The inverted pendulum, interface phonons and optic Tamm states

TL;DR

This paper introduces a novel theoretical framework linking wave propagation in periodic media to parametric oscillators, revealing new classes of phonons and extending the concept of optic Tamm states to periodic structures.

Contribution

It develops a new approach connecting wave behavior in periodic media with parametric oscillators, leading to the discovery of new phonon classes and an extension of optic Tamm states.

Findings

Identification of new classes of phonons in periodic media

Extension of optic Tamm states to periodic structures

Theoretical framework linking waves and parametric oscillators

Abstract

The propagation of waves in periodic media is related to the parametric oscillators. We transpose the possibility that a parametric pendulum oscillates in the vicinity of its unstable equilibrium positions to the case of waves in lossless unidimensional periodic media. This concept formally applies to any kind of wave. We apply and develop it to the case of phonons in realizable structures and evidence new classes of phonons. Discussing the case of electromagnetic waves, we show that our concept is related to optic Tamm states one but extends it to periodic Optic Tamm state.