We study the interference of evanescent electromagnetic waves generated from multi-slits in a metal film and demonstrate the anomalous bending of light at infrared frequencies due to negative refraction. We also calculate the diffraction of an incident plane electromagnetic waves by a metallic film with an arbitrary linear array of slits, slit separation, and slit dielectric material. In contrast to a double-convex shaped quartz lens, we show that a planar metallic film with a one-dimensional slit array can also focus polarized light in the near-field region when either the slit width or the slit dielectric material becomes spatially nonuniform.

1.
Z.
Sun
and
H. K.
Kim
, “
Refractive transmission of light and beam shaping with metallic nano-optic lenses
,”
Appl. Phys. Lett.
85
,
642
644
(
2004
).
2.
G.
Gumbs
and
D. H.
Huang
,
Properties of Interacting Low-Dimensional Systems
(
Wiley-VCH
,
Weinheim, Germany
,
2011
), Chaps. 4 and 5.
3.
H.
Shi
,
C.
Wang
,
C.
Du
,
X.
Luo
,
X.
Dong
, and
H.
Gao
, “
Beam manipulating by metallic nano-slits with variant widths
,”
Opt. Express
13
,
6815
6820
(
2005
).
4.
L.
Verslegers
,
P. B.
Catrysse
,
Z.
Yu
,
J. S.
White
,
E. S.
Barnard
,
M. L.
Brongersma
, and
S.
Fan
, “
Planar lenses based on nanoscale slit arrays in a metallic film
,”
Nano Lett.
9
,
235
238
(
2009
).
5.
Y.
Oshikane
,
T.
Kataoka
,
M.
Okuda
,
S.
Hara
,
H.
Inoue
, and
M.
Nakano
, “
Observation of nanostructure by scanning near-field optical microscope with small sphere probe
,”
Sci. Technol. Adv. Mater.
8
,
181
185
(
2007
).
6.
S.
Durant
,
Z.
Liu
,
J. M.
Steele
, and
X.
Zhang
, “
Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit
,”
J. Opt. Soc. Am. B
23
,
2383
2392
(
2006
).
7.
H.
Lee
,
Z.
Liu
,
Y.
Xiong
,
C.
Sun
, and
X.
Zhang
, “
Design, fabrication and characterization of a Far-field Superlens
,”
Solid State Commun.
146
,
202
207
(
2008
).
8.
W.
Srituravanich
,
N.
Fang
,
C.
Sun
,
Q.
Luo
, and
X.
Zhang
, “
Plasmonic nanolithography
,”
Nano Lett.
4
,
1085
1088
(
2004
).
9.
J.
Mai
,
L.
Fok
,
H.
Gao
,
X.
Zhang
, and
M.
Poo
, “
Axon initiation and growth cone turning on bound protein gradients
,”
J. Neurosci.
29
,
7450
7458
(
2009
).
10.
Y.
Zhang
,
V.
Yazdanpanah
,
M.
Yang
,
M.
Ozkan
, and
C. S.
Ozkan
, “
Normal and cancer breast epithelial cells endocytosis study of nanoparticles by combined AFM and NSOM microscopy
,” in Proceedings of the 7th IEEE International Confernce on Nanotechnology,
2007
, pp.
1028
1032
.
11.
D.
Zahor
,
A.
Radko
,
R.
Vago
, and
L. A.
Gheber
, “
Organization of mesenchymal stem cells is controlled by micropatterned silicon substrates
,”
Mater. Sci. Eng., C
27
,
117
121
(
2007
).
12.
M. J.
Rust
,
M.
Bates
, and
X.
Zhuang
, “
Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)
,”
Nat. Methods
3
,
793
796
(
2006
).
13.
E.
Hecht
,
Optics
, 2nd ed. (
Addison-Wesley
,
Reading, MA
,
1987
), pp.
128
149
.
14.
B. I.
Yakobson
,
A.
LaRosa
,
H. D.
Hallen
, and
M. A.
Paesler
, “
Thermal/optical effects in NSOM probes
,”
Ultramicroscopy
61
,
179
185
(
1995
).
15.
B.
Baumeier
,
T. A.
Leskova
, and
A. A.
Maradudin
, “
Transmission of light through a thin metal film with periodically and randomly corrugated surfaces
,”
J. Opt. A, Pure Appl. Opt.
8
,
S191
S207
(
2006
).
16.
T. A.
Leskova
,
A. A.
Maradudin
, and
W.
Zierau
, “
Synthetic spectra from rough surface scattering
,”
Waves Random Complex Media
16
,
531
544
(
2006
).
17.
R.
Mittra
and
S. W.
Lee
,
Analytical Techniques in the Theory of Guided Waves
(
McMillan and Company
,
New York
,
1971
).
18.
L.
Wendler
and
T.
Kraft
, “
Theory of grating-coupler-assisted infrared spectroscopy of lower-dimensional electron systems: Local optics of anisotropic multilayer systems with grating
,”
Physica B
271
,
33
98
(
1999
).
19.
D. H.
Huang
,
C.
Rhodes
,
P. M.
Alsing
, and
D. A.
Cardimona
, “
Effects of longitudinal field on transmitted near field in doped semi-infinite semiconductors with a surface conducting sheet
,”
J. Appl. Phys.
100
,
113711
(
2006
).
20.
D. H.
Huang
,
G.
Gumbs
,
P. M.
Alsing
, and
D. A.
Cardimona
, “
Nonlocal mode mixing and surface-plasmon-polariton-mediated enhancement of diffracted terahertz fields by a conductive grating
,”
Phys. Rev. B
77
,
165404
(
2008
).
21.
V. M.
Serdyuk
, “
Diffraction of a plane electromagnetic wave by a slot in a conducting screen of arbitrary thickness
,”
Tech. Phys.
50
,
1076
1083
(
2005
).
22.
V. M.
Serdyuk
, “
Exact solutions for electromagnetic wave diffraction by a slot and strip
,”
AEU, Int. J. Electron. Commun.
65
,
182
189
(
2011
).
23.
T. W.
Ebbsen
,
H. J.
Lezec
,
H. F.
Ghaemi
,
T.
Thio
, and
P. A.
Wolff
, “
Extraordinary optical transmission through subwavelength hole arrays
,”
Nature (London)
391
,
667
669
(
1998
).
24.
H. F.
Ghaemi
,
T.
Thio
,
D. E.
Grupp
,
T. W.
Ebbesen
, and
H. J.
Lezec
, “
Surface plasmons enhance optical transmission through subwavelength holes
,”
Phys. Rev. B
58
,
6779
6782
(
1998
).
25.
T.
Thio
,
H. F.
Ghaemi
,
H. J.
Lezec
,
P. A.
Wolff
, and
T. W.
Ebbesen
, “
Surface-plasmon-enhanced transmission through hole arrays in Cr films
,”
J. Opt. Soc. Am. B
16
,
1743
1748
(
1999
).
26.
L. D.
Wellems
,
D. H.
Huang
,
T. A.
Leskova
, and
A. A.
Maradudin
, “
Optical spectrum and electromagnetic-field distribution at double-groove metallic surface gratings
,”
J. Appl. Phys.
106
,
053705
(
2009
).
27.
B.
Hou
and
W.
Wen
, “
Transmission resonance of electromagnetic wave through metallic gratings: phase and field characterization
,”
Opt. Express
16
,
17098
17106
(
2008
).
28.
B.
Lee
,
S.
Kim
,
H.
Kim
, and
Y.
Lim
, “
The use of plasmonics in light beaming and focusing
,”
Prog. Quantnum Electron.
34
,
47
87
(
2010
).
29.
F. J.
Garcia-Vidal
,
L.
Martin-Moreno
,
T. W.
Ebbesen
, and
L.
Kuipers
, “
Light passing through subwavelength aperatures
,”
Rev. Mod. Phys.
82
,
729
787
(
2010
).
30.
C.-C.
Chang
,
Y. D.
Sharma
,
Y.-S.
Kim
,
J. A.
Bur
,
R. V.
Shenoi
,
S.
Krishna
,
D. H.
Huang
, and
S.-Y.
Lin
, “
A surface plasmon enhanced infrared photodetector based on InAs quantum dots
,”
Nano Lett.
10
,
1704
1709
(
2010
).
31.
S.
Pilevar
,
W. A.
Atia
, and
C. C.
Davis
, “
Reflection near-field scanning optical microscopy: an interferometric approach
,”
Ultramicroscopy
61
,
233
236
(
1995
).
32.
J. D.
Jackson
,
Classical Electrodynamics
, 2nd ed. (
John Wiley & Sons
,
New York
,
1975
), Chap. 16.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.