计算脉冲在非线性耦合器中演化的Matlab 程序
t'Eb#Nup3 +rsl(
08FY % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Bhu@ 2KdA % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
^0~c 7`k`V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>bA$SN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Yn4)Zhk k aM{@1m Bm %fid=fopen('e21.dat','w');
UV']NH h N = 128; % Number of Fourier modes (Time domain sampling points)
FL`1yD^2 M1 =3000; % Total number of space steps
w3<"g&n| J =100; % Steps between output of space
:'y{dbKp" T =10; % length of time windows:T*T0
dv'E:R(a T0=0.1; % input pulse width
s[3![
"^Y MN1=0; % initial value for the space output location
J1tzHa6 dt = T/N; % time step
m0|Ae@g~3 n = [-N/2:1:N/2-1]'; % Index
n{64g+ t = n.*dt;
au~] u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
9 ^PRX u20=u10.*0.0; % input to waveguide 2
*M w fod u1=u10; u2=u20;
)WVItqQKV U1 = u1;
\5Vp6^ U2 = u2; % Compute initial condition; save it in U
BbrT f"` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
fW.GNX8 w=2*pi*n./T;
_{e&@ d g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
% j *k L=4; % length of evoluation to compare with S. Trillo's paper
(_w
% dz=L/M1; % space step, make sure nonlinear<0.05
_Z+jQFKJ\8 for m1 = 1:1:M1 % Start space evolution
`6Ureui2? u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,u}<Ws8N u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
S5~`T7Ra ca1 = fftshift(fft(u1)); % Take Fourier transform
L\b]k,Ks f ca2 = fftshift(fft(u2));
X`yNR; > c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~$4]HDg c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
G la@l< u2 = ifft(fftshift(c2)); % Return to physical space
Z|ZBKcmg u1 = ifft(fftshift(c1));
<i}q=%W!1 if rem(m1,J) == 0 % Save output every J steps.
d"H<e}D U1 = [U1 u1]; % put solutions in U array
{)B9Z
I{+A U2=[U2 u2];
ORowx,(hX MN1=[MN1 m1];
sDLS*467 z1=dz*MN1'; % output location
_0,"vFdj end
.pZ o(* end
~`t%M?l hg=abs(U1').*abs(U1'); % for data write to excel
?R;nL{ ha=[z1 hg]; % for data write to excel
>ik1]!j]Lv t1=[0 t'];
ybZ} hh=[t1' ha']; % for data write to excel file
i8Fs0U4" %dlmwrite('aa',hh,'\t'); % save data in the excel format
I*D<J$ 9N figure(1)
XzT78 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
k)`$%[K8 figure(2)
~ J0,)_b%* waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
n{dP@_>WS .zvlRt.zl 非线性超快脉冲耦合的数值方法的Matlab程序 W|ReLM\ aS,a_b] 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。
+0]'| t F> 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
2m_'z : T_'n, 8 +"10q- *( k%MTG % This Matlab script file solves the nonlinear Schrodinger equations
~|&="K4,: % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
yeh8z:5Z O % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
'pan9PW
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1g1? zk8zO bxAsV/j C=1;
hUV k54~l M1=120, % integer for amplitude
@l'G[jN5 M3=5000; % integer for length of coupler
E;6~R M: N = 512; % Number of Fourier modes (Time domain sampling points)
H(G!t`K dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Mx8Gu^FW.d T =40; % length of time:T*T0.
n O~b=qO dt = T/N; % time step
%X;7--S%?g n = [-N/2:1:N/2-1]'; % Index
|/VL35b t = n.*dt;
75 ZH ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9# uIC7M w=2*pi*n./T;
=HVfJ"vK g1=-i*ww./2;
2B-.}OJ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
*B1 x`=
g3=-i*ww./2;
-'6< P1=0;
7Rnm%8?T P2=0;
:
(gZgMT P3=1;
! .AhzU1%Y P=0;
GuT6K}~|D for m1=1:M1
LfEvc2
v=g p=0.032*m1; %input amplitude
czI{qi5N s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
)!e3.C|V1W s1=s10;
Go 1 (@ s20=0.*s10; %input in waveguide 2
tQrS3Hz'nA s30=0.*s10; %input in waveguide 3
Z==!C= SBv s2=s20;
Hle\ON s3=s30;
&y7 0 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
.d~\Ysve %energy in waveguide 1
8lwFAiC8 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
CM9 XPr %energy in waveguide 2
/HkFlfPd p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
' WQdr( %energy in waveguide 3
PL@~Ys0 for m3 = 1:1:M3 % Start space evolution
(? \?it- s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
?q _^Rj$ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
}X]\VSF{ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
j$Nf%V 6Y sca1 = fftshift(fft(s1)); % Take Fourier transform
mQ}Gh_'ps sca2 = fftshift(fft(s2));
H?tUC bw sca3 = fftshift(fft(s3));
1AF%-<`?s sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
;1 |x sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
O|I+], sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Sh&iQ_vq
s3 = ifft(fftshift(sc3));
y7z( &M@ s2 = ifft(fftshift(sc2)); % Return to physical space
rVH6 QQF=\ s1 = ifft(fftshift(sc1));
2ev*CX6. end
'. ( ~ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
T~Ly^|Ihz p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
J!hFN]M<< p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
EyY],W1 Y P1=[P1 p1/p10];
X 4wH/q^ P2=[P2 p2/p10];
=A @>I0(7 P3=[P3 p3/p10];
vT c7an6fy P=[P p*p];
; F5"}x end
s\gp5MT figure(1)
R4{-Qv#8
q plot(P,P1, P,P2, P,P3);
:"QfF@Z{ E9+ HS 转自：
http://blog.163.com/opto_wang/
