计算脉冲在非线性耦合器中演化的Matlab 程序 diLjUC`69 sKX%<n$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
]rh)AE!Y( % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
iK"j@1 | % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
IP1|$b}sq % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
A*h)p@3t< mP)<;gm, %fid=fopen('e21.dat','w');
$Q:5KNF+p N = 128; % Number of Fourier modes (Time domain sampling points)
^/Hj^4 ~_U M1 =3000; % Total number of space steps
.~5cNu'#m J =100; % Steps between output of space
y(RbW_
? T =10; % length of time windows:T*T0
Hc@ Z7eQ3^ T0=0.1; % input pulse width
(WW,]#^
MN1=0; % initial value for the space output location
~P5!VNJ;r dt = T/N; % time step
^yRCR] oT n = [-N/2:1:N/2-1]'; % Index
]sjOn?YA+ t = n.*dt;
``kKi3TWJ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
r,6~?hG] u20=u10.*0.0; % input to waveguide 2
KG#|Cq u1=u10; u2=u20;
@ %z5]w U1 = u1;
p; n )YY$ U2 = u2; % Compute initial condition; save it in U
)`rC"N) ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-}UC daQ3 w=2*pi*n./T;
Iw"?%k\U g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
eT +MN` L=4; % length of evoluation to compare with S. Trillo's paper
9w K z p dz=L/M1; % space step, make sure nonlinear<0.05
{\t:{.F
A for m1 = 1:1:M1 % Start space evolution
f|VP _o< u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
d1j v>tu u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
= ]E1T8| ca1 = fftshift(fft(u1)); % Take Fourier transform
YA^9, q6u? ca2 = fftshift(fft(u2));
&TbnZnv c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
#G#gB c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
%h%r6EB1F u2 = ifft(fftshift(c2)); % Return to physical space
TF^]^XS' u1 = ifft(fftshift(c1));
m$J'n A if rem(m1,J) == 0 % Save output every J steps.
73xI8 U1 = [U1 u1]; % put solutions in U array
Zt ` ,D M U2=[U2 u2];
4
q W)R{% MN1=[MN1 m1];
F{T|lTl z1=dz*MN1'; % output location
: OI!YR%" end
v;K\#uc_ end
l:@.D|(o3 hg=abs(U1').*abs(U1'); % for data write to excel
`%ymg8 ^ ha=[z1 hg]; % for data write to excel
NHc+QMbou( t1=[0 t'];
dy`~%lX? hh=[t1' ha']; % for data write to excel file
Vxgc|E^J %dlmwrite('aa',hh,'\t'); % save data in the excel format
P 6=|C; [ figure(1)
sZ4H\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
R4qk/@]t figure(2)
103Ik6.o waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
NM]6 o 56': U29.] 非线性超快脉冲耦合的数值方法的Matlab程序 @pko zE- d'-^ VxO0 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
r?V|9B`$p 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
Vr0RdO v 5$zz w n6 uobo- !E7/:t4 % This Matlab script file solves the nonlinear Schrodinger equations
b '{D4/ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
zu|pL`X % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3 S 5QqAm % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$K
G?d>wx etDB|(,z C=1;
q{_buTARq M1=120, % integer for amplitude
RZ.5:v6 M3=5000; % integer for length of coupler
OIWo*
% N = 512; % Number of Fourier modes (Time domain sampling points)
L"b5P2{c dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
"iydXV=Q T =40; % length of time:T*T0.
6a ,YxR\ dt = T/N; % time step
{j q-d L n = [-N/2:1:N/2-1]'; % Index
'",5Bu#C t = n.*dt;
HxM-VK ' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`H|g ~7KD& w=2*pi*n./T;
0 s 4j> g1=-i*ww./2;
9%dNktt g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
. }1! MK5 g3=-i*ww./2;
)i>KYg w P1=0;
!kz \
{ P2=0;
"{:* fI;! P3=1;
kR_[p._ P=0;
D6m>>&E[' for m1=1:M1
[p( C:rH p=0.032*m1; %input amplitude
%q!nTG U~ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
m 8f_w s1=s10;
3whyIXs s20=0.*s10; %input in waveguide 2
$H 9x M s30=0.*s10; %input in waveguide 3
f[ywC$en s2=s20;
I'j? T. s3=s30;
l;C_A;y\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
2-6-kS) c %energy in waveguide 1
X3>(K1 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
U9q*zP_jV %energy in waveguide 2
a| >MueJ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
[ +1
i$d %energy in waveguide 3
R3<+z for m3 = 1:1:M3 % Start space evolution
qnlj~]NV s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
n- Xj> s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
5SjS~ 9 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
e?7paJ sca1 = fftshift(fft(s1)); % Take Fourier transform
'SY &-<t( sca2 = fftshift(fft(s2));
Il642#Gh sca3 = fftshift(fft(s3));
Ob6vg^# sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,yF)7fN sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4j*}|@x sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
J B|I/\(A s3 = ifft(fftshift(sc3));
y/ FisX s2 = ifft(fftshift(sc2)); % Return to physical space
^# 4s/mdVO s1 = ifft(fftshift(sc1));
zaZnL7ZJX end
8%4`Yj= p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
V#~. Jg7 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
/F_
:@#H p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
a:fHTU=\p P1=[P1 p1/p10];
Rc4EFHL P2=[P2 p2/p10];
%Z7!9+< P3=[P3 p3/p10];
r)t^qhn P=[P p*p];
u!i5Q end
'GFzI:Xr figure(1)
AUC<
m. plot(P,P1, P,P2, P,P3);
gY9"!IVe+
coWB KWF 转自：
http://blog.163.com/opto_wang/
