计算脉冲在非线性耦合器中演化的Matlab 程序 [2\`Wh:%P B!tt e ) % This Matlab script file solves the coupled nonlinear Schrodinger equations of
vY;Lc % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
!m(6/*PAl % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0N
T3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
r*p%e\ 3 3:;%@4f %fid=fopen('e21.dat','w');
gSe{ S N = 128; % Number of Fourier modes (Time domain sampling points)
l%w7N9 M1 =3000; % Total number of space steps
F 1zc4l6 J =100; % Steps between output of space
c//W# V2Q T =10; % length of time windows:T*T0
8c/Ii"1 T0=0.1; % input pulse width
8v6rS-iHP MN1=0; % initial value for the space output location
57M oO dt = T/N; % time step
!< X_XA n = [-N/2:1:N/2-1]'; % Index
|y=gp t = n.*dt;
G/ ^|oJ/G u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
x4( fW\ u20=u10.*0.0; % input to waveguide 2
&1u ?W%(Px u1=u10; u2=u20;
9=}/ t9k U1 = u1;
=H?N b:s U2 = u2; % Compute initial condition; save it in U
qnm9L w# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G7=8*@q>: w=2*pi*n./T;
%4-pw|': g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'Qfy+_0 L=4; % length of evoluation to compare with S. Trillo's paper
v4 .V%tg! dz=L/M1; % space step, make sure nonlinear<0.05
p-6.:y for m1 = 1:1:M1 % Start space evolution
HZ}'W<N u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
u A,{C%? u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
He*L"VpWv ca1 = fftshift(fft(u1)); % Take Fourier transform
u J y@ ca2 = fftshift(fft(u2));
p}!pT/KmpH c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
?-Z:N`YP c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
[}Iq-sz;0 u2 = ifft(fftshift(c2)); % Return to physical space
|V7a26h u1 = ifft(fftshift(c1));
~VGK#'X: if rem(m1,J) == 0 % Save output every J steps.
sI'HS+~pU U1 = [U1 u1]; % put solutions in U array
puyL(ohem U2=[U2 u2];
lyeoSd1AN MN1=[MN1 m1];
K;ML' z1=dz*MN1'; % output location
lpM{@ JC end
_t [%@G>P end
)K6{_~Kc\ hg=abs(U1').*abs(U1'); % for data write to excel
yLX#:
nm ha=[z1 hg]; % for data write to excel
!58JK f t1=[0 t'];
!{XO#e hh=[t1' ha']; % for data write to excel file
-XyuA:pxx %dlmwrite('aa',hh,'\t'); % save data in the excel format
N{yZk"fq:6 figure(1)
$ g^;*>yr waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ou-;k
} figure(2)
}.vy|^ X waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ZM .g +-9 K \ ]r 非线性超快脉冲耦合的数值方法的Matlab程序 Z}C%%2Iz 2fk 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。
f*~fslY,o 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
*X-$*
~J0 u"T^DrRlQ X9j+$X \j DIAP2LR ? % This Matlab script file solves the nonlinear Schrodinger equations
/0uinx % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
[)pT{QA % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
yB1>83!q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8gxLL59 *2 MTx C=1;
A&'%ou M1=120, % integer for amplitude
dp70sA!JF M3=5000; % integer for length of coupler
PsnU5f)` N = 512; % Number of Fourier modes (Time domain sampling points)
2cl~Va= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
tK
H!xit T =40; % length of time:T*T0.
M[{:o/]< dt = T/N; % time step
J5T#}!f n = [-N/2:1:N/2-1]'; % Index
aB) DX t = n.*dt;
A{%;Hd`0/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
>>D i w=2*pi*n./T;
Fm':sd)'X g1=-i*ww./2;
(c2\:hvy g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
^'4uTbxP_! g3=-i*ww./2;
{[?|RC;\Y P1=0;
;gnr\C*G P2=0;
LH;G : P3=1;
(^9M9+L[i P=0;
4 vS!99v) for m1=1:M1
&L]*]Xz; p=0.032*m1; %input amplitude
`.g8JC\_m s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
tV9 C33 s1=s10;
Z B &Uhi s20=0.*s10; %input in waveguide 2
| hM) e*" s30=0.*s10; %input in waveguide 3
KOx#L Gz s2=s20;
BkfBFUDQ s3=s30;
f4_G[?9, p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
gj^]}6-P %energy in waveguide 1
E;H(jVZ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
|lwN!KVQ, %energy in waveguide 2
>}*jsqaVU p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
OvG0U XRU %energy in waveguide 3
% U7f9 for m3 = 1:1:M3 % Start space evolution
s=
fKAxH s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
/ nF w s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
A5ID I<a s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
L? +|%[ sca1 = fftshift(fft(s1)); % Take Fourier transform
VBJ]d| sca2 = fftshift(fft(s2));
vq7%SE kES sca3 = fftshift(fft(s3));
CD[=z)<z{ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#.YcIR) sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
qL.Y_,[[ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
^)l@7XxD s3 = ifft(fftshift(sc3));
T+h{Aeg s2 = ifft(fftshift(sc2)); % Return to physical space
zEfD{I s1 = ifft(fftshift(sc1));
~|C1$.- end
pw yl,A p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
.G~5F- 8' p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@I6 A9do p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
p|V1G h< P1=[P1 p1/p10];
{OrE1 WHB P2=[P2 p2/p10];
c[lob{, P3=[P3 p3/p10];
em !R9J. P=[P p*p];
Sr 4 7u{n end
bnu0*Zg> figure(1)
}zxh:"# K plot(P,P1, P,P2, P,P3);
{; cB?II &"%|`gE 转自：
http://blog.163.com/opto_wang/
