In this letter, we first analyze the dispersion relation for achromatic focusing and obtain the achromatic focusing conditions for discretized unit cells of flat lenses. Then, we propose to engineer the dispersion of spoof surface plasmon polaritons (SSPPs) to satisfy the achromatic focusing conditions. Metallic blades structures are utilized to achieve the linear dispersion response by tailoring the weak dispersion region of SSPPs. A broadband achromatic flat focusing lens (AFFL) is implemented with delicate combinations of the blade structures. A prototype was designed, fabricated, and measured. Both the simulated and experimental results demonstrate that the proposed AFFL can achieve achromatic focusing from 7.5 to 9.0 GHz under the normal incidence.
References
1.
I.
Aghanejad
, H.
Abiri
, and A.
Yahaghi
, “Design of high-gain lens antenna by gradient-index metamaterials using transformation optics
,” IEEE Trans. Antennas Propag.
60
(9
), 4074
(2012
).2.
P. V.
Parimi
, W. T.
Lu
, P.
Vodo
, and S.
Sridhar
, “Photonic crystals: Imaging by flat lens using negative refraction
,” Nature
426
, 404
(2003
).3.
P. A.
Belov
, Y.
Hao
, and S.
Sudhakaran
, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens
,” Phys. Rev. B
73
, 033108
(2006
).4.
A.
Abbaspour-Tamijani
, L.
Zhang
, G.
Pan
, H. K.
Pan
, and H.
Alavi
, “Lens-enhanced phased array antenna system for high directivity beam-steering
,” in IEEE International Symposium on Antennas and Propagation (APSURSI)
(2011
), Vol. 3275, p. 3278.5.
M. A.
Al-Joumayly
and N.
Behdad
, “Wideband planar microwave lenses using sub-wavelength spatial phase shifters
,” IEEE Trans. Antennas Propag.
59
(12
), 4542
(2011
).6.
O.
Malyuskin
, V.
Fusco
, and A. G.
Schuchinsky
, “Phase conjugating wire FSS lens
,” IEEE Trans. Antennas Propag.
54
(5
), 1399
(2006
).7.
Z. L.
Lu
, J. A.
Murakowski
, C. A.
Schuetz
, S. Y.
Shi
, G. J.
Schneider
, and D. W.
Prather
, “Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies
,” Phys. Rev. Lett.
95
, 153901
(2005
).8.
E.
Almeida
, G.
Shalem
, and Y.
Prior
, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces
,” Nat. Commun.
7
, 10367
(2016
).9.
C.
Saeidi
and D.
Weide
, “Wideband plasmonic focusing metasurfaces
,” Appl. Phys. Lett.
105
, 053107
(2014
).10.
N.
Yu
and F.
Capasso
, “Flat optics with designer metasurfaces
,” Nat. Mater.
13
(2
), 139
(2014
).11.
M.
Kang
, T. H.
Feng
, H.-T.
Wang
, and J. S.
Li
, “Wave front engineering from an array of thin aperture antennas
,” Opt. Express
20
(14
), 15882
(2012
).12.
D.
Lin
, A.
Holsteen
, E.
Maguid
, G.
Wetzstein
, P.
Kik
, E.
Hasman
, and M. L.
Brongersma
, “Photonic multitasking interleaved Si nanoantenna phased array
,” Nano Lett.
16
(12
), 7671
(2016
).13.
M.
Khorasaninejad
, Z.
Shi
, A. Y.
Zhu
, W. T.
Chen
, V.
Sanjeev
, A.
Zaidi
, and F.
Capasso
, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion
,” Nano. Lett.
17
(3
), 1819
(2017
).14.
E.
Arbabi
, A.
Arbabi
, S. M.
Kamali
, Y.
Horie
, and A.
Faraon
, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules
,” Optica
3
, 628
(2016
).15.
M.
Khorasaninejad
, F.
Aieta
, P.
Kanhaiya
, M. A.
Kats
, P.
Genevet
, D.
Rousso
, and F.
Capasso
, “Achromatic metasurface lens at telecommunication wavelengths
,” Nano Lett.
15
, 5358
(2015
).16.
F.
Aieta
, M. A.
Kats
, P.
Genevet
, and F.
Capasso
, “Multiwavelength achromatic metasurfaces by dispersive phase compensation
,” Science
347
, 1342
(2015
).17.
Y.
Li
, X.
Li
, M. B.
Pu
, Z. Y.
Zhao
, X. L.
Ma
, Y. Q.
Wang
, and X. G.
Luo
, “Achromatic flat optical components via compensation between structure and material dispersions
,” Sci. Rep.
6
, 19885
(2016
).18.
J. R.
Cheng
and H.
Mosallaei
, “Truly achromatic optical metasurfaces: A filter circuit theory-based design
,” J. Opt. Soc. Am. B
32
, 2115
(2015
).19.
M.
Li
, M. A.
Al-Joumayly
, and N.
Behdad
, “Broadband true-time-delay microwave lenses based on miniaturized element frequency selective surfaces
,” IEEE Trans. Antennas Propag.
61
, 1166
(2013
).20.
M.
Li
and N.
Behdad
, “Broadband wideband true-time-delay microwave lenses based on metallo-dielectric and all-dielectric lowpass frequency selective surfaces
,” IEEE Trans. Antennas Propag.
61
, 4109
(2013
).21.
H. F.
Ma
and T. J.
Cui
, “Three-dimensional broadband and broad-angle transformation-optics lens
,” Nat. Commun.
1
, 124
(2010
).22.
X.
Chen
, H. F.
Ma
, X. Y.
Zou
, W. X.
Jiang
, and T. J.
Cui
, “Three-dimensional broadband and high-directivity lens antenna made of metamaterials
,” J. Appl. Phys.
110
, 044904
(2011
).23.
M. Q.
Qi
, W. X.
Tang
, H. X.
Xu
, H. F.
Ma
, and T. J.
Cui
, “Tailoring radiation patterns in broadband with controllable aperture field using metamaterials
,” IEEE Trans. Antennas Propag.
61
, 5792
(2013
).24.
M. Q.
Qi
, W. X.
Tang
, and T. J.
Cui
, “A broadband Bessel beam launcher using metamaterial lens
,” Sci. Rep.
5
, 11732
(2015
).25.
Z. J.
Xu
, T.
Li
, D. H.
Zhang
, C. C.
Yan
, D. D.
Li
, L. Y. M.
Tobing
, F.
Qin
, Y. K.
Wang
, X. N.
Shen
, and T.
Yu
, “Groove-structured metasurfaces for modulation of surface plasmon propagation
,” Appl. Phys. Express
7
, 052001
(2014
).26.
X. P.
Shen
and T. J.
Cui
, “Planar plasmonic metamaterial on a thin film with nearly zero thickness
,” Appl. Phys. Lett.
102
, 211909
(2013
).27.
J. H.
Lee
, J. W.
Yoon
, M. J.
Jung
, J. K.
Hong
, S. H.
Song
, and R.
Magnusson
, “A semiconductor metasurface with multiple functionalities: A polarizing beam splitter with simultaneous focusing ability
,” Appl. Phys. Lett.
104
, 233505
(2014
).28.
S. L.
Sun
, Q.
He
, S. Y.
Xiao
, Q.
Xu
, X.
Li
, and L.
Zhou
, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves
,” Nat. Mater.
11
, 426
(2012
).29.
J. F.
Wang
, S. B.
Qu
, H.
Ma
, Z.
Xu
, A. X.
Zhang
, H.
Zhou
, H. Y.
Chen
, and Y. F.
Li
, “High-efficiency spoof plasmon polariton coupler mediated by gradient metasurfaces
,” Appl. Phys. Lett.
101
, 201104
(2012
).30.
J. T.
Donohue
and J.
Gardelle
, “Dispersion relation for a three-dimensional lamellar grating
,” Phys. Rev. ST Accel. Beams
14
, 060709
(2011
).31.
Y. Q.
Liu
, L. B.
Kong
, C. H.
Du
, and P. K.
Liu
, “Analysis on dispersion characteristics of rectangular metal grating based on spoof surface plasmons
,” Acta Physica Sinica
64
, 174102
(2015
).32.
F. J.
Garcia-Vidal
, L.
Martin-Moreno
, and J. B.
Pendry
, “Surfaces with holes in them: New plasmonic metamaterials
,” J. Opt. A: Pure Appl. Opt.
7
, S97
(2005
).33.
Y. F.
Li
, J. Q.
Zhang
, S. B.
Qu
, J. F.
Wang
, M. D.
Feng
, J.
Wang
, and Z.
Xu
, “k-dispersion engineering of spoof surface plasmon polaritons for beam steering
,” Opt. Express
24
, 842
(2016
).© 2017 Author(s).
2017
Author(s)
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