U.S. patent application number 13/456316 was filed with the patent office on 2012-11-01 for three-dimensional coherent plasmonic nanowire arrays for enhancement of optical processes.
Invention is credited to Joshua D. Caldwell, Orest J. Glembocki, Sharka M. Prokes, Ronald W. Rendell.
Application Number | 20120273662 13/456316 |
Document ID | / |
Family ID | 47067190 |
Filed Date | 2012-11-01 |
United States Patent
Application |
20120273662 |
Kind Code |
A1 |
Caldwell; Joshua D. ; et
al. |
November 1, 2012 |
THREE-DIMENSIONAL COHERENT PLASMONIC NANOWIRE ARRAYS FOR
ENHANCEMENT OF OPTICAL PROCESSES
Abstract
A plasmonic grating sensor having periodic arrays of vertically
aligned plasmonic nanopillars, nanowires, or both with an
interparticle pitch ranging from .lamda./8-2.lamda., where .lamda.
is the incident wavelength of light divided by the effective index
of refraction of the sample; a coupled-plasmonic array sensor
having vertically aligned periodic arrays of plasmonically coupled
nanopillars, nanowires, or both with interparticle gaps sufficient
to induce overlap between the plasmonic evanescent fields from
neighboring nanoparticles, typically requiring edge-to-edge
separations of less than 20 nm; and a plasmo-photonic array sensor
having a double-resonant, periodic array of vertically aligned
subarrays of 1 to 25 plasmonically coupled nanopillars, nanowires,
or both where the subarrays are periodically spaced at a pitch on
the order of a wavelength of light.
Inventors: |
Caldwell; Joshua D.;
(Accokeek, MD) ; Glembocki; Orest J.; (Alexandria,
VA) ; Prokes; Sharka M.; (Columbia, MD) ;
Rendell; Ronald W.; (Washington, DC) |
Family ID: |
47067190 |
Appl. No.: |
13/456316 |
Filed: |
April 26, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61478987 |
Apr 26, 2011 |
|
|
|
Current U.S.
Class: |
250/214.1 |
Current CPC
Class: |
G01N 21/658
20130101 |
Class at
Publication: |
250/214.1 |
International
Class: |
G01J 1/42 20060101
G01J001/42 |
Claims
1. A plasmonic grating sensor, comprising vertically aligned
periodic arrays of plasmonic nanopillars, nanowires, or both
wherein there is an interparticle pitch that is between .lamda./8
and 2.lamda., where .lamda. is the incident wavelength of light
divided by the effective index of the sample used to stimulate the
device.
2. The plasmonic grating sensor of claim 1, wherein the
nanopillars, nanowires, or both comprise silver, gold, aluminum,
copper, or other metal used for its plasmonic properties or any
combination thereof.
3. The plasmonic grating sensor of claim 1, wherein the
nanopillars, nanowires, or both comprise a core-shell nanostructure
where a semiconductor or dielectric nanowire or nanopillar is
coated with a metal film.
4. A coupled-plasmonic array sensor, comprising vertically aligned
periodic arrays of plasmonically coupled nanopillars, nanowires, or
both wherein interparticle gaps small enough to enable overlap
between the evanescent plasmonic fields between two neighboring
nanoparticles, typically requiring edge-to-edge separations that
are less than 20 nm.
5. The coupled-plasmonic array sensor of claim 4, wherein the
nanopillars, nanowires, or both comprise a metal that exhibits
plasmonic effects under optical illumination.
6. The coupled-plasmonic array sensor of claim 4, wherein the
nanopillars, nanowires, or both comprise silver, gold, aluminum,
copper, or other metal used for its plasmonic properties or any
combination thereof.
7. The coupled-plasmonic array sensor of claim 4, wherein the
nanopillars, nanowires, or both comprise a core-shell nanostructure
where a semiconductor or dielectric nanowire or nanopillar is
coated with a metal film.
8. A plasmo-photonic array sensor, comprising a double-resonant,
periodic array of vertically aligned subarrays comprising from 1 to
25 plasmonically coupled nanopillars, nanowires, or both.
9. The plasmo-photonic array sensor of claim 8, wherein the
subarrays are periodically spaced at a pitch an interparticle pitch
that is between .lamda./8 and 2.lamda., where .lamda. is the
incident wavelength of light divided by the effective index of
refraction of the sample used to stimulate the device.
10. The plasmo-photonic array sensor of claim 8, wherein the
nanopillar, nanowires, or both in the subarrays have interparticle
gaps sufficient to induce overlap of the plasmonic evanescent
fields from neighboring nanoparticles, typically requiring
edge-to-edge separations of less than 20 nm.
11. The plasmo-photonic array sensor of claim 8, wherein the
nanopillars, nanowires, or both comprise a metal that exhibits
plasmonic effects under optical illumination.
12. The plasmo-photonic array sensor of claim 8, wherein the
nanopillars, nanowires, or both comprise silver, gold, aluminum,
copper, or other metal used for its plasmonic properties, or any
combination thereof.
13. The plasmo-photonic array sensor of claim 8, wherein the
nanopillars, nanowires, or both comprise a core-shell nanostructure
where a semiconductor or dielectric nanowire or nanopillar is
coated with a metal film.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This Application claims the benefit of U.S. Provisional
Application 61/478,987 filed on Apr. 26, 2011 by Joshua D. Caldwell
et al. entitled "THREE-DIMENSIONAL COHERENT PLASMONIC NANOWIRE
ARRAYS FOR ENHANCEMENT OF OPTICAL PROCESSES," the entire contents
of which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention relates generally to enhancing optical
processes and more specifically to plasmonic nanowire arrays for
enhancement of optical processes.
[0004] 2. Description of the Prior Art
[0005] Optical processes such as Raman scattering and fluorescence
are very useful in identifying materials of interest from their
optical or vibrational signatures. However, for trace levels (ppm
or lower) of chemical species these processes are typically too
weak to detect without some method of enhancing the optical process
(signal level). In addition, the light scattered via the Raman
process or fluoresence emission is incoherent, thus the light is
scattered or emitted into a broad, diffuse hemisphere. This further
adds to reduced efficiency in the collection aspect of any probing
system.
[0006] The problem of optically detecting the presence of trace
levels of materials can be addressed by using nanotextured
plasmonic materials, most commonly metals such Ag, Au, Cu or Al, to
name a few, which develop surface plasmon resonances where optical
stimulation (incident light) at the resonant frequency (wavelength)
can stimulate surface plasmons. Surface plasmons are resonant
oscillations of conduction electrons within a metal or
semiconductor that once excited induce very large local electric
fields that in turn increase the scattering intensity at the
surface, enhance the optical absorption of materials and/or sensors
and photovoltaics and provide increases in the efficiency and
intensity of optical emitters. One such benefit of these various
enhancements is the surface enhanced Raman scattering (SERS)
effect, where enhancements as high as 10.sup.6 from the individual
nanoparticles and as high as 10.sup.14 from clusters of two or more
nanoparticles have been reported. In addition, fluorescence
processes are also enhanced (SEFS) by as much as 10.sup.4.
[0007] Previous work in SERS and SEFS-based sensors for the
detection of trace amounts of chemicals, biochemical compounds,
explosive or chemical and biological warfare agents have
predominantly used collections of randomly arranged, isolated
plasmonic nanoparticles such as colloids or nanowires, aggregations
of such nanoparticles and/or patterned arrangements of sets of
closely-spaced nanoparticles (<20 nm gap), where interparticle
plasmonic coupling may be induced, with each set being separated
from its neighbor by relatively large distances. In this latter
case, large local plasmonic fields result, which within small
(.about.5-10 nm) regions have extremely high SERS/SEFS enhancement
factors. While such approaches are ideal for near-field
measurements such as NSOM or single molecule detection via SERS or
SEFS, this also leads to very low uniformity and reproducibility on
a large-area substrate. It is such large area substrates that are
most likely to be needed if SERS/SEFS based sensors are to attain a
market in homeland security, bio-/medical and/or defense
applications.
[0008] The current state of the art in surface-plasmon resonant
structures and SERS or SEFS substrates is focused on the
fabrication of uniform distributions of nanoparticles such a
nanospheres or the fabrication of metal-coated openings in the
substrate that are produced by Mesophotonics Inc. These substrates
are designed to maximize the SERS and/or SEFS intensity, but do not
attempt to benefit from plasmonic coupling between closely-spaced
nanostructures, long-range plasmonic coupling from large arrays of
such nanostructures or from patterning these structures into a 1D
or 2D diffraction gratings, whereby providing directionality and
reduced divergence for the emitted and/or scattered
irradiation.
BRIEF SUMMARY OF THE INVENTION
[0009] The aforementioned problems are overcome in the present
invention which provides a plasmonic grating sensor having
vertically aligned periodic arrays of plasmonic nanopillars,
nanowires, or both with an interparticle pitch from 200 to 2000 nm;
a near-field coupled-plasmonic array sensor having vertically
aligned periodic arrays of plasmonically coupled nanopillars,
nanowires, or both with interparticle gaps small enough to induce
overlapping evanescent plasmonic fields between neighboring
particles (typically with edge-to-edge separations of <20 nm)
within a large area, multiple particle architecture; and a
plasmo-photonic array sensor having a double-resonance, periodic
array of plasmonic nanoparticles distributed in subarrays of 1 to
25 plasmonically coupled nanopillars, nanowires, or other
nanoparticles such as colloids where the subarrays are periodically
spaced at a pitch on the order of a wavelength of light
(.lamda./8<pitch<3.lamda.; .lamda.=incident wavelength).
[0010] These and other features and advantages of the invention, as
well as the invention itself, will become better understood by
reference to the following detailed description, appended claims,
and accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] FIG. 1 is a schematic representation of three embodiments of
the present invention: (a) plasmonic 2D grating arrays, (b)
plasmonically-coupled arrays, and (c) plasmo-photonic arrays.
[0012] FIG. 2 is SEM images of 170 nm tall Si nanopillars (a) prior
to and (b) following Ag deposition via electron beam evaporation of
a silver source.
[0013] FIG. 3 is SEM images of (a) Au dots deposited via nanosphere
lithography and (b) ZnO nanowires grown via VLS using the Au dot
pattern in (a) as a catalyst.
[0014] FIG. 4 shows SERS intensity of the 998 cm.sup.-1 mode (C-H
wag) of a self-assembled monolayer of thiophenol on a Au-coated
(e-beam evaporation) Si nanopillar array as a function of
nanopillar periodicity (pitch).
[0015] FIG. 5 presents contour plots of the SERS enhancement factor
from a series of arrays as a function of interpillar gap (x-axis)
and Si nanopillar diameter (y-axis) for a self-assembled monolayer
of thiophenol on Ag-coated Si nanopillar arrays detected at (a)
457, (b) 488, (c) 514, (d) 532, (e) 633 and (f) 785 nm incident
excitation. The dark regions inside white lines indicate arrays
exhibiting high SERS enhancement, and the dark regions not enclosed
in white lines correspond to arrays with low enhancement. The line
to the right hand side of each plot indicates the optimal diameter
for the SERS response.
[0016] FIG. 6 shows numerical calculations of the expected SERS
enhancement as a function of incident wavelength for 150 nm
Au-coated Si nanopillars with interpillar gaps of 20, 15, 10, and 5
nm (from bottom to top)
[0017] FIG. 7 is a top view of the spatial distributions of the
calculated SERS enhancement within an array of 100 nm solid silver
nanowires with an interwire gap of 8 nm of an (a) perfect periodic
array and (b) a periodic array with one nanowire missing.
DETAILED DESCRIPTION OF THE INVENTION
[0018] The present invention pertains to three arrayed plasmonic
architectures that solve the need for a large area sensor with high
signal uniformity and reproducibility, while maintaining high
average SERS enhancement factors. The first structure is the
plasmonic-grating sensor, which comprises periodic arrays of
plasmonic nanoparticles with the interparticle pitch being on the
order of a wavelength of light within the medium
(.lamda./n.sub.eff; n.sub.eff is the effective index of refraction
for the material chosen) in the UV-Vis-NIR region of the
electromagnetic spectrum (200-2000 nm). The second structure is the
coupled-plasmonic array sensor, which comprises periodic arrays of
plasmonically coupled nanopillars/nanowires with interparticle gaps
small enough to enable overlap between the evanescent fields from
neighboring plasmonic nanoparticles, which typically requires
edge-to-edge separations between the nanoparticles of less than 20
nm The third structure is the plasmo-photonic array sensor, which
is a double-resonant, periodic array of nanoparticles where small
subarrays (1-25 nanowires) of coupled plasmonic nanoparticles that
are periodically spaced at a pitch on the order of a wavelength of
light. This last concept is designed to both induce plasmonic
coupling between the closely spaced nanoparticles in a subarray,
which in turn are spaced at fractions of the wavelength of light to
create a two-dimensional grating. This double resonant structure
enables the user to benefit from the large field enhancements (i.e.
large Raman or fluorescence signal response) due to the coupled
plasmonic subarrays, while focusing and directing the scattered or
emitted radiation at a preferred angle with respect to the
substrate surface. This latter benefit removes the divergence of
the optical signal, enabling the response to be collected more
efficiently at a distance. In the limit of an isolated pillar as
the subarray unit, this structure is the same as 1). A schematic of
the three sensor varieties discussed here are presented in FIG.
1(a)-(c). These sensors can be used as SERS- or SEFS-based sensors
or in more exotic optical devices, such as enhanced optical
collectors/photodetectors, enhanced emitters, wavelength
upconversion species, improved efficiency photovoltaics, or
magnetoplasmonic devices (where a magnetic medium is present) to
name a few.
[0019] An important component of all of these structures is the
periodic array of vertically aligned nanopillars/nanowires. These
can be constructed of either solid metal (Ag, Au, Al, Cu, etc.) or
core-shell nanostructures, where a semiconductor or dielectric
nanowire or nanopillar is overcoated with a thin metal film. The
metal in both cases is any metal that exhibits plasmonic effects
under optical illumination. For the purpose of the present
invention, nanowires are considered semiconductor, dielectric or
metal rods that are fabricated via growth methods
(vapor-liquid-solid, chemical vapor deposition, electrodeposition,
etc.), while nanopillars consist of rods that are formed via
etching processes (reactive ion etching, chemically-enhanced
etching, photo-chemical etching, wet-chemical etching, etc.). In
the context of the metal coating of the core-shell structures,
various coating morphologies and conformalities can be attained by
modifying the deposition process, these include, but are not
limited to electron beam evaporation or RF sputtering of a metal
source, chemical vapor deposition or atomic layer deposition, or
electro or electroless deposition. Presented in FIG. 2 are SEM
images of Si nanopillars fabricated through a mix of electron beam
lithography and reactive ion etching into a square periodic pattern
(a) prior to metal deposition, and after metal deposition via (b)
electron beam evaporation of Ag. Presented in FIG. 3 are SEM images
of (a) gold dots arranged in a hexagonal periodic pattern attained
through nanosphere lithography on a sapphire substrate and (b) of
vertical ZnO nanowires grown via the VLS process using the periodic
pattern of gold dots as the growth catalyst to define the position
and diameter of the nanowires. These two approaches represent two
methods of the many that are included under this effort for
fabricating periodic arrays of vertical nanopillars and nanowires,
with other combinations of these approaches also being valid
methods for attaining the same end result.
Plasmonic-Grating Sensor
[0020] The plasmonic-grating sensor (see FIG. 1(a)) relies on the
plasmonic fields present at each nanoparticle for providing the
enhancement of the optical process of interest. The array approach
provides a two-fold benefit, with the plasmonic particles providing
the enhancement of the optical process of interest and the 2D
grating established by the nanoparticle periodicity providing a
directionality to the emitted, scattered or transmitted light,
effectively taking an optical process that would be emitted into a
4.pi. solid angle, and instead focusing it into a tight solid angle
for increased photon density, and therefore increased signal
intensity. It has been shown for one specific geometry consisting
of Au-coated Si nanopillars that defining the interparticle pitch
to approximately one full wavelength leads to the largest
enhancement factors possible for a given architecture at normal
incidence. SERS results supporting this are presented in FIG. 4 for
Au-coated Si nanopillars with a self-assembled monolayer of benzene
thiol at 785 nm incident. Note that the peak SERS response as a
function of array periodicity (pitch) is observed at between 750
and 800 nm, which is very close to the incident wavelength.
Furthermore, we have shown that the optimal response of the sensor
for a given wavelength is dictated primarily by the
nanopillar/nanowire diameter or width, as shown in FIG. 5(a)-(f),
where contour plots of the SERS enhancement factor from each of the
100.times.100 nanopillar arrays in a given Ag-coated Si-nanopillar
array sample are presented as a function of nanopillar diameter and
interpillar gap at (a) 457, (b) 488, (c) 514, (d) 532, (e) 633 and
(f) 785 nm incident excitation. Note that the optimal response is
observed at a small range of diameters and that the peak response
shifts to smaller diameters as the incident wavelength is reduced.
As shown in the aforementioned figures, the SERS enhancement
factors measured from these types of arrays range from the
10.sup.5-10.sup.8 range, depending on the structural parameters and
incident wavelength, with an optimal response of
1.1.times.10.sup.8.
Coupled-Plasmonic Array Sensor
[0021] The coupled-plasmonic array sensor (see FIG. 1(b)) relies
upon interparticle plasmonic coupling between adjacent
nanopillars/nanowires within the array for providing the
enhancement of the optical process of interest. Interparticle
plasmonic coupling has two effects; 1) it induces a red-shift in
the spectral position of the surface plasmon resonance (SPR), which
dictates the wavelength where the optimal performance will be
observed and 2) it creates significantly larger plasmonic fields,
which in turn lead to dramatic enhancements of the optical process
of interest with respect to the isolated plasmonic particles
discussed for the plasmonic-grating sensor. Presented in FIG. 6 are
SERS enhancement curves calculated using COMSOL Multiphysics 4 for
semi-infinite arrays of periodically-spaced, Au-coated Si
nanopillars with interparticle separations of 5, 10, and 20 nm Note
that as the particles move closer together that the intensity of
the various peaks in the SPR spectra are increased, most notably
the most intense mode near 800 nm. There is also the aforementioned
red-shift in the peak position, as expected, when the nanopillars
are moved closer to one another. With respect to the
plasmonic-grating sensor, the coupled-plasmonic array sensor can
provide significantly larger enhancements of the optical processes
of interest, while enabling some fine control over the spectral
position of the SPR peaks and therefore upon the wavelength for the
optimal response. This effect was shown recently by the inventors
in Si nanopillar arrays overcoated with Ag via the PEALD process,
where arrays with separations between particles of approximately 2
nm were found to lead to 1-2 orders of magnitude increase in the
SERS enhancement beyond what was observed from widely separated
arrays. However, this comes at the cost of losing the ability to
redirect the light into a small solid angles that is enabled via
the presence of a 2D grating and also involves more complex
lithographic and metal deposition efforts. While the nanopillars in
these structures are in periodic arrays, the interparticle
separation and nanopillar size dictates that the incident light
cannot distinguish the particles from each other, and thus the
array is `seen` as an effective medium. From such structures
enhancement factors >10.sup.8 have been observed at various
wavelengths.
3) Plasmo-Photonic Array Sensor
[0022] A method for attaining the optimal plasmonic enhancement,
while still providing the 2D grating structure needed to redirect
the emitted/scattered light into a small solid angle can be
attained via the plasmo-photonic approach presented in FIG. 1(c).
In this case, the subarrays would feature either periodically- or
randomly-spaced nanoparticles with interparticle separations of
<20 nm. This provides the means for enhancing the optical
process of interest (e.g. SERS, SEFS, etc. In order to attain the
desired directionality of the emitted/scattered light, these
subarrays are periodically spaced in one or two dimensions to
create a diffraction grating of plasmonically-coupled
nanoparticles. By varying the periodicity (pitch) of the subarrays,
one can control the angle at which the enhanced light will be
emitted/scattered. By controlling the nanoparticle structure
(nanowire/nanopillar type, diameter, height; metal type and
thickness; etc.) one can control the overall enhancement and the
spectral position of the optimal response. This effectively
requires a double-resonant structure where the wavelength for the
desired diffraction response and the optimal plasmonic enhancement
coincide.
[0023] In addition to the simple arrays that utilize identical
nanowires as components, we can also envision several different
scenarios that would change the type of periodicity and the type of
unit cell. A more compact geometry would entail for example a
hexagonal structure with close packing where neighboring rows are
displaced from each other by half the period. This would produce a
structure that has a higher density of nanostructures.
[0024] In addition to changing the symmetry of the array it is
possible to modify a nanostructure array and repeat that
modification in a periodic fashion. The effects of removing a
nanowire from a subarray is shown in FIG. 7, where COMSOL
simulations of two arrays of solid silver nanowires where (a) no
nanowires are missing and (b) the central nanowire has been
removed. By simply removing a single nanowire, the electric fields
around the remaining wires are thus modified. The fields around the
wires directly above and below the missing structure have new
orthogonal fields that are increased in intensity in the direction
of the incident light polarization. In fact, as FIG. 7(b)
indicates, the plasmonic fields are actually increased by a factor
of two in comparison to the fields present within the perfect array
[FIG 7(a)]. This approach can be expanded by also changing the
relative size, shape or material of a given nanostructure within
the otherwise unchanged array or subarray in any of the three
sensor structures presented.
[0025] The plasmonic grating, plasmonically-coupled and
plasmo-photonic sensor arrays described above can be realized with
a variety of different components. As noted above, the nanowires
can be formed from pure metals that exhibit plasmonic effects such
as Au, Ag, Cu or Al or from dielectric/semiconductor core-shell
structures that are coated with a thin plasmonically-active metal
shell. The dielectric cores can be Si, SiO.sub.2, ZnO,
Ga.sub.2O.sub.3, GaN, SiC or virtually any other dielectric or
semiconducting material that can be fabricated or grown into such
closely-spaced, periodic arrays. The nanostructures can be created
via standard nanostructure growth techniques or via wet-chemical or
dry etching of an initial prepatterned substrate. In all of these
cases, the metal can be deposited via standard or exotic metal
deposition techniques such as e-beam evaporation, sputtering,
atomic layer deposition, electro- or electroless deposition,
chemical vapor deposition, etc.
[0026] Between the various fabrication techniques (nanowire growth
and nanopillar fabrication), the substrates on which these arrays
are fabricated are not limited except by fabrication restrictions.
Transparent substrates are appropriate for circumstances in which
illumination from below or through sample detection is required,
while a highly reflecting substrate (Si or double-bragg reflector)
would be more appropriate to situations that require attaining a
reflected return signal such as in standoff sensing or tagging,
tracking and locating schemes.
[0027] In addition to sensor arrays, such a method could be used to
provide enhancements and directionality to emitters such as
light-emitting or laser diodes, where either the core of the
nanostructure itself or the underlying substrate is used as the
source of the emission and the array is designed such that the
plasmon resonance of the subarrays will enhance either the
absorption of an incident exciting light source or the
photoluminescence emission process. For example, in the latter
case, one could envision an array of ZnO nanowire emitters coated
with silver. Such nanowires have both an ultraviolet bandedge
emission and a blue defect band emission. If a blue emitter was
desired, one could design the SPR of the subarrays to be peaked at
a wavelength within the bandedge emission, thus enabling the
initial excitation of both sources via electrical processes, while
subsequently reabsorbing a significant portion of the bandedge
emission. This reabsorbed energy would then induce further defect
band emission, enhancing the output. In addition, such a process
could also be created via a double or multiple quantum well or
quantum dot structures with two distinct band gaps (i.e.
absorption/emission characteristics) with the plasmonic array tuned
to enhance the absorption of the wider gap structure that would
emit and in turn optically pump the lower gap system, thereby
leading again to enhanced emission. One could also envision
tailoring the plasmon resonance to be located at a desired
wavelength within the bandwidth of the defect band emission,
simultaneously increasing the emission intensity via the
surface-enhanced fluorescence process and also narrowing the
bandwidth of the emission due to the relatively narrow SPR with
respect to the emission line. It is possible to use two arrays in
concert for sensing applications, one at the sensor side used to
enhance the intensity of the emitted or scattered light and another
on the detecting side to enhance the collection of this irradiated
signal. The matched sensing elements would increase the collection
efficiency by using the arrays to match the spectral and angular
characteristic of the return signal. The additional enhancement on
the sensing end would aid in the signal to noise of the detection
system. Finally, one can envision a wide array of applications in
metamaterials, with similar structures serving as methods for
attaining very small focused spots of emitted light in the near
field (superlensing effects) or cloaking for example.
[0028] The above descriptions are those of the preferred
embodiments of the invention. Various modifications and variations
are possible in light of the above teachings without departing from
the spirit and broader aspects of the invention. It is therefore to
be understood that the claimed invention may be practiced otherwise
than as specifically described. Any references to claim elements in
the singular, for example, using the articles "a," "an," "the," or
"said," are not to be construed as limiting the element to the
singular.
* * * * *