计算脉冲在非线性耦合器中演化的Matlab 程序 N \Wd 0b =^D{ZZw{ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
$ix*xm. 4m % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
`ek On@T0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;x~[om21; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
l0g`;BI_ /{7we$+,p %fid=fopen('e21.dat','w');
y | 0I3n]e N = 128; % Number of Fourier modes (Time domain sampling points)
8~s-@3J M1 =3000; % Total number of space steps
@[] A&)B J =100; % Steps between output of space
PdNxuy T =10; % length of time windows:T*T0
f8X /kz T0=0.1; % input pulse width
M~ ^ {S[o MN1=0; % initial value for the space output location
Z d]2>h dt = T/N; % time step
eV x
&S a n = [-N/2:1:N/2-1]'; % Index
4t;m^Iv t = n.*dt;
J&jNONu? u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
!YJ^BI u20=u10.*0.0; % input to waveguide 2
G*$a81dAX u1=u10; u2=u20;
!&=%#i U1 = u1;
0Fi&7% U2 = u2; % Compute initial condition; save it in U
( O>oN~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
H%:u9DlEK/ w=2*pi*n./T;
&ivPY g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
fX 41o # L=4; % length of evoluation to compare with S. Trillo's paper
FeM,$&G: dz=L/M1; % space step, make sure nonlinear<0.05
05>xQx?"m4 for m1 = 1:1:M1 % Start space evolution
^"?b!=n! u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
J@I-tS u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
>RMp`HxDf ca1 = fftshift(fft(u1)); % Take Fourier transform
Fo1|O&> ca2 = fftshift(fft(u2));
;*8nd-\ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
:/
yR c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
>5|;8v-r
u2 = ifft(fftshift(c2)); % Return to physical space
VS I.c`=, u1 = ifft(fftshift(c1));
M+N7JpR if rem(m1,J) == 0 % Save output every J steps.
$CY B&|d U1 = [U1 u1]; % put solutions in U array
) 5M9Ro7 U2=[U2 u2];
rLm:qu(F1 MN1=[MN1 m1];
[! v|
M z1=dz*MN1'; % output location
?8LRd5LH end
yv!,iK9 end
+J~q:b. hg=abs(U1').*abs(U1'); % for data write to excel
! "Q8KV ha=[z1 hg]; % for data write to excel
[Bz'c1 t1=[0 t'];
u+RdC;_ hh=[t1' ha']; % for data write to excel file
H#j oc0?P %dlmwrite('aa',hh,'\t'); % save data in the excel format
7
i |_PP_ figure(1)
9g*MBe: waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
&Z^,- Y figure(2)
?+bDFM} waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
pSq3\#Twr CbA2?( 1o1 非线性超快脉冲耦合的数值方法的Matlab程序 v$`AN4)} sDH|k@K 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。
Z`l9 7$\ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"16-K%} L|3wG Y9E 8 '2lc ~!,Q<? % This Matlab script file solves the nonlinear Schrodinger equations
O_p:`h:;M % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
BlV k?n % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
f(O`t }Ed % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Rp 2~d .+H8c. C=1;
_`JY A M1=120, % integer for amplitude
!S/hH% C M3=5000; % integer for length of coupler
=9
TAs? = N = 512; % Number of Fourier modes (Time domain sampling points)
#@m*yJg< dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
at/v.U |F T =40; % length of time:T*T0.
%rQ5 <U dt = T/N; % time step
1 D fB9n n = [-N/2:1:N/2-1]'; % Index
fWR]L47n t = n.*dt;
bT @7& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#pxc6W / w=2*pi*n./T;
=#i#IF42? g1=-i*ww./2;
GRC=G&G g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3:rH1vG.m g3=-i*ww./2;
2&W(@w T$ P1=0;
<%JRZYZ P2=0;
Q r;es,f P3=1;
>NN |vj P=0;
>? ,arER for m1=1:M1
Dk|<&uVV p=0.032*m1; %input amplitude
V 'Gi2gNaP s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
YZCPS6PuE s1=s10;
N1UE u,j s20=0.*s10; %input in waveguide 2
: 5@cj j s30=0.*s10; %input in waveguide 3
U/M(4H3>H s2=s20;
;<#fZ0(l; s3=s30;
O \L(I079 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
s
&v<5W2P %energy in waveguide 1
xXK7i\ny p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
kRgyvA,*; %energy in waveguide 2
`5`Pv'` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
$&m^WrZaY %energy in waveguide 3
181-m7W for m3 = 1:1:M3 % Start space evolution
Y9m'RFZr s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Kg>+5~+E?q s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Y. yM 1 z s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
I0O)MR< sca1 = fftshift(fft(s1)); % Take Fourier transform
:&`Yz
sca2 = fftshift(fft(s2));
oJ`ih&Q8 sca3 = fftshift(fft(s3));
Vzz0)`*hQ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
-o F #a 8 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
"2CiW6X[M sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
M~7?m/Wj s3 = ifft(fftshift(sc3));
"t8mQ;n s2 = ifft(fftshift(sc2)); % Return to physical space
+I 2P{ 7 s1 = ifft(fftshift(sc1));
B[-%A!3
F end
dH!k {3bL p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
b]mRn{r? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
=[`wyQe`_ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
E8>npDF v. P1=[P1 p1/p10];
C^r 3r 6 P2=[P2 p2/p10];
#l-,2C~ P3=[P3 p3/p10];
-nO('(t P=[P p*p];
o C U8;z end
~SJOynSz, figure(1)
Yh:*.@ plot(P,P1, P,P2, P,P3);
7 .+kcqX P-No;/!B# 转自：
http://blog.163.com/opto_wang/
