Nonlocal optics of plasmonic nanowire metamaterials

Abstract

We present an analytical description of the nonlocal optical response of plasmonic nanowire metamaterials that enable negative refraction, subwavelength light manipulation, and emission lifetime engineering. We show that dispersion of optical waves propagating in nanowire media results from coupling of transverse and longitudinal electromagnetic modes supported by the composite and derive the nonlocal effective medium approximation for this dispersion. We derive the profiles of electric field across the unit cell, and use these expressions to solve the long-standing problem of additional boundary conditions in calculations of transmission and reflection of waves by nonlocal nanowire media. We verify our analytical results with numerical solutions of Maxwell's equations and discuss generalization of the developed formalism to other uniaxial metamaterials.Nanowire-based composites have recently attracted significant attention due to their unusual and counterintuitive optical properties that include negative refraction, subwavelength confinement of optical radiation, and modulation of photonic density of states [1][2][3]. Due to relatively low loss and ease of fabrication, nanowire composites found numerous applications in subwavelength imaging, biosensing, acousto-optics, and ultrafast alloptical processing, spanning visible to THz frequencies [4][5][6][7][8]. Wire materials are a sub-class of uniaxial metamaterials that have homogeneous internal structure along one pre-selected direction. In all, this class of composites represents a flexible platform for engineering of optical landscape from all-dielectric birefringent media, to epsilon-near-zero, to hyperbolic, and epsilon-near-infinity regimes, each of which has its own class of benefits and applications [9,10].In this work, we present an analytical technique that provides adequate description of electromagnetism in wire-based metamaterials taking into account nonlocal optical response originating from the homogenization procedure. The approach can be straightforwardly extended to describe optics of coaxial-cable-like media [11] and numerous other uniaxial composites. The developed formalism reconciles the local and nonlocal effectivemedium theories often used to describe the optics of nanowire composites in different limits [12][13][14][15]. More importantly, the formalism relates the origin of optical nonlocality to collective (averaged over many nanowires) plasmonic excitation of wire composite, and provides the recipe to implement additional boundary conditions in composite structures.We illustrate the developed technique on the example of plasmonic nanowire metamaterials, formed by an array of aligned plasmonic nanowires embedded in a dielectric host. For simplicity, we fix the frequency of electromagnetic excitations and the unit cell parameters of the system, and vary only the permittivity of the wire inclusions. (The developed formalism can be readily applied for systems where both permittivity and frequency are changed at the same time.) We assume tha...

Bulk plasmon‐polaritons in hyperbolic nanorod metamaterial waveguides

“…a). As expected, the ordinary wave has a typical dispersion for a transparent dielectric, lying to the right of the light line in the AAO matrix since the effective refractive index is increased due to the presence of metal, with the resonance–the so‐called epsilon‐very‐large (EVL) regime –determined by cylindrical surface plasmon (CSP) excitations on the rods . At the same time, the dispersion of extraordinary waves is that of a typical Drude‐like metal with an effective plasma frequency 2.2 eV corresponding to the metamaterial's transition from the elliptic to the hyperbolic regime.…”

“…However, as a result of the anisotropy of the metamaterial, electron plasma oscillations may still give rise to bulk plasmon‐polaritons propagating in the metamaterial below the plasma frequency in directions determined by the dispersion relation, , where k x,y and k z are the wavevector components along the x , y and z directions, respectively, ω is the electromagnetic field frequency, and c 0 is the speed of light in vacuum. In a microscopic consideration of the plasmonic nanorod metamaterial studied here, these bulk plasmon‐polaritons arise from interacting CSPs supported by individual nanorods forming the metamaterial , but can also be observed in multilayered metal–dielectric–metal metamaterials, where they arise from interacting smooth‐film SPP modes . The isofrequency contours of the metamaterial dispersion for TE (elliptic) and TM (hyperbolic) modes show striking differences in the allowed wavevector ranges, which determines the dissimilar behavior of these modes in both the infinite metamaterial as well as in a metamaterial slab (Fig.…”

“…c). This regime, however, takes place in the wavelength range and for loss parameters where nonlocal, spatial dispersion effects occur and that requires a different theoretical treatment .…”

“…In the vicinity of the resonance, the term becomes negative and is to be taken into account to establish the hyperbolic behavior of the waveguide when the ENZ frequency is close to this resonance. However, in the epsilon near‐zero (ENZ) regime, near the effective bulk‐plasma frequency , a different treatment is needed to take into account nonlocal effects , a scenario not considered here. It is important to emphasize that for typical metamaterial geometries, the condition for negative group velocity is satisfied for all TM‐mode orders and any waveguide thickness.…”

Second‐Harmonic Generation from Hyperbolic Plasmonic Nanorod Metamaterial Slab

“…While the centrosymmetric crystal lattice of gold, limits the source of the second‐order nonlinearity to the surface nonlinear contributions, the nanostructured geometry of the Au nanorod metamaterial may exploit a large surface area with high field confinement to provide efficient second‐harmonic generation. Due to the fact that this internal structure of the metamaterial and the local fields inside the metamaterial are paramount for the description and understanding of SHG processes, the effective medium approximation for the metamaterial description is not applicable for modelling SHG processes and full‐vectorial, microscopic considerations should be employed.…”