Here, we numerically investigate the existence of negative group refraction in graphene-based hyperbolic metamaterials (HMM) at THz frequencies. The hyperbolic dispersion of the graphene-based HMM can be tuned by varying the chemical potential and surrounding dielectric layer thickness. The negative group and positive phase indices of refraction are observed for oblique incidence at far below the critical frequency, which permits negative energy refraction and forward wavefront propagation. The highly confined bulk plasmon modes are also observed in the negative group index region that further evidence the negative refraction behaviour of the graphene-based hyperbolic metamaterials.
REFERENCES
1.
V. G.
Veselago
, Sov. Phys. Usp.
10
, 509
(1968
).2.
S.
Zhang
, W.
Fan
, N. C.
Panio
, K. J.
Malloy
, R. M.
Osgood
, and S. R. J.
Brueck
, Phys. Rev. Lett.
95
, 137404
(2005
).3.
J. B.
Pendry
, Phys. Rev. Lett.
85
, 3966
(2000
).4.
M. W.
Klein
, C.
Enkrich
, M.
Wegener
, and S.
Linden
, Science
313
, 502
(2006
).5.
S.
Zhang
, Y. S.
Park
, J.
Li
, X.
Lu
, W.
Zhang
, and X.
Zhang
, Phys. Rev. Lett.
102
, 023901
(2009
).6.
A. K.
Popov
, S. A.
Myslivets
, and V. M.
Shalaev
, Opt. Lett.
34
, 1165
(2009
).7.
D. R.
Smith
, P.
Kolinko
, and D.
Schurig
, J. Opt. Soc. Am. B
21
, 1032
(2004
).8.
A. J.
Hoffman
, L.
Alekseyev
, S. S.
Howard
, K. J.
Franz
, D.
Wasserman
, V. A.
Podolskiy
, E. E.
Narimanov
, D. L.
Sivco
, and C.
Gmachl
, Nature Mater.
6
, 946
(2007
).9.
M. A.
Noginov
, Y. A.
Barnakov
, G.
Zhu
, T.
Tumkur
, H.
Li
, and E. E.
Narimanov
, Appl. Phys. Lett.
94
, 151105
(2009
).10.
A. A.
Govyadinov
and E. E.
Narimanov
, Phys. Rev. B
73
, 155108
(2006
).11.
J. B.
Pendry
, Science
306
, 1353
(2004
).12.
V. A.
Podolskiy
and E. E.
Narimanov
, Phys. Rev. B
71
, 201101
(2005
).13.
D. R.
Smith
, W. J.
Padilla
, D. C.
Vier
, S. C.
Nemat-Nasser
, and S.
Shultz
, Phys. Rev. Lett.
84
, 4184
(2000
).14.
Z.
Jacob
, L. V.
Alekseyev
, and E.
Narimanov
, Opt. Express
14
, 8247
(2006
).15.
M. A.
Noginov
, H.
Li
, Y. A.
Barnakov
, D.
Dryden
, G.
Nataraj
, G.
Zhu
, C. E.
Bonner
, M.
Mayy
, Z.
Jacob
, and E. E.
Narimanov
, Opt. Lett.
35
, 1863
(2010
).16.
A. V.
Kabashin
, P.
Evans
, S.
Pastkovsky
, W.
Hendren
, G. A.
Wurtz
, R.
Atkinson
, R.
Pollard
, V. A.
Podolskiy
, and A. V.
Zayats
, Nature Mater.
8
, 867
(2009
).17.
Z.
Jacob
, I. I.
Smolyaninov
, and E. E.
Narimanov
, Appl. Phys. Lett.
100
, 181105
(2012
).18.
A. N.
Grigorenko
, M.
Polini
, and K. S.
Novoselov
, Nature Photon.
6
, 749
(2012
).19.
L.
Ju
, B.
Geng
, J.
Horng
, C.
Girit
, M.
Martin
, Z.
Hao
, H. A.
Bechtel
, X.
Liang
, A.
Zettl
, Y. R.
Shen
, and F.
Wang
, Nat. Nanotechnol.
6
, 630
(2011
).20.
A.
Vakil
and N.
Engheta
, Science
332
, 1291
(2011
).21.
K. V.
Sreekanth
and T.
Yu
, J. Opt.
15
, 055002
(2013
).22.
M.
Jablan
, H.
Buljan
, and M.
Soljacic
, Phys. Rev. B
80
, 245435
(2009
).23.
J.
Horng
, C. F.
Chen
, B.
Geng
, C.
Girit
, Y.
Zhang
, Z.
Hao
, H. A.
Bechtel
, M.
Martin
, A.
Zettl
, M. F.
Crommie
, Y. R.
Shen
, and F.
Wang
, Phys. Rev. B
83
, 165113
(2011
).24.
L. A.
Falkovsky
and S. S.
Pershoguba
, Phys. Rev. B
76
, 153410
(2007
).25.
V.
Ryzhii
, M.
Ryzhii
, and T.
Otsuji
, J. Appl. Phys.
101
, 083114
(2007
).26.
I. V.
Iorsh
, I. S.
Mukhin
, I. V.
Shadrivov
, P. A.
Belov
, and Y. S.
Kivshar
, Phys. Rev. B
87
, 075416
(2013
).27.
M. A. K.
Othman
, C.
Guclu
, and F.
Capolino
, Opt. Express
21
, 7614
(2013
).28.
J.
Sun
, J.
Zhou
, B.
Li
, and F.
Kang
, Appl. Phys. Lett.
98
, 101901
(2011
).29.
C. H.
Gan
, Appl. Phys. Lett.
101
, 111609
(2012
).30.
A. J.
Hoffman
, A.
Sridhar
, P. X.
Braun
, L.
Alekseyev
, S. S.
Howard
, K. J.
Franz
, L.
Cheng
, F. S.
Choa
, D. L.
Sivco
, V. A.
Podolskiy
, E. E.
Narimanov
, and C.
Gmachl
, J. Appl. Phys.
105
, 122411
(2009
).31.
M.
Grzegorczyk
, M.
Chen
, B.
Wu
, and J. A.
Kong
, IEEE Trans. Microwave Theory Tech.
53
, 1443
(2005
).32.
I.
Avrutsky
, I.
Salakhutdinov
, J.
Elser
, and V.
Podolskiy
, Phys. Rev. B
75
, 241402
(2007
).© 2013 AIP Publishing LLC.
2013
AIP Publishing LLC
You do not currently have access to this content.
