Abstract

We design plano–concave silicon lenses with coupled gradient-index plasmonic metacoatings for ultrawide apertured focusing utilizing a reduced region of 20λ2. The anomalous refraction induced in the planar input side of the lens and in the boundary of the wavelength-scale focal region boosts the curvature of the emerging wavefront, thus significantly enhancing the resolution of the tightly focused optical wave. The formation of a light tongue with dimensions approaching those of the concave opening is here evidenced. This scheme is expected to have potential applications in optical trapping and detection.

© 2016 Optical Society of America

1. INTRODUCTION

Tight focusing of electromagnetic waves is essential to a myriad of applications, such as photolithography and optical trapping, typically using dielectric thick lenses of high numerical aperture (NA). However, the unceasing miniaturization and integrability of photonic devices imposes severe restrictions on the implementation of such sorts of bulky pieces. In this context, concave positive lenses composed of meta-atoms to change the sign of its macroscopic refractive index might be incorporated in high-NA focusing platforms within a reduced region [14]. Epsilon-near-zero plano–concave lenses also prove a good performance prompted by the phenomenon of energy squeezing [5,6]. In particular, such architectures cannot operate at optical frequencies mainly due to material losses and demanding fabrication challenges.

Advances in current techniques for nanofabrication, some of them based on plasmonics, have opened new prospects for producing compact, planar focusing systems. Plasmonic flat lenses enabling a plane-wave efficient shaping into an output converging wavefront within a subwavelength interaction space have been developed using arrays of nanoholes [7,8], nanoslits [9,10], nanoparticles [11,12], corrugations [13], and nanoantennas [14,15]. In the previous examples, the mechanism set behind the control of the scattered light relies on the suitable spatial distribution of engineered, subwavelength phase shifters included on the active surface [16]. Therefore, a critical design aspect of the focusing device is the choice of the elementary scatterers for obtaining the required phase distribution.

In the so-called metasurfaces, Mie resonances lead to controllable phase discontinuities, which are applied to administrate the beam shaping [15]. Alternatively, the phase of the electromagnetic field may change after passing through a subwavelength metal–dielectric structure on the basis of a modal coupling to the external radiation. Such a phenomenon is suitably explained in terms of an effective refractive index, and can be achieved with extremely high performance in transmission [17]. For instance, a set of metallic slits with controllable width can locally tune the effective index of refraction of the guided plasmonic modes [18]. These sorts of ultrathin nanostructures are here coined as graded-index metacoatings.

Flat metalenses offer some advantages accessibly to manufacture and integrate in complex devices; however, they suffer from severe geometrical restrictions to attain extremely high numerical apertures [19,20]. An alternative design relies on sculpturing a concave surface. In such a manner an aplanatic metasurface patterned on a spherical substrate has been proposed to focus light without coma and spherical aberrations [21]. The concept of metamaterials with engineered dispersion in curvilinear coordinates, with coaxial and concentric geometries, has been extensively exploited, for instance, in hyperlensing [2224]

Previously we presented a design of nonplanar metacoatings composed of subwavelength metal–dielectric arrays to accelerate optical waves in the near field [2527]. These nanostructures allow us to grade ultrahigh indices of refraction together with high transmissivity, demonstrating controllable phase and amplitude responses over subwavelength propagation ranges for TM-polarized waves. Here, we utilize such a basic concept to engineer gradient-index ultrathin coatings, in a parallelizable assembly, as focusing elements with high efficiency. In fact, advantages of cascading a set of metasurfaces have been previously reported, for instance, as a polarization rotator [28], as an efficient cylindrical-vector-vortex beam generator [29], and as a polarization-controlled lens [30]. Conveniently implemented over the two sides of a plano–concave (divergent) dielectric microlens, we achieve miniaturized lenses with aberration-free high-numerical-aperture focalization.

2. LENS DESIGN

The medullary component of our focusing device is a bulky dielectric lens, which, without loss of generality, we consider as immersed in air. Light impinges over the flat surface of the lens, and the exit spherical surface has a short radius R>0, whose center is set at a given point C, as depicted in Fig. 1. Here we consider that R remains in the scale of the wavelength, although our approach is not strictly restricted to such a regime. Under certain circumstances, this arrangement enables a high-aperture focusing of light emerging from the concave surface of the lens. From the geometrical point of view, the optical power is carried by the second surface of the thick lens characterized by a paraxial focal length,

f=R1n,
where n denotes the refractive index of the lens. If n>1 as occurs in natural dielectric materials, the lens is divergent with negative focal length, f<0, disabling to focus light behind the concave surface, as illustrated in Fig. 1(a). Therefore, focusing is only available with a refractive index below the unity, which can be achieved by using metamaterials [6]. In the specific case of epsilon-near-zero metamaterials, setting n=0, light is focused at the center of curvature of the concave exit surface, as shown in Fig. 1(b) [5]. This arrangement has recently been demonstrated experimentally in microwave frequencies and presents fascinating characteristics, such as reduced aberrations in configurations with numerical apertures close to unity [31]. An increased numerical aperture might be achieved by means of negative-index plano–concave lenses, as shown in Fig. 1(c). However, thick negative-index metamaterials in the near-infrared and visible frequency range exhibit a deficient performance mainly due to material Ohmic losses and inhomogeneities scattering.

 

Fig. 1. Schematics based on optical rays of the focusing action of plano–concave dielectric lenses. (a) Transparent dielectrics with an index of refraction higher than unity lead to a diverging configuration. (b) An epsilon-near-zero metamaterial enables us to focus light at the center of curvature of the concave surface. (c) An increased numerical aperture is attained by using negative-index metamaterials. (d) Our proposal based on coupled metacoatings set at the entrance and exit surfaces of a transparent dielectric thick lens. A focused beam of semiaperture angle Ω will be generated by passing through the gradient-index flat metasurface. The converging wave field propagating inside the lens will be refocused at F by means of the active curved metacoating, having an increased semiaperture angle Ω.

Download Full Size | PPT Slide | PDF

Our approach is based on a transparent dielectric thick lens coated by graded-index ultrathin metasurfaces, as illustrated in Fig. 1(d). Therefore, material losses have a reduced impact in the lens performance. The coated metasurfaces, here coined metacoatings, are designed to compensate the negative optical power of the plano–concave dielectric lens. We propose a first metacoating set on the entrance flat surface to transform the incident plane wave into a spherical wave of center at F, coinciding with the center of curvature C of the concave surface in the lens. Such appropriate configuration reduces losses derived by reflections in the curved interface, and establishes a first numerical aperture in terms of the beam angle Ω. In order to even further increase the numerical aperture of the lens, a second metacoating is placed in the concave surface. A controlled focal shift a<R leads to a magnified far-field angle of the resulting converging wave [32]. As a result, the transmitted wave field will focus at F by free-space propagation, characterized by a numerical aperture NA=sin(Ω). Assuming that the focal point F of the coupled metacoating thick lens is located closer to the concave surface than F, that is, a=FF¯>0, the numerical aperture

NA=NA1+(a/R)22(a/R)cosΩ
is also higher than the numerical aperture NA=sinΩ of the single-coated lens [32]. Specifically NA reaches the unity when a=RcosΩ. Note that the transverse and on-axis resolutions are dependent on the overall numerical aperture of the focusing lens. In particular, this procedure leads to a critically improved axial resolution, which is determined by the inverse squared of the value of NA.

Next we design the gradient-index metasurfaces, which are overlaid on the lens surfaces, taking over the wavefront management of the incident plane wave. Without loss of generality, we will consider cylindrical lenses enabling a description of the problem in two dimensions. Note that the dielectric material of the thick lens having a refractive index n has a minor significance in the functioning of the focusing device. Following the Fermat’s principle by evaluating equal optical path lengths, a normally incident plane wave passing through the first flat metacoating will be focused at the point F, found at a distance f1 and transversally centered at y=0, provided that the phase shift produced by the gradient-index metasurface yields

φ1(y)=φ1(0)+nk(f1y2+f12),
where k=2π/λ is the wavenumber in vacuum, φ1(0) is an arbitrary phase, and y is the transverse coordinate indicating the distance from the optical axis. Assuming an ultrathin metacoating of width d, the gradient index is then given by n1(y)=φ1(y)/kd. Of course, this approach disregards multiple reflections produced at the metacoating facets, and a more rigorous treatment will be implemented below.

As mentioned above, the cylindrical metacoating set at the back of the thick lens has a center of curvature C that is located exactly at the focal point F. Note that the constraint R<f1 must be considered, where f1R stands for the vertex distance of the plano–concave lens. Therefore the wavefront of the impinging field remains concentric to the concave metacoating arriving at normal incidence. The induced phase shift on such a metasurface will reshape the incident wavefront by increasing its curvature. The field emerging from the nanolens then propagates in free space to focus at the point F that is shifted a length a toward the rear metacoating. The dephase induced by the cylindrical metasurface is [32]

φ2(θ)=φ2(0)+k[(Ra)R2+a22aRcosθ],
where φ2(0) is again an arbitrary phase term, and θ is the azimuthal coordinate as measured from C and determining the angle from the optical axis. In practical terms, φ2 will be operative in the range |θ|Ω. If the width of the back metacoating is again d, the gradient index is now given by n2(θ)=φ2(θ)/kd.

To illustrate the impact of ideal metacoatings, Fig. 2(a) shows the intensity distribution of the magnetic field, |H|2, produced by a nonuniform magnetic surface current set on the front lens facet and having a phase distribution governed by the expression given in Eq. (3). The numerical simulations are calculated for a silicon plano–concave nanolens (n=3.69) of radius R=3  μm at a wavelength λ=800  nm by using COMSOL Multiphysics, which is a finite element analysis software environment for modeling and simulation of electromagnetic systems. In Fig. 2(a), the length of the surface current is 8 μm, and it is designed to focus light at a distance f1=3.2  μm. In this way we generate a focused field around the center of curvature C with semiaperture angle Ω=51.3°. The effect of the back metacoating on the nanolens focal field is simulated in Fig. 2(b), where we introduce a cylindrical surface current of curvature center set at C and with semiaperture angle Ω. Additionally, a phase distribution of the surface current following Eq. (4), for a focal shift a=1.5  μm, is implemented in the numerical simulation. It is evident that the shaped focal field is axially shifted from C to the focal point F. In addition, an increased semiangular aperture Ω=81.3°, which is estimated with Eq. (2), will also make the numerical aperture NA grow accordingly. Moreover, the enlarged numerical aperture leads to a resolution improvement in terms of the full width at half-maximum (FWHM) of the intensity, as measured along the x-axis, which is reduced from 1.5 to 0.76 μm, as shown in Fig. 2(c). Finally, the transverse resolution experiences a negligible improvement of 20 nm (the FWHM yields 0.40 μm with the back phased current), as evidenced in Fig. 2(d), due to its proximity to the diffraction limit.

 

Fig. 2. (a) Intensity distribution |H|2 generated by a nonuniform surface current with modulated phase distribution given by Eq. (3) and set at the front surface of a plano–concave Si lens (sketched in white solid line), mimicking the effect of the designer metacoating. In (b) we set the surface current with phase distribution given by Eq. (4) at the back surface of the Si lens. Normalized intensity of the magnetic field in the focal volume of the flat (cylindrical) surface current, represented in green solid lines (red dashed lines) as measured along (c) the x-axis and (d) the y-axis. On-axis resolution critically improves with an active cylindrical surface while transverse resolution does not change significantly.

Download Full Size | PPT Slide | PDF

3. ULTRATHIN GRADED-INDEX METACOATINGS

Next we proceed to design ultrathin metacoatings for the proper generation of the phase distribution φ1(y) and φ2(θ), given in Eqs. (3) and (4), respectively, all along the front surface and back surface of the plano–concave lens. A great variety of strategies can be found in the literature for such a purpose, for instance gradient metasurfaces utilizing the Pancharatnam–Berry phase elements [33,34], which in addition can provide a good efficiency. However, plano–concave cylindrical lenses may benefit from simplicity in the fabrication of the active metacoating if, for instance, their elementary units should not be patterned along the cylinder axis. A subwavelength metallic film of thickness dλ including nanoslits with controlled width proved to be good candidates for a tunable phase manipulation not only for spherical wavefronts [32] but also to accelerate focal beams and to create light capsules [2527]. The resulting metacoating can be considered as a graded-index uniaxial metamaterial by simply altering the metal filling fraction f=wm/(wm+wd) along the corresponding spatial coordinates, y and θ, where wd and wm stand for the width of the slit and the metallic segment, respectively. Assuming that wm remains below the penetration depth of the wave field inside the metal, the periodic array of metallic slits with nanoscale size optically behaves like an effective uniaxial crystal [35,36]. When light passes through the metallic slits, coupled surface plasmons are excited enabling wave propagation with characteristic propagation constant. In these circumstances, the multilayered metal–dielectric material behaves like a semitransparent effective medium exhibiting extreme anisotropy. Assuming that the incident plane wave is polarized perpendicularly to the nanoslits, the effective index of refraction of such metallodielectric metamaterial is approximately estimated as [37]

neff=εdεmfεd+(1f)εm,
where εm and εd denote the relative permittivities of the metal and the medium in the slits, respectively.

As illustration, we show in Fig. 3 the effective index of refraction evaluated for a gold metamaterial patterned by a uniform distribution of nanoslits of constant thickness, wd=15  nm. For a convenient design of the metamaterial, we consider that the nanoslits are filled with silicon, a material that is also employed for the bulky plano–concave lens. Alternatively, one might propose a holey metacoating where the metallic slits are filled with air, but its lower index of refraction in comparison with Si critically limits the range of practical neff. At a wavelength λ=800  nm we set εm=23.36+i0.77 for Au and εd=13.64 (=n2) for Si. An increasing metal filling fraction enables us to establish an ultrahigh effective index neff that surpasses the refractive index of silicon. However, this is attained at the cost of growing Ohmic losses. For instance, a wave field propagating in an all-dielectric medium will gain a phase shift of π/2  rad if, instead, the material now includes metallic components of wm=8.7  nm (Re(neff)=5.69=n+λ/4d), assuming a propagation length as short as d=100  nm. Incremental phase shifts of π/2  rad can be obtained with Au elements of wm=14.2  nm and wm=17.7  nm, providing effective indices Re(neff)=7.69 and Re(neff)=9.69, respectively.

 

Fig. 3. Effective index of refraction evaluated with Eq. (5) for a gold-silicon periodic medium at a wavelength of λ=800  nm. Silicon layers are set with a fixed width wd=15  nm. The metal filling fraction is governed by the Au films width wm.

Download Full Size | PPT Slide | PDF

Note that the giant modulation of the effective index of refraction of our nanogratings cannot be experienced by plane waves with TE polarization. In this case, the electric field is set along the nanoslits, and the real part of neff decreases when the metal filling factor grows [26,32]. For wm higher than 9 nm, the multilayered metamaterial behaves like a metal with Re(neff)0 and increasing Im(neff). As a consequence, the designed metacoating is highly sensitive to the polarization of the incident light, and can only be used for TM-polarized incoming light.

The estimation of such rapidly evolving phase shifts reached by wave fields in our Au-Si metamaterials is only approximate and more accurate evaluations are required to take into account, for instance, nonlocal effects [38], setting some bounds in the homogenization of the metallodielectric medium, and also cavity resonances derived from multiple reflections in the metacoating interfaces [37], as we will detail below. Figure 4 shows the phase shift gained by a TM-polarized plane wave field of λ=800  nm after passing through a gold film of width d=100  nm including Si-filled nanoslits of thickness wd=15  nm. The numerical simulations are again performed with COMSOL Multiphysics, which confirm (not shown in the figure) that the phase shift gained by the incident wave field is approximately proportional to the real part of neff as evaluated by Eq. (5), at least for metacoatings of moderate and low filling fraction where wm remains below 15 nm. Figure 4(a) refers to the phase behavior of a nanopatterned film when a beam impinges from air and propagates in Si after passing through such an ultrathin device, as occurring in the front metacoating of a plano–concave lens. The simulations reproducing the conditions of the metacoating at the back of the plano–concave lens are depicted in Fig. 4(b). Note that for a high metal filling fraction, we found that Eq. (5) overestimates the effective index of refraction of the metal–dielectric metamaterial. Nevertheless, we verify from our results (not entirely shown in the figure) that changing the parameter wm, which determines the metal filling fraction of the nanostructure, enables a phase detuning of the transmitted optical signal within the required range of 2π rad.

 

Fig. 4. Phase shift gained by a TM-polarized plane wave traversing through an Au-Si metacoating of thickness d=100  nm, as set in an air/silicon plane interface. For simplicity, we represent the phase shift in an interval ranging from π to π. The slit width of the periodic nanostructure is fixed at wd=15  nm and we vary the metal width wm. In (a) the beam impinges from air, and in (b) from silicon. The red dashed line establishes the phase shift measured for an all-dielectric coating (wm=0). Red squares illustrate that metamaterials with wm=9, 15, and 23 nm producing incremental phase shifts of approximately π/2  rad with respect to a nonconducting film.

Download Full Size | PPT Slide | PDF

Cavity resonances produced in the metacoating may lead to enhanced losses set in addition to Ohmic losses which are naturally present in the metal. This effect is illustrated in Fig. 5, where we evaluate the transmittance (also reflectance and absorptance) of our metacoatings of width d=100  nm and nanoslit thickness wd=15  nm, employing our numerical solver based on the finite element method (FEM). Figure 5 evidences the relevance of absorption in the metamaterial for certain values of wm and also the loss of transmitted intensity driven by reflections. Furthermore, nanostructures with values of wm higher than 25 nm are opaque in practical terms, a length which roughly represents the penetration depth in the metal. We point out that surface plasmon resonances enabling extraordinary optical transmission, which is caused by the periodicity of the metallic nanostructure, are negligible in our case due to the deep subwavelength scale of Λ=wm+wd [39]. Now it is evident that a spatial modulation of the metal filling fraction in the metacoating leads not only to a graded-index neff, which modifies the phase of the transmitted field, but also contributes to the formation of gray zones where the intensity of the field can drop severely.

 

Fig. 5. Transmittance (T), reflectance (R), and absorptance (A) calculated for Au-Si metacoatings as described in Fig. 4, varying the width wm of the metallic wires. The beam impinges from (a) air and from (b) Si.

Download Full Size | PPT Slide | PDF

On the other hand, we may analytically estimate the amplitude and the phase transformation undergone by the scattered (magnetic) field after passing through the metallodielectric nanostructured film, by introducing the zero-order transmission amplitude: [37]

t=τ12τ23exp(ikneffd)1ρ21ρ23exp(2ikneffd).
Here, τ12 and τ23 are transmission coefficients at the front and back surface of the metacoating, respectively; ρ21 and ρ23 are reflection coefficients at the two ends of the nanostructure, in all cases containing both magnitude and phase. These coefficients are evaluated using ταβ=nβ/(nα+nβ) and ραβ=ταβ1, where n2=neff. Transmittance is simply computed as T=|t|2(n1/n3). Then our metamaterial reaches its optimal transmittance when arg(ρ21ρ23)+2kdRe(neff) satisfies the resonance condition reaching an entire multiple of 2π rad.

From the analysis given above, it is apparent that an optimized response of the nanogratings in terms of the transmission efficiency might be achieved provided that the width of the Si layers in the multilayered nanostructure is not fixed but it can also vary appropriately. Nevertheless, further restrictions derived from fabrication tolerances in current nanotechnology support us to disregard narrower Si layers, enabling metamaterials with ultrahigh effective index of refraction, and also thinner metacoatings.

At this point we are in a position with the above-given analysis to design the elements of our graded-index metacoatings. From a practical point of view, it is appropriate to perform a discrete phase shift rather than to apply a continuous modulation of the incident wavefront. In this case, a finite number of metal–dielectric nanostructures are necessary to obtain the outlined phase range. In particular, we provide four periodic metallodielectric nanostructures producing incremental phase shifts of π/2  rad, which has been proved to yield a satisfactory beam shaping [26]. We first consider an all-dielectric film (wm=0), which demonstrates an optimal transmittance. In agreement with the results shown in Fig. 4, the remaining three Au-Si slit composites with prescribed dephases of π/2  rad are then identified by wm=9,15,23  nm, respectively, when the silicon layer width is kept fixed as wd=15  nm. These values are highlighted in red squares in Fig. 4. It is worth noting that current technology allows us to assemble ultrathin, uniformly continuous metallic films of thicknesses of only 5 nm with reduced surface roughness of around 0.2 nm [40]. As a consequence, the values of wm are here set as an integer in units of nanometers, and therefore the phase shift produced by these four elements of the graded-index metacoating are not exactly π/2  rad; nevertheless, the produced deviation is small enough to be neglected.

Finally, we show the performance of our metallic gratings with different values of d. In Fig. 6 we illustrate the high-to-moderate transparency of gratings with wm=9,15,23  nm and lengths d ranging from 100 to 400 nm. As expected, Fabry–Perot resonances with a periodic behavior governed by the effective index of refraction are responsible for the sinusoidal modulation of the transmitted field. Specifically, here we verify that Eq. (5) clearly overestimates neff in the case of wm=23  nm. Finally, we recognize that our approach does not permit an engineered phase modulation coinciding with peak transmittances through the elements of the metacoating, at least for short lengths d.

 

Fig. 6. Transmittance of metallic nanostructures with different Au wire width wm as a function of thickness d of the metacoating, calculated at a wavelength λ=800  nm. Here we set wd=15  nm.

Download Full Size | PPT Slide | PDF

4. RESULTS AND DISCUSSION

Next we show some FEM-based numerical simulations to illustrate the validity of our approach, which relies on the use of coupled metacoatings set on the front and back surfaces of a wavelength-scale plano–concave lens thus enabling a plane wave to be tightly focused. As detailed above, the first metacoating is designed to convert a plane wavefront into a cylindrical wavefront that is concentric to the back surface at the point C, and the second metasurface further increases the angular aperture of the miniaturized lens. The metacoatings are composed of four types of zones, three of them constituted by metal–dielectric subwavelength gratings to induce controlled phase shifts in multiples of π/2 with respect to bulk Si. We considered nanopatterned films of thickness d=100  nm with slits of wd=15  nm, arranged in arrays of period Λ1=24  nm, Λ2=30  nm, and Λ3=38  nm. The phase pattern of the transmitted fields, approaching the continuous distribution given in Eqs. (3) and (4), are symmetric with respect to the center of each metacoating, and therefore the designed metacoatings exhibit a mirror symmetry with respect to y=0.

Figure 7(a) shows the refractive behavior of a bare Si plano–concave lens of radius R=3  μm and vertex distance of 200 nm when a TM-polarized plane wave is used with λ=800  nm. Note that the effective area of the thick lens including the concave focal region is roughly Aeff=2Rf1, which represents an extent of only 30λ2. In agreement with Fig. 1(a), the beam spreads out by passing through the thick lens and it is unable to focus light. Figure 7(b) shows the performance of the same Si plano–concave lens but including a flat metacoating in its front surface to focus the beam at a distance of 3.2 μm from it, exactly at the center point C. In particular, the central element of the metacoating (Si) has a semilength of 400 nm, followed by a nanograting of period Λ3 and total length of 304 nm (eight periods), an elementary grating of period Λ2 and 210 nm length (seven periods), and a metal–dielectric periodic nanostructure of period Λ1 and length of 192 nm (eight periods); this sequence of elementary gratings is repeated to gain the necessary phase shift φ1(y) given in Eq. (3). Comparing with Fig. 2(a), one can realize that the result of using elementary gratings to induce phase shifts of π/2  rad is in a good agreement with the optimal designer metacoating producing a continuous phase distribution. Finally, we combine the action of a flat metacoating and a cylindrical metacoating set simultaneously, as shown in Fig. 7(c), thus obtaining a focal shift of a=1.5  μm and consequently a superresolved focal spot. The arched metacoating has a central silicon piece of apical semiangle 15°, assembled to a periodic nanostructure of Au filling factor f=0.61 and aperture angle Δθ=11.7° (16 periods), a cylindrical nanograting of f=0.50 and angle 9.12° (15 periods), a curved metamaterial of f=0.38 and angular range of 7.9° (17 periods), and so on to achieve the designed phase shift φ2(θ). In particular, the on-axis FWHM of the field intensity is decreased from 1.12 μm for the case shown in Fig. 7(b) to 0.84 μm measured from Fig. 7(c).

 

Fig. 7. FEM-based numerical simulations showing the intensity of the magnetic field when a monochromatic TM-polarized plane wave passes through a Si plano–concave lens of radius R=3  μm and vertex distance of 200 nm: (a) without metacoatings, (b) including a single metacoating set on the flat front surface, and (c) with coupled metacoatings lying on the front and back surfaces of the lens. (d) Close-up of patterned Au nanoslit arrays in the flat (top) and concave (bottom) surfaces of the Si lens.

Download Full Size | PPT Slide | PDF

Here we point out that in spite of the low transmittance experienced by the elementary grating with wm=23  nm in comparison with other metal–dielectric nanostructures, such a phase shifter is still applicable. The modulation undergone by the real amplitude of the scattered field has minimal effect regarding the construction of the focused wave, which might remind a Fresnel zone plate. It affects the energy efficiency of the lens and perhaps in the emergence of sidelobes and secondary peaks. It can be seen by comparing the resulting focal field in Fig. 2(b), where no amplitude modulation is applied, and Fig. 7(c).

Note that the metacoatings used in Fig. 7 are engineered to provide the maximum energy density at focus F, a condition that is satisfied when the metal–dielectric gratings are symmetrically set off-axis. In this case, the central zone around y=0 shaping a major energy flux of the resultant focused field presents reduced losses derived by reflection and absorption, as shown in Fig. 5. To illustrate such an effect, in Fig. 8 we consider metacoatings whose central zone is formed by a metal–dielectric grating of period Λ=38  nm, which presents dramatic losses due to its high metal filling factor. In order to obtain the required phase shift described in Eqs. (3) and (4), the distribution of elementary metallodielectric gratings should be permuted accordingly. When such lossy nanostructure is set in the central zone of the front metacoating and the back metacoating simultaneously, the plano–concave focusing lens is essentially opaque, as shown in Fig. 8(a). The impact of setting such lossy grating in the central zone is much notable on the cylindrical back metacoating rather than in the flat front metacoating, as depicted in Figs. 8(b) and 8(c). In the latter case, however, spurious spots appear in the focal volume, with special relevance of that located at the central point C. Finally, the noisy focal waves are clearly corrected when semitransparent phase shifters are set in the central zone of the coupled metacoatings, as shown in Fig. 8(d).

 

Fig. 8. Intensity distribution produced in the focal region of a Si plano–concave lens including metacoatings with different arrangements of elementary metal–dielectric gratings. (a) A metallic grating of period Λ3=38  nm is used at the central zone of both metacoatings. Alternatively, we use an all-dielectric central zone for one metacoating and a metallic grating of period Λ3 in the center of (b) the cylindrical metacoating, and (c) the front flat metacoating. In (d) we reproduce Fig. 7(c), where the central zone of both metacoatings has no metallic components, but here using the same color map of previous subfigures.

Download Full Size | PPT Slide | PDF

Our plano–concave lens with coupled metacoatings also presents a favorable performance under oblique incident illumination. For a comprehensive analysis of the refraction (and reflection) phenomenon involved in the interaction of monochromatic beams entering in metal–dielectric multilayered metamaterials, see Ref. [41]. As shown in Fig. 9, the beam is not focused at the focal point F but the spot is laterally displaced as long as the impinging plane wave is tilted for paraxial angles ranging from θ=5° to θ=15°. The resulting focal wave does not present a significant atrophy of the beam shape and, consequently, the lateral and on-axis resolution remain practically unaltered.

 

Fig. 9. Intensity distribution of focal waves produced by tilted TM-polarized plane waves with angles (a) θ=5°, (b) 10°, and (c) 15°, all measured with respect to the optical axis y=0.

Download Full Size | PPT Slide | PDF

In specific applications, such as particle trapping and sensing, it might be of interest to use high-numerical-aperture plano–concave lenses in the scale of the wavelength where Rλ. In this case, the concave opening operates like an optical mouth within which it is possible to observe the formation of a focal wave in the form of a light tongue with appropriate dimensions. Here we explore the behavior of our proposal as pushed to such a limit. In Fig. 10 we show the intensity of a focused wave field performed by a metacoated plano–concave lens of inner radius R=2  μm where the focal point shifted from C a distance a=1  μm, again using a working wavelength of λ=800  nm. Since f1 is kept fixed for simplicity, the thickness of the Si lens increased from 0.2 to 1.1 μm, which carries no impact in the generation of the focal wave. Here the effective area of the thick lens including the focal region decreases to Aeff=20λ2. As suggested above, an all-dielectric central zone is used to maximize the energy efficiency of the focusing device. The resultant focal spot again remains near the diffraction limit without a significant distortion in comparison with a virtually aberration-free focal wave. We may conclude that the reduction of the lens radius can be proceeded in effect, however, limited by diffraction.

 

Fig. 10. Intensity of the magnetic field in the focal region of a metacoated Si plano–concave lens of radius R=2  μm, setting the focal shift parameter as a=1  μm.

Download Full Size | PPT Slide | PDF

5. CONCLUSIONS

We designed cascaded metacoatings for the plano–concave surfaces of a wavelength-scale silicon lens to tightly focus light in the interior of the hollow opening in the form of a light tongue, which can shift laterally by controlling the tilt angle of the incident plane wave. The gradient-index metacoatings are here composed of a patterned gold film with engineered nanoslits, thus offering reduced Ohmic losses and efficient coupling to the exterior radiation. We point out that parallelization of metacoatings and alternatively metasurfaces might be carried out by means of auxiliary phase shifters like nanoholes and nanoantennas. Furthermore, suitable designs for terahertz and lower frequencies can also benefit from engineered metamaterials with ultrahigh index of refraction [4244]. Mid-IR wavefront shaping can be carried out also using all-dielectric subwavelength high-index-contrast gratings offering a low-loss performance [45]. Finally, compact multifocal nanolenses might be developed following, for instance, the procedure of Refs. [46,47]. Implemented in a lenslet array, multifunctional platforms might be conceived for potential applications in sensing and optical trapping, where the light tongue is optically activated.

Funding

Spanish Ministerio de Economía y Competitividad (MINECO) (TEC2014-53727-C2-1-R).

REFERENCES

1. C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004). [CrossRef]  

2. P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005). [CrossRef]  

3. B. D. F. Casse, W. T. Lu, Y. J. Huang, and S. Sridhar, “Nano-optical microlens with ultrashort focal length using negative refraction,” Appl. Phys. Lett. 93, 053111 (2008). [CrossRef]  

4. J. Xu, Y. Zhong, S. Wang, Y. Lu, H. Wan, J. Jiang, and J. Wang, “Focus modulation of cylindrical vector beams by using 1D photonic crystal lens with negative refraction effect,” Opt. Express 23, 26978–26985 (2015). [CrossRef]  

5. M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Planoconcave lens by negative refraction of stacked subwavelength hole arrays,” Opt. Express 16, 9677–9683 (2008). [CrossRef]  

6. M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165130 (2012). [CrossRef]  

7. H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010). [CrossRef]  

8. S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett. 13, 159–163 (2013). [CrossRef]  

9. C. Ma and Z. Liua, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010). [CrossRef]  

10. 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). [CrossRef]  

11. A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18, 123–133 (2010). [CrossRef]  

12. Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014). [CrossRef]  

13. P. Wróbel, J. Pniewski, T. J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by a concentrically corrugated silver film without a hole,” Phys. Rev. Lett. 102, 183902 (2009). [CrossRef]  

14. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012). [CrossRef]  

15. N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013). [CrossRef]  

16. A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33, A31–A50 (2016). [CrossRef]  

17. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009). [CrossRef]  

18. S. Ishii, A. V. Kildishev, V. M. Shalaev, K.-P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett. 36, 451–453 (2011). [CrossRef]  

19. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015). [CrossRef]  

20. S. J. Byrnes, A. Lenef, F. Aieta, and F. Capasso, “Designing large, high-efficiency, high-numerical aperture, transmissive meta-lenses for visible light,” Opt. Express 24, 5110–5124 (2016). [CrossRef]  

21. F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013). [CrossRef]  

22. J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010). [CrossRef]  

23. Y. A. Barnakov, N. Kiriy, P. Black, H. Li, A. V. Yakim, L. Gu, M. Mayy, E. E. Narimanov, and M. A. Noginov, “Toward curvilinear metamaterials based on silver-filled alumina templates,” Opt. Mater. Express 1, 1061–1064 (2011). [CrossRef]  

24. D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).

25. M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Highly localized accelerating beams using nano-scale metallic gratings,” Opt. Commun. 334, 79–84 (2015). [CrossRef]  

26. M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, C. Díaz-Aviñó, and J. J. Miret, “Accelerating wide-angle converging waves in the near field,” J. Opt. 17, 015602 (2015). [CrossRef]  

27. M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Light capsules shaped by curvilinear meta-surfaces,” Appl. Phys. B 120, 551–556 (2015).

28. C.-P. Huang, “Efficient and broadband polarization conversion with the coupled metasurfaces,” Opt. Express 23, 32015–32024 (2015). [CrossRef]  

29. X. Yi, X. Ling, Z. Zhang, Y. Li, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014). [CrossRef]  

30. C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102, 231116 (2013). [CrossRef]  

31. V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015). [CrossRef]  

32. M. Naserpour, C. J. Zapata-Rodríguez, C. Díaz-Aviñó, M. Hashemi, and J. J. Miret, “Ultrathin high-index metasurfaces for shaping focused beams,” Appl. Opt. 54, 7586–7591 (2015). [CrossRef]  

33. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014). [CrossRef]  

34. F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016). [CrossRef]  

35. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. J. Exp. Theor. Phys. 2, 466–475 (1956).

36. E. Popov and S. Enoch, “Mystery of the double limit in homogenization of finitely or perfectly conducting periodic structures,” Opt. Lett. 32, 3441–3443 (2007). [CrossRef]  

37. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

38. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007). [CrossRef]  

39. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef]  

40. W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18, 5124–5134 (2010). [CrossRef]  

41. C. Díaz-Aviñó, D. Pastor, C. J. Zapata-Rodríguez, M. Naserpour, R. Kotyński, and J. J. Miret, “Some considerations on the transmissivity of trirefringent metamaterials,” J. Opt. Soc. Am. B 33, 116–125 (2016). [CrossRef]  

42. J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Appl. Phys. Lett. 102, 093903 (2009). [CrossRef]  

43. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011). [CrossRef]  

44. S. Lee, “Colloidal superlattices for unnaturally high-index metamaterials at broadband optical frequencies,” Opt. Express 23, 28170–28181 (2015). [CrossRef]  

45. Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, and O. Boyraz, “Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces,” J. Opt. Soc. Am. B 33, 189–194 (2016). [CrossRef]  

46. E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010). [CrossRef]  

47. M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodríguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
    [Crossref]
  2. P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
    [Crossref]
  3. B. D. F. Casse, W. T. Lu, Y. J. Huang, and S. Sridhar, “Nano-optical microlens with ultrashort focal length using negative refraction,” Appl. Phys. Lett. 93, 053111 (2008).
    [Crossref]
  4. J. Xu, Y. Zhong, S. Wang, Y. Lu, H. Wan, J. Jiang, and J. Wang, “Focus modulation of cylindrical vector beams by using 1D photonic crystal lens with negative refraction effect,” Opt. Express 23, 26978–26985 (2015).
    [Crossref]
  5. M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Planoconcave lens by negative refraction of stacked subwavelength hole arrays,” Opt. Express 16, 9677–9683 (2008).
    [Crossref]
  6. M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165130 (2012).
    [Crossref]
  7. H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
    [Crossref]
  8. S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett. 13, 159–163 (2013).
    [Crossref]
  9. C. Ma and Z. Liua, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
    [Crossref]
  10. 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).
    [Crossref]
  11. A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18, 123–133 (2010).
    [Crossref]
  12. Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
    [Crossref]
  13. P. Wróbel, J. Pniewski, T. J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by a concentrically corrugated silver film without a hole,” Phys. Rev. Lett. 102, 183902 (2009).
    [Crossref]
  14. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
    [Crossref]
  15. N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
    [Crossref]
  16. A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33, A31–A50 (2016).
    [Crossref]
  17. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
    [Crossref]
  18. S. Ishii, A. V. Kildishev, V. M. Shalaev, K.-P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett. 36, 451–453 (2011).
    [Crossref]
  19. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
    [Crossref]
  20. S. J. Byrnes, A. Lenef, F. Aieta, and F. Capasso, “Designing large, high-efficiency, high-numerical aperture, transmissive meta-lenses for visible light,” Opt. Express 24, 5110–5124 (2016).
    [Crossref]
  21. F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
    [Crossref]
  22. J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
    [Crossref]
  23. Y. A. Barnakov, N. Kiriy, P. Black, H. Li, A. V. Yakim, L. Gu, M. Mayy, E. E. Narimanov, and M. A. Noginov, “Toward curvilinear metamaterials based on silver-filled alumina templates,” Opt. Mater. Express 1, 1061–1064 (2011).
    [Crossref]
  24. D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
  25. M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Highly localized accelerating beams using nano-scale metallic gratings,” Opt. Commun. 334, 79–84 (2015).
    [Crossref]
  26. M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, C. Díaz-Aviñó, and J. J. Miret, “Accelerating wide-angle converging waves in the near field,” J. Opt. 17, 015602 (2015).
    [Crossref]
  27. M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Light capsules shaped by curvilinear meta-surfaces,” Appl. Phys. B 120, 551–556 (2015).
  28. C.-P. Huang, “Efficient and broadband polarization conversion with the coupled metasurfaces,” Opt. Express 23, 32015–32024 (2015).
    [Crossref]
  29. X. Yi, X. Ling, Z. Zhang, Y. Li, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
    [Crossref]
  30. C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102, 231116 (2013).
    [Crossref]
  31. V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
    [Crossref]
  32. M. Naserpour, C. J. Zapata-Rodríguez, C. Díaz-Aviñó, M. Hashemi, and J. J. Miret, “Ultrathin high-index metasurfaces for shaping focused beams,” Appl. Opt. 54, 7586–7591 (2015).
    [Crossref]
  33. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
    [Crossref]
  34. F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
    [Crossref]
  35. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. J. Exp. Theor. Phys. 2, 466–475 (1956).
  36. E. Popov and S. Enoch, “Mystery of the double limit in homogenization of finitely or perfectly conducting periodic structures,” Opt. Lett. 32, 3441–3443 (2007).
    [Crossref]
  37. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  38. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
    [Crossref]
  39. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
    [Crossref]
  40. W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18, 5124–5134 (2010).
    [Crossref]
  41. C. Díaz-Aviñó, D. Pastor, C. J. Zapata-Rodríguez, M. Naserpour, R. Kotyński, and J. J. Miret, “Some considerations on the transmissivity of trirefringent metamaterials,” J. Opt. Soc. Am. B 33, 116–125 (2016).
    [Crossref]
  42. J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Appl. Phys. Lett. 102, 093903 (2009).
    [Crossref]
  43. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
    [Crossref]
  44. S. Lee, “Colloidal superlattices for unnaturally high-index metamaterials at broadband optical frequencies,” Opt. Express 23, 28170–28181 (2015).
    [Crossref]
  45. Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, and O. Boyraz, “Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces,” J. Opt. Soc. Am. B 33, 189–194 (2016).
    [Crossref]
  46. E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
    [Crossref]
  47. M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodríguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
    [Crossref]

2016 (6)

2015 (9)

S. Lee, “Colloidal superlattices for unnaturally high-index metamaterials at broadband optical frequencies,” Opt. Express 23, 28170–28181 (2015).
[Crossref]

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, C. Díaz-Aviñó, M. Hashemi, and J. J. Miret, “Ultrathin high-index metasurfaces for shaping focused beams,” Appl. Opt. 54, 7586–7591 (2015).
[Crossref]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Highly localized accelerating beams using nano-scale metallic gratings,” Opt. Commun. 334, 79–84 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, C. Díaz-Aviñó, and J. J. Miret, “Accelerating wide-angle converging waves in the near field,” J. Opt. 17, 015602 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Light capsules shaped by curvilinear meta-surfaces,” Appl. Phys. B 120, 551–556 (2015).

C.-P. Huang, “Efficient and broadband polarization conversion with the coupled metasurfaces,” Opt. Express 23, 32015–32024 (2015).
[Crossref]

J. Xu, Y. Zhong, S. Wang, Y. Lu, H. Wan, J. Jiang, and J. Wang, “Focus modulation of cylindrical vector beams by using 1D photonic crystal lens with negative refraction effect,” Opt. Express 23, 26978–26985 (2015).
[Crossref]

2014 (3)

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

X. Yi, X. Ling, Z. Zhang, Y. Li, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

2013 (4)

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102, 231116 (2013).
[Crossref]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
[Crossref]

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett. 13, 159–163 (2013).
[Crossref]

2012 (3)

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165130 (2012).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).

2011 (3)

2010 (6)

W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18, 5124–5134 (2010).
[Crossref]

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[Crossref]

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18, 123–133 (2010).
[Crossref]

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

C. Ma and Z. Liua, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
[Crossref]

2009 (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).
[Crossref]

P. Wróbel, J. Pniewski, T. J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by a concentrically corrugated silver film without a hole,” Phys. Rev. Lett. 102, 183902 (2009).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[Crossref]

J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Appl. Phys. Lett. 102, 093903 (2009).
[Crossref]

2008 (2)

B. D. F. Casse, W. T. Lu, Y. J. Huang, and S. Sridhar, “Nano-optical microlens with ultrashort focal length using negative refraction,” Appl. Phys. Lett. 93, 053111 (2008).
[Crossref]

M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Planoconcave lens by negative refraction of stacked subwavelength hole arrays,” Opt. Express 16, 9677–9683 (2008).
[Crossref]

2007 (2)

E. Popov and S. Enoch, “Mystery of the double limit in homogenization of finitely or perfectly conducting periodic structures,” Opt. Lett. 32, 3441–3443 (2007).
[Crossref]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

2005 (1)

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[Crossref]

2004 (1)

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

2001 (1)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. J. Exp. Theor. Phys. 2, 466–475 (1956).

Ahmadi, A.

Aieta, F.

S. J. Byrnes, A. Lenef, F. Aieta, and F. Capasso, “Designing large, high-efficiency, high-numerical aperture, transmissive meta-lenses for visible light,” Opt. Express 24, 5110–5124 (2016).
[Crossref]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
[Crossref]

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Alù, A.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Antosiewicz, T. J.

P. Wróbel, J. Pniewski, T. J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by a concentrically corrugated silver film without a hole,” Phys. Rev. Lett. 102, 183902 (2009).
[Crossref]

Aoust, G.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Avrutsky, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Ayza, M. S.

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Ball, A. J.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Barnakov, Y. A.

Barnard, E. S.

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).
[Crossref]

Bartal, G.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

Beruete, M.

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165130 (2012).
[Crossref]

M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Planoconcave lens by negative refraction of stacked subwavelength hole arrays,” Opt. Express 16, 9677–9683 (2008).
[Crossref]

Black, P.

Blanchard, R.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Boyraz, O.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, and O. Boyraz, “Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces,” J. Opt. Soc. Am. B 33, 189–194 (2016).
[Crossref]

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

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).
[Crossref]

Byrnes, S. J.

Campillo, I.

Capasso, F.

S. J. Byrnes, A. Lenef, F. Aieta, and F. Capasso, “Designing large, high-efficiency, high-numerical aperture, transmissive meta-lenses for visible light,” Opt. Express 24, 5110–5124 (2016).
[Crossref]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
[Crossref]

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Capolino, F.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Casse, B. D. F.

B. D. F. Casse, W. T. Lu, Y. J. Huang, and S. Sridhar, “Nano-optical microlens with ultrashort focal length using negative refraction,” Appl. Phys. Lett. 93, 053111 (2008).
[Crossref]

Catrysse, P. B.

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).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[Crossref]

Chaumet, P. C.

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[Crossref]

Chen, K.-P.

Chen, S.

Chen, W.

Choi, H.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

Choi, M.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Chum, C. C.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Deng, J.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Díaz-Aviñó, C.

Ding, L.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Drachev, V. P.

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

Eleftheriades, G. V.

Elser, J.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Engheta, N.

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165130 (2012).
[Crossref]

Enoch, S.

Epstein, A.

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

Fan, S.

J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Appl. Phys. Lett. 102, 093903 (2009).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[Crossref]

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).
[Crossref]

Faraon, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Ferrand, P.

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[Crossref]

Gaburro, Z.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Gao, H.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

Genevet, P.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Ghadarghadr, S.

Grbic, A.

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102, 231116 (2013).
[Crossref]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

Gu, L.

Hashemi, M.

M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodríguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, C. Díaz-Aviñó, M. Hashemi, and J. J. Miret, “Ultrathin high-index metasurfaces for shaping focused beams,” Appl. Opt. 54, 7586–7591 (2015).
[Crossref]

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

Hong, M.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Horie, Y.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Huang, C.-P.

Huang, Y.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, and O. Boyraz, “Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces,” J. Opt. Soc. Am. B 33, 189–194 (2016).
[Crossref]

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Huang, Y. J.

B. D. F. Casse, W. T. Lu, Y. J. Huang, and S. Sridhar, “Nano-optical microlens with ultrashort focal length using negative refraction,” Appl. Phys. Lett. 93, 053111 (2008).
[Crossref]

Hyun, J. K.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

Ishii, S.

Jiang, J.

Kalyoncu, S. K.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, and O. Boyraz, “Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces,” J. Opt. Soc. Am. B 33, 189–194 (2016).
[Crossref]

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Kang, K.-Y.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Kang, S. B.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Kats, M.

Kats, M. A.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Kildishev, A. V.

Kim, Y.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Kiriy, N.

Kotynski, R.

Kwak, M. H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Lauhon, L. J.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

Lee, M. H.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

Lee, S.

Lee, S. H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Lee, Y.-H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Lenef, A.

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

Li, H.

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

Li, Y.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

X. Yi, X. Ling, Z. Zhang, Y. Li, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref]

Lin, D.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

Ling, X.

Liu, Y.

Liu, Z.

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

Liua, Z.

C. Ma and Z. Liua, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
[Crossref]

Lu, D.

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).

Lu, W. T.

B. D. F. Casse, W. T. Lu, Y. J. Huang, and S. Sridhar, “Nano-optical microlens with ultrashort focal length using negative refraction,” Appl. Phys. Lett. 93, 053111 (2008).
[Crossref]

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[Crossref]

Lu, Y.

J. Xu, Y. Zhong, S. Wang, Y. Lu, H. Wan, J. Jiang, and J. Wang, “Focus modulation of cylindrical vector beams by using 1D photonic crystal lens with negative refraction effect,” Opt. Express 23, 26978–26985 (2015).
[Crossref]

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Luo, H.

Ma, C.

C. Ma and Z. Liua, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
[Crossref]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

Mayy, M.

Mei, S.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Min, B.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Miret, J. J.

C. Díaz-Aviñó, D. Pastor, C. J. Zapata-Rodríguez, M. Naserpour, R. Kotyński, and J. J. Miret, “Some considerations on the transmissivity of trirefringent metamaterials,” J. Opt. Soc. Am. B 33, 116–125 (2016).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, C. Díaz-Aviñó, M. Hashemi, and J. J. Miret, “Ultrathin high-index metasurfaces for shaping focused beams,” Appl. Opt. 54, 7586–7591 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Highly localized accelerating beams using nano-scale metallic gratings,” Opt. Commun. 334, 79–84 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, C. Díaz-Aviñó, and J. J. Miret, “Accelerating wide-angle converging waves in the near field,” J. Opt. 17, 015602 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Light capsules shaped by curvilinear meta-surfaces,” Appl. Phys. B 120, 551–556 (2015).

Moal, E. L.

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[Crossref]

Moazami, A.

M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodríguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
[Crossref]

Monticone, F.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Mosallaei, H.

Mudry, E.

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[Crossref]

Narimanov, E. E.

Naserpour, M.

M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodríguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
[Crossref]

C. Díaz-Aviñó, D. Pastor, C. J. Zapata-Rodríguez, M. Naserpour, R. Kotyński, and J. J. Miret, “Some considerations on the transmissivity of trirefringent metamaterials,” J. Opt. Soc. Am. B 33, 116–125 (2016).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, C. Díaz-Aviñó, M. Hashemi, and J. J. Miret, “Ultrathin high-index metasurfaces for shaping focused beams,” Appl. Opt. 54, 7586–7591 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Light capsules shaped by curvilinear meta-surfaces,” Appl. Phys. B 120, 551–556 (2015).

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, C. Díaz-Aviñó, and J. J. Miret, “Accelerating wide-angle converging waves in the near field,” J. Opt. 17, 015602 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Highly localized accelerating beams using nano-scale metallic gratings,” Opt. Commun. 334, 79–84 (2015).
[Crossref]

Navarro-Cía, M.

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165130 (2012).
[Crossref]

M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Planoconcave lens by negative refraction of stacked subwavelength hole arrays,” Opt. Express 16, 9677–9683 (2008).
[Crossref]

Nielsen, J. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

Noginov, M. A.

Odom, T. W.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

Orazbayev, B.

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

Pacheco-Peña, V.

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

Parimi, P. V.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[Crossref]

Park, N.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Pastor, D.

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

Pendry, J. B.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

Pfeiffer, C.

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102, 231116 (2013).
[Crossref]

Pniewski, J.

P. Wróbel, J. Pniewski, T. J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by a concentrically corrugated silver film without a hole,” Phys. Rev. Lett. 102, 183902 (2009).
[Crossref]

Podolskiy, V. A.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Popov, E.

Qin, F.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Qiu, C.-W.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Rho, J.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. J. Exp. Theor. Phys. 2, 466–475 (1956).

Salakhutdinov, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Sentenac, A.

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[Crossref]

Shalaev, V. M.

Shen, J.-T.

J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Appl. Phys. Lett. 102, 093903 (2009).
[Crossref]

Shin, J.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Appl. Phys. Lett. 102, 093903 (2009).
[Crossref]

Sorolla, M.

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165130 (2012).
[Crossref]

M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Planoconcave lens by negative refraction of stacked subwavelength hole arrays,” Opt. Express 16, 9677–9683 (2008).
[Crossref]

Sridhar, S.

B. D. F. Casse, W. T. Lu, Y. J. Huang, and S. Sridhar, “Nano-optical microlens with ultrashort focal length using negative refraction,” Appl. Phys. Lett. 93, 053111 (2008).
[Crossref]

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[Crossref]

Szoplik, T.

P. Wróbel, J. Pniewski, T. J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by a concentrically corrugated silver film without a hole,” Phys. Rev. Lett. 102, 183902 (2009).
[Crossref]

Tanielian, M. H.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

Teng, J.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Teniente, J.

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

Tetienne, J.-P.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

Thompson, M. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

Thoreson, M. D.

Torres, V.

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

Torun, R.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, and O. Boyraz, “Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces,” J. Opt. Soc. Am. B 33, 189–194 (2016).
[Crossref]

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Verslegers, L.

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).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[Crossref]

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

Vier, D. C.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

Vodo, P.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[Crossref]

Wan, H.

Wang, J.

Wang, S.

Wen, S.

White, J. S.

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).
[Crossref]

Wróbel, P.

P. Wróbel, J. Pniewski, T. J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by a concentrically corrugated silver film without a hole,” Phys. Rev. Lett. 102, 183902 (2009).
[Crossref]

Xiong, Y.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

Xu, J.

Yakim, A. V.

Yang, J.-C.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

Ye, Z.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Yi, X.

Yin, X.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

Yu, N.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Yu, Z.

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).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[Crossref]

Zakery, A.

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Light capsules shaped by curvilinear meta-surfaces,” Appl. Phys. B 120, 551–556 (2015).

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Highly localized accelerating beams using nano-scale metallic gratings,” Opt. Commun. 334, 79–84 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, C. Díaz-Aviñó, and J. J. Miret, “Accelerating wide-angle converging waves in the near field,” J. Opt. 17, 015602 (2015).
[Crossref]

Zapata-Rodríguez, C. J.

C. Díaz-Aviñó, D. Pastor, C. J. Zapata-Rodríguez, M. Naserpour, R. Kotyński, and J. J. Miret, “Some considerations on the transmissivity of trirefringent metamaterials,” J. Opt. Soc. Am. B 33, 116–125 (2016).
[Crossref]

M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodríguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, C. Díaz-Aviñó, M. Hashemi, and J. J. Miret, “Ultrathin high-index metasurfaces for shaping focused beams,” Appl. Opt. 54, 7586–7591 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Highly localized accelerating beams using nano-scale metallic gratings,” Opt. Commun. 334, 79–84 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, C. Díaz-Aviñó, and J. J. Miret, “Accelerating wide-angle converging waves in the near field,” J. Opt. 17, 015602 (2015).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Light capsules shaped by curvilinear meta-surfaces,” Appl. Phys. B 120, 551–556 (2015).

Zhang, L.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Zhang, S.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Zhang, X.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

Zhang, Z.

Zhao, Q.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, and O. Boyraz, “Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces,” J. Opt. Soc. Am. B 33, 189–194 (2016).
[Crossref]

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Zhong, Y.

Zhou, X.

Appl. Opt. (1)

Appl. Phys. B (1)

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Light capsules shaped by curvilinear meta-surfaces,” Appl. Phys. B 120, 551–556 (2015).

Appl. Phys. Lett. (9)

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102, 231116 (2013).
[Crossref]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[Crossref]

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[Crossref]

B. D. F. Casse, W. T. Lu, Y. J. Huang, and S. Sridhar, “Nano-optical microlens with ultrashort focal length using negative refraction,” Appl. Phys. Lett. 93, 053111 (2008).
[Crossref]

C. Ma and Z. Liua, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
[Crossref]

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[Crossref]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Appl. Phys. Lett. 102, 093903 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

IEEE Trans. Antennas Propag. (1)

V. Torres, B. Orazbayev, V. Pacheco-Peña, J. Teniente, M. Beruete, M. Navarro-Cía, M. S. Ayza, and N. Engheta, “Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle,” IEEE Trans. Antennas Propag. 63, 231–239 (2015).
[Crossref]

J. Opt. (1)

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, C. Díaz-Aviñó, and J. J. Miret, “Accelerating wide-angle converging waves in the near field,” J. Opt. 17, 015602 (2015).
[Crossref]

J. Opt. Soc. Am. B (3)

Nano Lett. (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).
[Crossref]

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett. 13, 159–163 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Nat. Commun. (3)

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, “Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies,” Nat. Commun. 1, 143 (2010).
[Crossref]

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Nature (1)

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Opt. Commun. (2)

M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodríguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
[Crossref]

M. Naserpour, C. J. Zapata-Rodríguez, A. Zakery, and J. J. Miret, “Highly localized accelerating beams using nano-scale metallic gratings,” Opt. Commun. 334, 79–84 (2015).
[Crossref]

Opt. Express (9)

C.-P. Huang, “Efficient and broadband polarization conversion with the coupled metasurfaces,” Opt. Express 23, 32015–32024 (2015).
[Crossref]

X. Yi, X. Ling, Z. Zhang, Y. Li, X. Zhou, Y. Liu, S. Chen, H. Luo, and S. Wen, “Generation of cylindrical vector vortex beams by two cascaded metasurfaces,” Opt. Express 22, 17207–17215 (2014).
[Crossref]

S. J. Byrnes, A. Lenef, F. Aieta, and F. Capasso, “Designing large, high-efficiency, high-numerical aperture, transmissive meta-lenses for visible light,” Opt. Express 24, 5110–5124 (2016).
[Crossref]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
[Crossref]

A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18, 123–133 (2010).
[Crossref]

J. Xu, Y. Zhong, S. Wang, Y. Lu, H. Wan, J. Jiang, and J. Wang, “Focus modulation of cylindrical vector beams by using 1D photonic crystal lens with negative refraction effect,” Opt. Express 23, 26978–26985 (2015).
[Crossref]

M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Planoconcave lens by negative refraction of stacked subwavelength hole arrays,” Opt. Express 16, 9677–9683 (2008).
[Crossref]

S. Lee, “Colloidal superlattices for unnaturally high-index metamaterials at broadband optical frequencies,” Opt. Express 23, 28170–28181 (2015).
[Crossref]

W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18, 5124–5134 (2010).
[Crossref]

Opt. Lett. (2)

Opt. Mater. Express (1)

Phys. Rev. B (1)

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165130 (2012).
[Crossref]

Phys. Rev. Lett. (3)

P. Wróbel, J. Pniewski, T. J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by a concentrically corrugated silver film without a hole,” Phys. Rev. Lett. 102, 183902 (2009).
[Crossref]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref]

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[Crossref]

Sci. Adv. (1)

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2, e1501168 (2016).
[Crossref]

Science (1)

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

Sov. Phys. J. Exp. Theor. Phys. (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. J. Exp. Theor. Phys. 2, 466–475 (1956).

Other (1)

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1. Schematics based on optical rays of the focusing action of plano–concave dielectric lenses. (a) Transparent dielectrics with an index of refraction higher than unity lead to a diverging configuration. (b) An epsilon-near-zero metamaterial enables us to focus light at the center of curvature of the concave surface. (c) An increased numerical aperture is attained by using negative-index metamaterials. (d) Our proposal based on coupled metacoatings set at the entrance and exit surfaces of a transparent dielectric thick lens. A focused beam of semiaperture angle Ω will be generated by passing through the gradient-index flat metasurface. The converging wave field propagating inside the lens will be refocused at F by means of the active curved metacoating, having an increased semiaperture angle Ω .
Fig. 2.
Fig. 2. (a) Intensity distribution | H | 2 generated by a nonuniform surface current with modulated phase distribution given by Eq. (3) and set at the front surface of a plano–concave Si lens (sketched in white solid line), mimicking the effect of the designer metacoating. In (b) we set the surface current with phase distribution given by Eq. (4) at the back surface of the Si lens. Normalized intensity of the magnetic field in the focal volume of the flat (cylindrical) surface current, represented in green solid lines (red dashed lines) as measured along (c) the x -axis and (d) the y -axis. On-axis resolution critically improves with an active cylindrical surface while transverse resolution does not change significantly.
Fig. 3.
Fig. 3. Effective index of refraction evaluated with Eq. (5) for a gold-silicon periodic medium at a wavelength of λ = 800    nm . Silicon layers are set with a fixed width w d = 15    nm . The metal filling fraction is governed by the Au films width w m .
Fig. 4.
Fig. 4. Phase shift gained by a TM-polarized plane wave traversing through an Au-Si metacoating of thickness d = 100    nm , as set in an air/silicon plane interface. For simplicity, we represent the phase shift in an interval ranging from π to π . The slit width of the periodic nanostructure is fixed at w d = 15    nm and we vary the metal width w m . In (a) the beam impinges from air, and in (b) from silicon. The red dashed line establishes the phase shift measured for an all-dielectric coating ( w m = 0 ). Red squares illustrate that metamaterials with w m = 9 , 15, and 23 nm producing incremental phase shifts of approximately π / 2    rad with respect to a nonconducting film.
Fig. 5.
Fig. 5. Transmittance (T), reflectance (R), and absorptance (A) calculated for Au-Si metacoatings as described in Fig. 4, varying the width w m of the metallic wires. The beam impinges from (a) air and from (b) Si.
Fig. 6.
Fig. 6. Transmittance of metallic nanostructures with different Au wire width w m as a function of thickness d of the metacoating, calculated at a wavelength λ = 800    nm . Here we set w d = 15    nm .
Fig. 7.
Fig. 7. FEM-based numerical simulations showing the intensity of the magnetic field when a monochromatic TM-polarized plane wave passes through a Si plano–concave lens of radius R = 3    μm and vertex distance of 200 nm: (a) without metacoatings, (b) including a single metacoating set on the flat front surface, and (c) with coupled metacoatings lying on the front and back surfaces of the lens. (d) Close-up of patterned Au nanoslit arrays in the flat (top) and concave (bottom) surfaces of the Si lens.
Fig. 8.
Fig. 8. Intensity distribution produced in the focal region of a Si plano–concave lens including metacoatings with different arrangements of elementary metal–dielectric gratings. (a) A metallic grating of period Λ 3 = 38    nm is used at the central zone of both metacoatings. Alternatively, we use an all-dielectric central zone for one metacoating and a metallic grating of period Λ 3 in the center of (b) the cylindrical metacoating, and (c) the front flat metacoating. In (d) we reproduce Fig. 7(c), where the central zone of both metacoatings has no metallic components, but here using the same color map of previous subfigures.
Fig. 9.
Fig. 9. Intensity distribution of focal waves produced by tilted TM-polarized plane waves with angles (a)  θ = 5 ° , (b) 10°, and (c) 15°, all measured with respect to the optical axis y = 0 .
Fig. 10.
Fig. 10. Intensity of the magnetic field in the focal region of a metacoated Si plano–concave lens of radius R = 2    μm , setting the focal shift parameter as a = 1    μm .

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

f = R 1 n ,
NA = NA 1 + ( a / R ) 2 2 ( a / R ) cos Ω
φ 1 ( y ) = φ 1 ( 0 ) + n k ( f 1 y 2 + f 1 2 ) ,
φ 2 ( θ ) = φ 2 ( 0 ) + k [ ( R a ) R 2 + a 2 2 a R cos θ ] ,
n eff = ε d ε m f ε d + ( 1 f ) ε m ,
t = τ 12 τ 23 exp ( i k n eff d ) 1 ρ 21 ρ 23 exp ( 2 i k n eff d ) .

Metrics