计算脉冲在非线性耦合器中演化的Matlab 程序 4ye`;hXy $@u^Jt, ? % This Matlab script file solves the coupled nonlinear Schrodinger equations of
-aH?7HV } % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
-9H!j4]T? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3'sWlh f; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
QN} 3S0 S\v&{ %fid=fopen('e21.dat','w');
+4:+qGAJ{ N = 128; % Number of Fourier modes (Time domain sampling points)
M[
~2,M&H M1 =3000; % Total number of space steps
6t7;}t]t J =100; % Steps between output of space
B
GEJiLH T =10; % length of time windows:T*T0
)HzITsFZKT T0=0.1; % input pulse width
!aW*dD61 MN1=0; % initial value for the space output location
vY0V{u ?J dt = T/N; % time step
Xg!|F[i n = [-N/2:1:N/2-1]'; % Index
XJxs4a1[t t = n.*dt;
z[lRb]:i[ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
5>1Y= "B u20=u10.*0.0; % input to waveguide 2
:LIKp; u1=u10; u2=u20;
rt@-Pw!B U1 = u1;
y`B!6p
5j U2 = u2; % Compute initial condition; save it in U
"m P*}VF ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
e}Af"LI w=2*pi*n./T;
Pu%>j'A g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
$MJDB L=4; % length of evoluation to compare with S. Trillo's paper
Y3MR:{} dz=L/M1; % space step, make sure nonlinear<0.05
0ZID
@^ for m1 = 1:1:M1 % Start space evolution
2GD mZl u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^d5. /M8Bd u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
5k%N<e` ` ca1 = fftshift(fft(u1)); % Take Fourier transform
xZ @O"*{ ca2 = fftshift(fft(u2));
AXU!-er$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
S~a:1
_Wl c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Etr8lm E u2 = ifft(fftshift(c2)); % Return to physical space
ZvnZ}t >? u1 = ifft(fftshift(c1));
DT(Zv2 if rem(m1,J) == 0 % Save output every J steps.
%*Z2Gef?H U1 = [U1 u1]; % put solutions in U array
Lx:9@3'7' U2=[U2 u2];
-< d MD_ MN1=[MN1 m1];
)V$! z1=dz*MN1'; % output location
N>6yacTB end
2W:?#h3 end
XF f+efh hg=abs(U1').*abs(U1'); % for data write to excel
sO4 }kxZ ha=[z1 hg]; % for data write to excel
norc!?L t1=[0 t'];
Hj4w
i| hh=[t1' ha']; % for data write to excel file
Ye=7Y57Nr %dlmwrite('aa',hh,'\t'); % save data in the excel format
d$pf[DJQo figure(1)
_~S^#ut+ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
!qGx (D{\ figure(2)
W$MEbf%1 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
xc]C# q #&2N,M!Q 非线性超快脉冲耦合的数值方法的Matlab程序 SSsQu^A iJKm27 "> 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
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r Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
K^qUlyv \,bFm,kC? %:;[M|. Hv7D+ j8M % This Matlab script file solves the nonlinear Schrodinger equations
i!}nGJGg
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
gK#fuQ$hH % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ZR q}g: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s)DNLx
B M$tywC C=1;
wZ3 vF)2s M1=120, % integer for amplitude
~CdseSo 9 M3=5000; % integer for length of coupler
6 k=Wt7C N = 512; % Number of Fourier modes (Time domain sampling points)
rIWN!@.J dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
-MW(={# T =40; % length of time:T*T0.
9oxf)pjw dt = T/N; % time step
]-Y]Q%A4 n = [-N/2:1:N/2-1]'; % Index
<QW1fE t = n.*dt;
f}ij=Y9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
RJs G ]` w=2*pi*n./T;
eKFc
W5O g1=-i*ww./2;
:2Rci`lp g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
?O>JtEz~lQ g3=-i*ww./2;
.L{+O6*c P1=0;
|e; z"-3 P2=0;
{f-/,g~ P3=1;
=^AZx)K wd P=0;
YM.IRj2/1 for m1=1:M1
*9{Wn7pck/ p=0.032*m1; %input amplitude
{*Wwu
f. s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
+ :Q/<^Z s1=s10;
5b4V/d*
' s20=0.*s10; %input in waveguide 2
)7 %]<2V% s30=0.*s10; %input in waveguide 3
W]Tt8 s2=s20;
(5DGs_> s3=s30;
qkG;YGio p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
#`)-$vUv^f %energy in waveguide 1
`k%#0E*H p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
7{ 6. %energy in waveguide 2
/ z?7ic0
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
PEn^.v @ %energy in waveguide 3
/(pD^D for m3 = 1:1:M3 % Start space evolution
wp GnS s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
QT l._j@ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
DCzPm/#b s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
! E#.WX sca1 = fftshift(fft(s1)); % Take Fourier transform
svRaU7<UDN sca2 = fftshift(fft(s2));
,u^0V"hJ sca3 = fftshift(fft(s3));
A*U'SCg(G sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
/F}\V
^ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4m(>" dHP sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
\bQ!> l\ s3 = ifft(fftshift(sc3));
G$`4.,g s2 = ifft(fftshift(sc2)); % Return to physical space
JG4*B|3 s1 = ifft(fftshift(sc1));
YYr&r.6 end
GfPz^F=ie. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
(BQ3M- p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
$ $ f$$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
gWH9=%! P1=[P1 p1/p10];
>!F ,y3"5S P2=[P2 p2/p10];
f\r4[gU@ P3=[P3 p3/p10];
3U.qN0] P=[P p*p];
g E+OQWu end
/lQ0`^yB figure(1)
%
j{pz plot(P,P1, P,P2, P,P3);
"?&bh@P& dq/?&X 转自：
http://blog.163.com/opto_wang/
