The Born series method is a classical approach to describe the properties of various physical systems. Despite the tremendous advantage of this approach which leads to save the time of complicated systems simulation, it has an assumption in the origin about a small value that can be treated as a decomposition parameter. This fact brings strong limitations on the use of this approach for studying optical systems, especially resonant ones. In this paper, it is observed how the Born series method can be used for the special case of metalens designing.

1.
J.
Tian
,
H.
Luo
,
Y.
Yang
,
F.
Ding
,
Y.
Qu
,
D.
Zhao
,
M.
Qiu
, and
S. I.
Bozhevolnyi
.
Active control of anapole states by structuring the phase-change alloy Ge2Sb2Te5
.
Nat. Commun.
,
10
:
396
,
2019
.
2.
A.
Karvounis
,
B.
Gholipour
,
K. F.
MacDonald
, and
N. I.
Zheludev
.
All-dielectric phase-change reconfigurable metasurface
.
Appl. Phys. Lett.
,
109
(
5
):
051103
,
2016
.
3.
A.
Krizhevsky
,
I.
Sutskever
, and
G. E.
Hinton
. Imagenet classification with deep convolutional neural networks. In
F.
Pereira
,
C. J. C.
Burges
,
L.
Bottou
, and
K. Q.
Weinberger
, editors,
Advances in Neural Information Processing Systems 25
, pages
1097
1105
.
Curran Associates, Inc
.,
2012
.
4.
G.
Hinton
,
L.
Deng
,
D.
Yu
,
G.
Dahl
,
A. r.
Mohamed
,
N.
Jaitly
,
A.
Senior
,
V.
Vanhoucke
,
P.
Nguyen
,
T.
Sainath
, and
B.
Kingsbury
.
Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups
.
IEEE Signal Process. Mag.
,
29
(
6
):
82
97
,
2012
.
5.
R. J.
Lin
,
V.-C.
Su
,
S.
Wang
,
M. K.
Chen
,
T. L.
Chung
,
Y. H.
Chen
,
H. Y.
Kuo
,
J.-W.
Chen
,
J.
Chen
,
Y.-T.
Huang
,
J.-H.
Wang
,
C. H.
Chu
,
P. C.
Wu
,
T.
Li
,
Z.
Wang
,
S.
Zhu
, and
D. P.
Tsai
.
Achromatic metalens array for full-colour light-field imaging
.
Nat. Nanotechnol.
,
14
(
3
):
227
231
,
2019
.
6.
K.
Yao
,
R.
Unni
, and
Y.
Zheng
.
Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale
.
Nanophotonics
,
8
(
3
):
339
366
,
2019
.
7.
S.
Molesky
,
Z.
Lin
,
A. Y.
Piggott
,
W.
Jin
,
J.
Vucković
, and
A. W.
Rodriguez
.
Inverse design in nanophotonics
.
Nat. Photonics
,
12
(
11
):
659
670
,
2018
.
8.
D.
Sell
,
J.
Yang
,
E. W.
Wang
,
T.
Phan
,
S.
Doshay
, and
J. A.
Fan
.
Ultra-high-efficiency anomalous refraction with dielectric metasurfaces
.
ACS Photonics
,
5
(
6
):
2402
2407
,
2018
.
9.
R.
Pestourie
,
C.
Pérez-Arancibia
,
Z.
Lin
,
W.
Shin
,
F.
Capasso
, and
S. G.
Johnson
.
Inverse design of large-area metasurfaces
.
Opt. Express
,
26
(
26
):
33732
33747
,
2018
.
10.
M.
Khorasaninejad
and
F.
Capasso
.
Metalenses: Versatile multifunctional photonic components
.
Science
,
358
(
6367
):
eaam8100
,
2017
.
11.
J.
Engelberg
,
C.
Zhou
,
N.
Mazurski
,
J.
Bar-David
,
A.
Kristensen
, and
U.
Levy
.
Near-IR wide-field-of-view huygens metalens for outdoor imaging applications
.
Nanophotonics
,
9
(
2
):
361
370
,
2020
.
12.
G.-Y.
Lee
,
J.-Y.
Hong
,
S.
Hwang
,
S.
Moon
,
H.
Kang
,
S.
Jeon
,
H.
Kim
,
J.-H.
Jeong
, and
B.
Lee
.
Metasurface eyepiece for augmented reality
.
Nat. Commun.
,
9
:
4562
,
2018
.
13.
A. Y.
Zhu
,
W.-T.
Chen
,
M.
Khorasaninejad
,
J.
Oh
,
A.
Zaidi
,
I.
Mishra
,
R. C.
Devlin
, and
F.
Capasso
.
Ultra-compact visible chiral spectrometer with meta-lenses
.
APL Photonics
,
2
(
3
):
036103
,
2017
.
14.
M.
Meem
,
S.
Banerji
,
A.
Majumder
,
F. G.
Vasquez
,
B.
Sensale-Rodriguez
, and
R.
Menon
.
Broadband lightweight flat lenses for long-wave infrared imaging
.
PNAS
,
116
(
43
):
21375
21378
,
2019
.
15.
Z. H.
Fan
,
D. X.
Wang
,
R. S.
Chen
, and
E. K. N.
Yung
.
The application of iterative solvers in discrete dipole approximation method for computing electromagnetic scattering
.
Microw. Opt. Techn. Lett.
,
48
:
1741
1746
,
2006
.
16.
O.
Keller
,
M.
Xiao
, and
S.
Bozhevolnyi
.
Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach
.
Surf. Sci.
,
280
:
217
230
,
1993
.
17.
S.
Wang
,
P. C.
Wu
,
V.-C.
Su
,
Y.-C.
Lai
,
C. H.
Chu
,
J.-W.
Chen
,
S.-H.
Lu
,
J.
Chen
,
B.
Xu
,
C.-H.
Kuan
,
T.
Li
,
S.
Zhu
, and
D. P.
Tsai
.
Broadband achromatic optical metasurface devices
.
Nat. Commun.
,
8
:
187
,
2017
.
18.
M.
Khorasaninejad
,
W. T.
Chen
,
R. C.
Devlin
,
J.
Oh
,
A. Y.
Zhu
, and
F.
Capasso
.
Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging
.
Science
,
352
(
6290
):
1190
1194
,
2016
.
19.
M.
Khorasaninejad
,
A. Y.
Zhu
,
C.
Roques-Carmes
,
W. T.
Chen
,
J.
Oh
,
I.
Mishra
,
R. C.
Devlin
, and
F.
Capasso
.
Polarization-insensitive metalenses at visible wavelengths
.
Nano Lett.
,
16
(
11
):
7229
7234
,
2016
.
20.
I.
Tanriover
and
H. V.
Demir
.
Broad-band polarization-insensitive all-dielectric metalens enabled by intentional off-resonance waveguiding at mid-wave infrared
.
Appl. Phys. Lett.
,
114
(
4
):
043105
,
2019
.
21.
A. B.
Evlyukhin
,
C.
Reinhardt
,
A.
Seidel
,
B. S.
Luk'yanchuk
, and
B. N.
Chichkov
.
Optical response features of Si-nanoparticle arrays
.
Phys. Rev. B
,
82
(
4
):
045404
,
2010
.
22.
T. H.
Cormen
,
C. E.
Leiserson
,
R. L.
Rivest
, and
C.
Stein
.
Introduction to algorithms
.
The MIT Press
,
2009
.
23.
M.
Kerker
,
D.-S.
Wang
, and
C. L.
Giles
.
Electromagnetic scattering by magnetic spheres
.
J. Opt. Soc. Am.
,
73
(
6
):
765
767
,
1983
.
24.
B.
García-Cámara
,
J. M.
Saiz
,
F.
González
, and
F.
Moreno
.
Nanoparticles with unconventional scattering properties: Size effects
.
Opt. Commun.
,
283
(
3
):
490
496
,
2010
.
25.
D. E.
Aspnes
and
A. A.
Studna
.
Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV
.
Phys. Rev. B
,
27
(
2
):
985
,
1983
.
This content is only available via PDF.
You do not currently have access to this content.