We propose a perfectly reflecting acoustic metasurface which is designed by replacing the curved segments of the traditional Fresnel reflector by flat Fano-resonant sub-wavelength unit cells. To preserve the original Fresnel focusing mechanism, the unit cell phase follows a specific phase profile which is obtained by applying the generalized Snell's law and Fermat's principle. The reflected curved phase fronts are thus created at the air-metasurface boundary by tailoring the metasurface dispersion as dictated by Huygens' principle. Since the unit cells are implemented by sub-wavelength double slit-shaped cavity resonators, the impinging sound waves are perfectly reflected producing acoustic focusing with negligible absorption. We use plane-wave solution and full-wave simulations to demonstrate the focusing effects. The simulation results closely follow the analytical predictions.
References
1.
S.
Datta
, “Classical wave propagation in periodic and random media
,” Ph.D. thesis (Iowa State University
, 1994
).2.
E.
Yablonovitch
, Phys. Rev. Lett.
58
, 2059
(1987
).3.
S.
John
, Phys. Rev. Lett.
58
, 2486
(1987
).4.
R.
Zengerle
, J. Mod. Opt.
34
, 1589
(1987
).5.
T. F.
Krauss
, M.
Richard
, and S.
Brand
, Nature
383
, 699
(1996
).6.
B.
Gralak
, S.
Enoch
, and G.
Tayeb
, JOSA A
17
, 1012
(2000
).7.
M.
Notomi
, Opt. Quantum Electron.
34
, 133
(2002
).8.
R. V.
Craster
and S.
Guenneau
, Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking
(Springer Science and Business Media
, 2012
), Vol. 166
.9.
E.
Lheurette
, Metamaterials and Wave Control
(John Wiley and Sons
, 2013
).10.
Z.
Liu
, X.
Zhang
, Y.
Mao
, Y.
Zhu
, Z.
Yang
, C. T.
Chan
, and P.
Sheng
, Science
289
, 1734
(2000
).11.
C.
Poulton
, A.
Movchan
, R.
McPhedran
, N.
Nicorovici
, and Y.
Antipov
, Proc. R. Soc. London, Ser. A
456
, 2543
–2559
(2000
).12.
S.
Yang
, J. H.
Page
, Z.
Liu
, M. L.
Cowan
, C. T.
Chan
, and P.
Sheng
, Phys. Rev. Lett.
93
, 024301
(2004
).13.
L.
Feng
, X.-P.
Liu
, Y.-B.
Chen
, Z.-P.
Huang
, Y.-W.
Mao
, Y.-F.
Chen
, J.
Zi
, and Y.-Y.
Zhu
, Phys. Rev. B
72
, 033108
(2005
).14.
X.
Zhang
and Z.
Liu
, Appl. Phys. Lett.
85
, 341
(2004
).15.
X.
Hu
, Y.
Shen
, X.
Liu
, R.
Fu
, and J.
Zi
, Phys. Rev. E
69
, 030201
(2004
).16.
M.
Farhat
, S.
Guenneau
, S.
Enoch
, G.
Tayeb
, A.
Movchan
, and N.
Movchan
, Phys. Rev. E
77
, 046308
(2008
).17.
M.
Farhat
, S.
Guenneau
, S.
Enoch
, and A.
Movchan
, J. Comput. Appl. Math.
234
, 2011
(2010
).18.
J.
Page
, A.
Sukhovich
, S.
Yang
, M. L.
Cowan
, F.
Van Der Biest
, A.
Tourin
, M.
Fink
, Z.
Liu
, C. T.
Chan
, and P.
Sheng
, Phys. Status Solidi B
241
, 3454
(2004
).19.
Y.
Pennec
, J. O.
Vasseur
, B.
Djafari-Rouhani
, L.
Dobrzyński
, and P. A.
Deymier
, Surf. Sci. Rep.
65
, 229
(2010
).20.
G.
Dupont
, M.
Farhat
, A.
Diatta
, S.
Guenneau
, and S.
Enoch
, Wave Motion
48
, 483
(2011
).21.
M. D.
Guild
, M. R.
Haberman
, and A.
Alù
, Wave Motion
48
, 468
(2011
).22.
P.-Y.
Chen
, M.
Farhat
, S.
Guenneau
, S.
Enoch
, and A.
Alù
, Appl. Phys. Lett.
99
, 191913
(2011
).23.
A. N.
Norris
, Proc. R. Soc. London, Ser. A
464
, 2411
–2434
(2008
).24.
M.
Farhat
, S.
Guenneau
, and S.
Enoch
, Phys. Rev. B
85
, 020301
(2012
).25.
T.
Bückmann
, M.
Thiel
, M.
Kadic
, R.
Schittny
, and M.
Wegener
, Nat. Commun.
5
, 4130
(2014
).26.
J.
Li
and C.
Chan
, Phys. Rev. E
70
, 055602
(2004
).27.
Y.
Ding
, Z.
Liu
, C.
Qiu
, and J.
Shi
, Phys. Rev. Lett.
99
, 093904
(2007
).28.
S.
Guenneau
, A.
Movchan
, G.
Pétursson
, and S. A.
Ramakrishna
, New J. Phys.
9
, 399
(2007
).29.
Z.
Liang
, T.
Feng
, F. L. S.
Lok
, K. B.
Ng
, C. H.
Chan
, J.
Wang
, S.
Han
, S.
Lee
, and J.
Li
, Sci. Rep.
3
, 1614
(2013
).30.
J. B.
Pendry
, Phys. Rev. Lett.
85
, 3966
(2000
).31.
S. A.
Cummer
and D.
Schurig
, New J. Phys.
9
, 45
(2007
).32.
M.
Fleischhauer
, A.
Imamoglu
, and J. P.
Marangos
, Rev. Mod. Phys.
77
, 633
(2005
).33.
N.
Liu
, L.
Langguth
, T.
Weiss
, J.
Kästel
, M.
Fleischhauer
, T.
Pfau
, and H.
Giessen
, Nat. Mater.
8
, 758
–762
(2009
).34.
M.
Amin
, R.
Ramzan
, and O.
Siddiqui
, Sci. Rep.
8
, 2357
(2018
).35.
B.
Luk'yanchuk
, N. I.
Zheludev
, S. A.
Maier
, N. J.
Halas
, P.
Nordlander
, H.
Giessen
, and C. T.
Chong
, Nat. Mater.
9
, 707
–715
(2010
).36.
C.
Wu
, A. B.
Khanikaev
, R.
Adato
, N.
Arju
, A. A.
Yanik
, H.
Altug
, and G.
Shvets
, Nat. Mater.
11
, 69
–75
(2012
).37.
F.
Liu
, M.
Ke
, A.
Zhang
, W.
Wen
, J.
Shi
, Z.
Liu
, and P.
Sheng
, Phys. Rev. E
82
, 026601
(2010
).38.
A.
Santillán
and S. I.
Bozhevolnyi
, Phys. Rev. B
84
, 064304
(2011
).39.
M.
Amin
, A.
Elayouch
, M.
Farhat
, M.
Addouche
, A.
Khelif
, and H.
Bağci
, J. Appl. Phys.
118
, 164901
(2015
).40.
41.
S.
Wahlström
, J. Audio Eng. Soc.
33
, 418
(1985
).42.
C.
Pfeiffer
and A.
Grbic
, Phys. Rev. Lett.
110
, 197401
(2013
).43.
M.
Dubois
, C.
Shi
, Y.
Wang
, and X.
Zhang
, Appl. Phys. Lett.
110
, 151902
(2017
).44.
A.
Díaz-Rubio
and S.
Tretyakov
, Phys. Rev. B
96
, 125409
(2017
).45.
N.
Yu
, P.
Genevet
, M. A.
Kats
, F.
Aieta
, J.-P.
Tetienne
, F.
Capasso
, and Z.
Gaburro
, Science
334
, 333
(2011
).46.
A.
Epstein
and G. V.
Eleftheriades
, J. Opt. Soc. Am. B
33
, A31
(2016
).47.
G.
Ma
, M.
Yang
, S.
Xiao
, Z.
Yang
, and P.
Sheng
, Nat. Mater.
13
, 873
(2014
).48.
K.
Song
, M.
Anzan-Uz-Zaman
, J.-H.
Kwak
, J.-Y.
Jung
, J.
Kim
, and S.
Hur
, AIP Adv.
7
, 035315
(2017
).49.
A.
Davis
and F.
Kühnlenz
, Opt. Photonik
2
, 52
(2007
).50.
S.
Guenneau
and S. A.
Ramakrishna
, C. R. Phys.
10
, 352
(2009
).51.
Y.
Ding
, E. C.
Statharas
, K.
Yao
, and M.
Hong
, Appl. Phys. Lett.
110
, 241903
(2017
).52.
Y.
Li
, B.
Liang
, Z.-M.
Gu
, X.-Y.
Zou
, and J.-C.
Cheng
, Sci. Rep.
3
, 2546
(2013
).53.
Y.
Xie
, W.
Wang
, H.
Chen
, A.
Konneker
, B.-I.
Popa
, and S. A.
Cummer
, Nat. Commun.
5
, 5553
(2014
).54.
L.
Zigoneanu
, B.-I.
Popa
, and S. A.
Cummer
, Phys. Rev. B
84
, 024305
(2011
).55.
M.
Ruphuy
, O.
Siddiqui
, and O. M.
Ramahi
, J. Opt. Soc. Am. A
32
, 1700
(2015
).56.
P.
Clemmow
, The Plane Wave Spectrum Representation of Electromagnetic Fields
(Pergamon Press Ltd
, 1966
).57.
58.
C.
Ott
, A.
Kaldun
, P.
Raith
, K.
Meyer
, M.
Laux
, J.
Evers
, C. H.
Keitel
, C. H.
Greene
, and T.
Pfeifer
, Science
340
, 716
(2013
).59.
M.
Amin
, M.
Farhat
, and H.
Baci
, Sci. Rep.
3
, 2105
(2013
).60.
M.
Amin
, R.
Ramzan
, and O.
Siddiqui
, Appl. Phys. Lett.
110
, 181904
(2017
).61.
A. E.
Miroshnichenko
, S.
Flach
, and Y. S.
Kivshar
, Rev. Mod. Phys.
82
, 2257
(2010
).62.
M.
Rahmani
, B.
Luk'yanchuk
, and M.
Hong
, Laser Photonics Rev.
7
, 329
(2013
).63.
M.
Amin
, M.
Farhat
, and H.
Bağci
, Opt. Express
22
, 6966
(2014
).64.
M.
O'Donnell
, E.
Jaynes
, and J.
Miller
, J. Acoust. Soc. Am.
69
, 696
(1981
).65.
A.
Grbic
and G. V.
Eleftheriades
, Phys. Rev. Lett.
92
, 117403
(2004
).66.
O.
Siddiqui
and G. V.
Eleftheriades
, Appl. Phys. Lett.
85
, 1292
(2004
).67.
G. V.
Eleftheriades
and O. F.
Siddiqui
, IEEE Trans. Microwave Theory Tech.
53
, 396
(2005
).© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.