi2@H s1=s10;
}-`4D Hgq s20=0.*s10; %input in waveguide 2
E" vS $ s30=0.*s10; %input in waveguide 3
!n%j)`0M s2=s20;
E*lxVua s3=s30;
+cRn%ioVi p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ptaKf4P^r %energy in waveguide 1
R@2X3s: p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
h@BY]80 %energy in waveguide 2
H;"4 C8K7 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
V .2 _i* %energy in waveguide 3
[-x7_=E# for m3 = 1:1:M3 % Start space evolution
w2'5#`m s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
|l!aB(NW s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
P2nu;I_ & s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
tl>7^ hH sca1 = fftshift(fft(s1)); % Take Fourier transform
WY]s |2a sca2 = fftshift(fft(s2));
Ea=P2:3* sca3 = fftshift(fft(s3));
yh=N@Z*zP sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Xnh8e sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
f
*)Z)6E sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
DaV a} s3 = ifft(fftshift(sc3));
K>
e7 pu s2 = ifft(fftshift(sc2)); % Return to physical space
!_(Tq yg& s1 = ifft(fftshift(sc1));
: E?V. end
Z6m)tZVM p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
M3Kfd p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
%|4UsWZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
WF "k[2 P1=[P1 p1/p10];
# fM'>$N P2=[P2 p2/p10];
)`}:8y? P3=[P3 p3/p10];
PI<vxjOK` P=[P p*p];
I}Q2Vu< end
MO]&bHH7; figure(1)
Q@H V- (A plot(P,P1, P,P2, P,P3);
g,Y/M3>( B erwI
7!= 转自：
http://blog.163.com/opto_wang/
