Bulk polaritons in a biaxial crystal at the interface with a perfect metal
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Bulk Polaritons in a Biaxial Crystal at the Interface with a Perfect Metal V. I. Alshits and V. N. Lyubimov Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskiі pr. 59, Moscow, 119333 Russia email: [email protected] Received January 26, 2009
Abstract—The orientation of the plane where the tangential electric field component becomes zero is indi cated for any plane bulk electromagnetic wave propagating in an infinite transparent medium of arbitrary anisotropy. Thus, the existence of this wave (bulk polariton) in this plane (interface with an ideal conductor) is ensured. The characteristics of such polaritons of two independent branches with coinciding wave normals (isonormal polaritons) or Poynting vector directions (isoray polaritons) are compared. PACS numbers: 71.36.+c DOI: 10.1134/S1063774509060066
INTRODUCTION It is known that a transparent isotropic medium with an electric permittivity ε allows for the propaga tion of plane electromagnetic waves in any direction with the phase velocity v = c/ ε (с is the speed of light in vacuum) and a polarization determined by the pair of electric and magnetic field amplitudes E ⊥ H, which can be arbitrarily oriented in a plane that is orthogonal to the wave normal m. Thus, an infinite number of waves with different polarizations can propagate along any direction m in an isotropic medium. In a crystal with a tensor electric permittivity ε, only two waves with different velocities v1, 2(m) and certain polarizations {E1, 2(m), H1, 2(m)} can propagate in each direction m (except for the optical axis direc tions). It is important that the vector amplitudes Еα and Нα (α = 1, 2), remaining orthogonal, set a plane in the crystal that can be nonperpendicular to the vec tor m (however, the condition Нα ⊥ m is always satis fied). This means that the Poynting (energy flux) vec tors Pα = Еα × Нα in the isonormal waves under con sideration generally have directions differing from the wave normal. In a halfinfinite dielectric medium, the bulk waves with an energy flux oblique to its boundary should be transformed at the latter (reflected, refracted, or absorbed). At grazing incidence, when the wave energy flux Pα is parallel to the interface, a bulk wave can propagate in this medium only when a certain boundary condition is satisfied (the wave is referred to as a polariton in this case). For example, at the inter face with a perfect metal whose permittivity is infinite (|εm | ∞), this condition is reduced to the require
ment for the tangential electric field component to be zero [1]: Еt = 0.
(1)
In an isotropic solid, only one polariton with a strictly determined polarization may propagate along any m direction when its electric component E is orthogonal to the interface. The situation in crystals is more com plicated. Bulk polaritons were described in [2, 3] for opti cally uniaxial crystals with a randomy oriented surface coated by a perfect metal. If such crystals are infinite, waves of two types (ordin
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