This article reviews recent progress towards the design of near-field flat focusing mirrors, focusing/imaging light patterns in reflection. An important feature of such flat focusing mirrors is their transverse invariance, as they do not possess any optical axis. We start with a review of the physical background to the different focusing mechanisms of near- and far-field focusing. These near-field focusing devices like flat lenses and the reviewed near-field focusing mirrors can implement planar focusing devices without any optical axis. In contrast, various types of far-field planar focusing devices, such as high-contrast gratings and metasurfaces, unavoidably break the transverse invariance due to their radially symmetrical structures. The particular realizations of near-field flat focusing mirrors including Bragg-like dielectric mirrors and dielectric subwavelength gratings are the main subjects of the review. The first flat focusing mirror was demonstrated with a chirped mirror and was shown to manage an angular dispersion for beam focusing, similar to the management of chromatic dispersion for pulse compression. Furthermore, the reviewed optimized chirped mirror demonstrated a long near-field focal length, hardly achieved by a flat lens or a planar hyperlens. Two more different configurations of dielectric subwavelength gratings that focus a light beam at normal or oblique incidence are also reviewed. We also summarize and compare focusing performance, limitations, and future perspectives between the reviewed flat focusing mirrors and other planar focusing devices including a flat lens with a negative-index material, a planar hyperlens, a high-contrast grating, and a metasurface.

1.
Z. D.
Popovic
,
R. A.
Sprague
, and
G. A.
Connell
,
Appl. Opt.
27
,
1281
(
1988
).
2.
Y. M.
Sabry
,
B.
Saadany
,
D.
Khalil
, and
T.
Bourouina
,
Light Sci. Appl.
2
,
94
(
2013
).
3.
F.
Lu
,
F. G.
Sedgwick
,
V.
Karagodsky
,
C.
Chase
, and
C. J.
Chang-Hasnain
,
Opt. Express
18
,
12606
(
2010
).
4.
D.
Fattal
,
J.
Li
,
Z.
Peng
,
M.
Fiorentino
, and
R. G.
Beausoleil
,
Nat. Photonics
4
,
466
(
2010
).
5.
N.
Yu
and
F.
Capasso
,
Nat. Mater.
13
,
139
(
2014
).
6.
L.
Huang
,
X.
Chen
,
H.
Mühlenbernd
,
G.
Li
,
B.
Bai
,
Q.
Tan
,
G.
Jin
,
T.
Zentgraf
, and
S.
Zhang
,
Nano Lett.
12
,
5750
(
2012
).
7.
F.
Aieta
,
P.
Genevet
,
M. A.
Kats
,
N.
Yu
,
R.
Blanchard
,
Z.
Gaburro
, and
F.
Capasso
,
Nano Lett.
12
,
4932
(
2012
).
8.
S.
Zhang
,
M.-H.
Kim
,
F.
Aieta
,
A.
She
,
T.
Mansuripur
,
I.
Gabay
,
M.
Khorasaninejad
,
D.
Russo
,
X.
Wang
,
M.
Triccoli
,
N.
Yu
, and
F.
Capasso
,
Opt. Express
24
,
18024
(
2016
).
9.
M.
Khorasaninejad
,
M. W. T.
Chen
,
R. C.
Devlin
,
J.
Oh
,
A. Y.
Zhu
, and
F.
Capasso
,
Science
352
,
1190
(
2016
).
10.
V. G.
Veselago
,
Sov. Phys. Usp.
10
,
509
(
1968
).
11.
12.
R. A.
Shelby
,
D. R.
Smith
, and
S.
Schultz
,
Science
292
,
77
(
2001
).
13.
E.
Cubukcu
,
K.
Aydin
,
E.
Ozbay
,
S.
Foteinopoulou
, and
C. M.
Soukoulis
,
Nature
423
,
604
(
2003
).
14.
A. A.
Houck
,
J. B.
Brock
, and
I. L.
Chuang
,
Phys. Rev. Lett.
90
,
137401
(
2003
).
15.
H. J.
Lezec
,
J. A.
Dionne
, and
H. A.
Atwater
,
Science
316
,
430
(
2007
).
16.
J.
Yao
,
J. Z.
Liu
,
Y.
Liu
,
Y.
Wang
,
C.
Sun
,
G.
Bartal
,
A. M.
Stacy
, and
X.
Zhang
,
Science
321
,
930
(
2008
).
17.
Z.
Lu
,
J. A.
Murakowski
,
C. A.
Schuetz
,
S. N.
Shi
,
G. J.
Schneider
, and
D. W.
Prather
,
Phys. Rev. Lett.
95
,
153901
(
2005
).
18.
R.
Zengerle
and
P. C.
Hoang
,
Opt. Express
13
,
5719
(
2005
).
19.
D. R.
Smith
,
W. J.
Padilla
,
D. C.
Vier
,
S. C.
Nemat-Nasser
, and
S.
Schultz
,
Phys. Rev. Lett.
84
,
4184
(
2000
).
20.
D. R.
Smith
,
J. B.
Pendry
, and
M. C. K.
Wiltshire
,
Science
305
,
788
(
2004
).
21.
P. V.
Parimi
,
W. T.
Lu
,
P.
Vodo
, and
S.
Sridhar
,
Nature
426
,
404
(
2003
).
22.
S.
Zhang
,
L.
Yin
, and
N.
Fang
,
Phys. Rev. Lett.
102
,
194301
(
2009
).
23.
E.
Yablonovitch
,
Phys. Rev. Lett.
58
,
2059
(
1987
).
24.
25.
T.
Miyashita
,
Meas. Sci. Technol.
16
,
R47
(
2005
).
26.
C. M.
Soukoulis
and
M.
Wegener
,
Nat. Photonics
6
,
346
(
2011
).
27.
S. A.
Ramakrishna
and
J. B.
Pendry
,
Phys. Rev. B
67
,
201101
(
2003
).
28.
T.
Xu
,
A.
Agrawal
,
M.
Abashin
,
K. J.
Chau
, and
H. J.
Lezec
,
Nature
497
,
470
(
2013
).
29.
Z.
Liu
,
H.
Lee
,
Y.
Xiong
,
C.
Sun
, and
X.
Zhang
,
Science
315
,
1686
(
2007
).
30.
J.
Rho
,
Z.
Ye
,
Y.
Xiong
,
X.
Yin
,
X. Z.
Liu
,
H.
Choi
,
G.
Bartal
, and
X.
Zhang
,
Nat. Commun.
1
,
143
(
2010
).
31.
Y. C.
Cheng
,
S.
Kicas
,
J.
Trull
,
M.
Peckus
,
C.
Cojocaru
,
R.
Vilaseca
,
R.
Drazdys
, and
K.
Staliunas
,
Sci. Rep.
4
,
6326
(
2015
).
32.
W.
Wang
,
H.
Xing
,
L.
Fang
,
Y.
Liu
,
J.
Ma
,
L.
Lin
,
C.
Wang
, and
X.
Luo
,
Opt. Express
16
,
21142
(
2008
).
33.
Y.
Xiong
,
Z.
Liu
, and
X.
Zhang
,
Appl. Phys. Lett.
94
,
203108
(
2009
).
34.
J. B.
Pendry
,
D.
Schurig
, and
D. R.
Smith
,
Science
312
,
1780
(
2006
).
35.
Y. C.
Cheng
,
M.
Peckus
,
S.
Kicas
,
J.
Trull
,
C.
Cojocaru
,
R.
Vilaseca
,
R.
Drazdys
, and
K.
Staliunas
,
Phys. Rev. A
87
,
45802
(
2013
).
36.
Y. C.
Cheng
,
S.
Kicas
, and
K.
Staliunas
,
J. Nanophotonics
9
,
93084
(
2015
).
37.
Y. C.
Cheng
and
K.
Staliunas
,
J. Nanophotonics
8
,
84093
(
2014
).
38.
K.
Staliunas
and
S.
Longhi
,
Phys. Rev. A
78
,
33606
(
2008
).
39.
M.
Born
and
E.
Wolf
,
Principles of Optics: electromagnetic Theory of Propagation, Interference and Diffraction of Light
(
Cambridge University Press
,
1999
).
40.
J.
Trull
,
J. L.
Maigyte
,
V.
Mizeikis
,
M.
Malinauskas
,
S.
Juodkazis
,
C.
Cojocaru
,
M.
Rutkauskas
,
M.
Peckus
,
V.
Sirutkaitis
, and
K.
Staliunas
,
Phys. Rev. A
84
,
33812
(
2011
).
41.
C.-H.
Ho
,
Y.-C.
Cheng
,
L.
Maigyte
,
H.
Zeng
,
J.
Trull
,
C.
Cojocaru
,
D. S.
Wiersma
, and
K.
Staliunas
,
Appl. Phys. Lett.
106
,
021113
(
2015
).
42.
A.
Cebrecos
,
V.
Romero-Garcia
,
R.
Picó
,
I.
Pérez-Arjona
,
V.
Espinosa
,
V. J.
Sánchez-Morcillo
, and
K.
Staliunas
,
J. Appl. Phys.
111
,
104910
(
2012
).
43.
L.
Walmsley
,
L.
Waxe
, and
C.
Dorrer
,
Rev. Sci. Instrum.
72
,
1
(
2001
).
44.
J.
Zhou
,
G.
Taft
,
C.-P.
Huang
,
M. M.
Murnane
,
H. C.
Kapteyn
, and
I. P.
Christov
,
Opt. Lett.
19
,
1149
(
1994
).
45.
Q.
Qin
,
H.
Lu
,
S. N.
Zhu
,
C. S.
Yuan
,
Y. Y.
Zhu
, and
N. B.
Ming
,
Appl. Phys. Lett.
82
,
4654
(
2003
).
46.
R. D.
Meade
,
K. D.
Brommer
,
A. M.
Rappe
, and
J. D.
Joannopoulos
,
Phys. Rev. B
44
,
13772
(
1991
).
47.
A. Z.
Genack
and
N.
Garcia
,
Phys. Rev. Lett.
66
,
2064
(
1991
).
48.
K. M.
Leung
and
Y. F.
Liu
,
Phys. Rev. Lett.
65
,
2646
(
1990
).
49.
Z.
Zhang
and
S.
Satpathy
,
Phys. Rev. Lett.
65
,
2650
(
1990
).
50.
K. M.
Ho
,
C. T.
Chan
, and
C. M.
Soukoulis
,
Phys. Rev. Lett.
65
,
3152
(
1990
).
51.
K. O.
Hill
,
F.
Bilodeau
,
B.
Malo
,
T.
Kitagawa
,
S.
Thériault
,
D. C.
Johnson
,
J.
Albert
, and
K.
Takiguchi
,
Opt. Lett.
19
,
1314
(
1994
).
52.
53.
S.
Shi
,
C.
Chen
, and
D. W.
Prather
,
J. Opt. Soc. Am. A
21
,
1769
(
2004
).
54.
N.
Matuschek
,
L.
Gallmann
,
D. H.
Sutter
,
G.
Steinmeyer
, and
U.
Keller
,
Appl. Phys. B: Lasers Opt.
71
,
509
(
2000
).
55.
F. X.
Kärtner
,
U.
Morgner
,
R.
Ell
,
T.
Schibli
,
J. G.
Fujimoto
,
E. P.
Ippen
,
V.
Scheuer
,
G.
Angelow
, and
T.
Tschudi
,
J. Opt. Soc. Am. B
18
,
882
(
2001
).
56.
R.
Szipőcs
and
A.
Kőházi-Kis
,
Appl. Phys. B: Lasers Opt.
65
,
115
(
1997
).
57.
C. A.
Rivera
,
S. E.
Bradforth
, and
G.
Tempea
,
Opt. Express
18
,
18615
(
2010
).
58.
G.
Hernandez
,
Fabry–Perot Interferometers
(
Cambridge University Press
,
1986
).
59.
B.
Golubovic
,
R. R.
Austin
,
M. K.
Steiner-Shepard
,
M. K.
Reed
,
S. A.
Diddams
,
D. J.
Jones
, and
A. G.
Van Engen
,
Opt. Lett.
25
,
275
(
2000
).
60.
Y.-P.
Li
,
S.-H.
Chen
, and
C.-C.
Lee
,
Appl. Opt.
45
,
1525
(
2006
).
61.
A. V.
Tikhonravov
,
M. K.
Trubetskov
, and
G. W.
DeBell
,
Appl. Opt.
35
,
5493
(
1996
).
62.
M.
Trubetskov
,
A.
Tikhonravov
, and
V.
Pervak
,
Opt. Express
16
,
20637
20647
(
2008
).
63.
A.
Taflove
,
IEEE Trans. Electromagn. Compat.
22
,
191
(
1980
).
64.
A. V.
Tikhonravov
,
M. K.
Trubetskov
, and
T. V.
Amotchkina
,
Appl. Opt.
47
,
5103
(
2008
).
65.
V.
Pervak
,
M. K.
Trubetskov
, and
A. V.
Tikhonravov
,
Opt. Express
19
,
2371
(
2011
).
66.
A. V.
Tikhonravov
,
M. K.
Trubetskov
, and
G. W.
DeBell
,
Appl. Opt.
46
,
704
(
2007
).
67.
J. A.
Dobrowolski
,
Appl. Opt.
4
,
937
(
1965
).
68.
P. J.
Martin
,
J. Mater. Sci.
21
,
1
(
1986
).
69.
D. W.
Peters
,
S. A.
Kemme
, and
G. R.
Hadley
,
J. Opt. Soc. Am. A
21
,
981
(
2004
).
70.
T. K.
Gaylord
,
W. E.
Baird
, and
M. G.
Moharam
,
Appl. Opt.
25
,
4562
(
1986
).
71.
J. M.
dos Santos
and
L. M.
Bernardo
,
Appl. Opt.
36
,
8935
8938
(
1997
).
72.
T.
Tamir
and
H. L.
Bertoni
,
J. Opt. Soc. Am.
61
,
1397
(
1971
).
73.
Y. C.
Cheng
,
J.
Redondo
, and
K.
Staliunas
,
Phys. Rev. A
89
,
33814
(
2014
).
74.
M.
Deubel
,
G.
von Freymann
,
M.
Wegener
,
S.
Pereira
,
K.
Busch
, and
C. M.
Soukoulis
,
Nat. Mater.
3
,
444
(
2004
).
75.
S.
Maruo
and
J. T.
Fourkas
,
Laser Photonics Rev.
2
,
100
(
2008
).
76.
Y. C.
Cheng
,
H.
Zeng
,
J.
Trull
,
C.
Cojocaru
,
M.
Malinauskas
,
T.
Jukna
,
D. S.
Wiersma
, and
K.
Staliunas
,
Opt. Lett.
39
,
6086
(
2014
).
77.
V.
Karagodsky
,
F. G.
Sedgwick
, and
C. J.
Chang-Hasnain
,
Opt. Express
18
,
16973
(
2010
).
78.
A.
Arbabi
,
Y.
Horie
,
A. J.
Ball
,
M.
Bagheri
, and
A.
Faraon
,
Nat. Commun
6
,
7069
(
2015
).
79.
J. M.
Kontio
,
J.
Simonen
,
K.
Leinonen
,
M.
Kuittinen
, and
T.
Niemi
,
Opt. Lett.
35
,
2564
(
2010
).
80.
L.
Carletti
,
R.
Malureanu
,
J.
Mørk
, and
I.-S.
Chung
,
Opt. Express
19
,
23567
(
2011
).
81.
C.
Chang-Hasnain
and
W.
Yang
,
Adv. Opt. Photonics
4
,
379
(
2012
).
82.
Y.
Zhou
,
M. C. Y.
Huang
, and
C. J.
Chang-Hasnain
,
IEEE Photonics Technol. Lett.
20
,
434
(
2008
).
83.
Y.
Zhou
,
M. C. Y.
Huang
,
C.
Chase
,
V.
Karagodsky
,
M.
Moewe
,
B.
Pesala
,
F. G.
Sedgwick
, and
C. J.
Chang-Hasnain
,
IEEE J. Select. Top. Quantum Electron.
15
,
1485
(
2009
).
84.
M.
Kim
,
A. M. H.
Wong
, and
G. V.
Eleftheriades
,
Phys. Rev. X
4
,
041042
(
2014
).
85.
S.
Keren-Zur
,
O.
Avayu
,
L.
Michaeli
, and
T.
Ellenbogen
,
ACS Photonics
3
,
117
(
2016
).
86.
D.
Lin
,
P.
Fan
,
E.
Hasman
, and
M. L.
Brongersma
,
Science
345
,
298
(
2014
).
87.
Y.
Yang
,
W.
Wang
,
P.
Moitra
,
I. I.
Kravchenko
,
D. P.
Briggs
, and
J.
Valentine
,
Nano Lett.
14
,
1394
(
2014
).
88.
N.
Yu
,
P.
Genevet
,
M. A.
Kats
,
F.
Aieta
,
J. P.
Tetienne
,
F.
Capasso
, and
Z.
Gaburro
,
Science
334
,
333
(
2011
).
89.
M.
Tymchenko
,
J. S.
Gomez-Diaz
,
J.
Lee
,
N.
Nookala
,
M. A.
Belkin
, and
A.
Alù
,
Phys. Rev. B
94
,
214303
(
2016
).
90.
S.
Sun
,
S. K.-Y.
Yang
,
C.-M.
Wang
,
T.-K.
Juan
,
W. T.
Chen
,
C. Y.
Liao
,
Q.
He
,
S.
Xiao
,
W.-T.
Kung
,
G.-Y.
Guo
,
L.
Zhou
, and
D. P.
Tsai
,
Nano Lett.
12
,
6223
(
2012
).
91.
X.-Y.
Jiang
,
J.-S.
Ye
,
J.-W.
He
,
X.-K.
Wang
,
D.
Hu
,
S.-F.
Feng
,
Q.
Kan
, and
Y.
Zhang
,
Opt. Express
21
,
30030
(
2013
).
92.
M.
Khorasaninejad
,
A. Y.
Zhu
,
C.
Roques-Carmes
,
W. T.
Chen
,
J.
Oh
,
I.
Mishra
,
R. C.
Devlin
, and
F.
Capasso
,
Nano Lett.
16
,
7229
7234
(
2016
).
93.
Z.
Ma
,
S. M.
Hanham
,
P.
Albella
,
B.
Ng
,
H. T.
Lu
,
Y.
Gong
,
S. A.
Maier
, and
M.
Hong
,
ACS Photonics
3
,
1010
(
2016
).
94.
A.
Pors
,
M. G.
Nielsen
,
R. L.
Eriksen
, and
S. I.
Bozhevolnyi
,
Nano Lett.
13
,
829
(
2013
).
95.
D.
Lu
and
Z.
Liu
,
Nat. Commun
3
,
1205
(
2012
).
96.
R.
Yang
,
W.
Zhu
, and
J.
Li
,
Opt. Express
22
,
2043
(
2014
).
97.
V. J.
Yallapragada
,
A. P.
Ravishankar
,
G. L.
Mulay
,
G. S.
Agarwal
, and
V. G.
Achanta
,
Sci. Rep.
6
,
19319
(
2016
).
98.
A.
Teklu
,
M. A.
Breazeale
,
N. F.
Declercq
,
R. D.
Hasse
, and
M. S.
McPherson
,
J. Appl. Phys.
97
,
84904
(
2005
).
99.
K.
Staliunas
,
Y. C.
Cheng
,
S.
Kicas
,
J.
Trull
,
C.
Cojocaru
,
M.
Peckus
,
R.
Vilaseca
,
R.
Drazdys
, and
K.
Staliunas
 et al., “
Flat focusing mirrors
,” in
2015 17th International Conference on Transparent Optical Networks
(ICTON, Budapest, 2015), pp.
1
4
.
100.
S.
Yang
,
T.
Xu
,
H.
Ruda
, and
M.
Cowan
,
Phys. Rev. B
72
,
75128
(
2005
).
101.
J.
Lee
,
M.
Tymchenko
,
C.
Argyropoulos
,
P.-Y.
Chen
,
F.
Lu
,
F. C.
Demmerle
,
G.
Boehm
,
M.-C.
Amann
,
A.
Alù
, and
M. A.
Belkin
,
Nature
511
,
65
(
2014
).
102.
G.
Li
,
S.
Chen
,
P.
Nitipat
,
B.
Reineke
,
P. W. H.
Wong
,
E. Y. B.
Pun
,
K. W.
Cheah
,
T.
Zentgraf
, and
S.
Zhang
,
Nat. Mater.
14
,
607
(
2015
).
103.
R. L.
Fork
,
O. E.
Martinez
, and
J. P.
Gordon
,
Opt. Lett.
9
,
150
(
1984
).
104.
Y. A.
Vlasov
and
S. J.
McNab
,
Opt. Express
12
,
1622
(
2004
).

Supplementary Material

You do not currently have access to this content.