Scaling theory of wave confinement in classical and quantum periodic systems

Abstract

Functional defects in periodic media confine waves - acoustic, electromagnetic, electronic, spin, etc. - in various dimensions, depending on the structure of the defect. While defects are usually modelled by a superlattice with a typical band-structure representation of energy levels, determining the confinement associated with a given band is highly non-trivial and no analytical method is known to date. Therefore, we propose a rigorous method to classify the dimensionality of the confinement. Starting from the confinement energy and the mode volume, we use finite-size scaling to find that ratios of these quantities to certain powers yield the confinement dimensionality of each band. This classification has negligible additional computational costs compared to a band structure calculation and is valid for any type of wave in both quantum and classical regimes, and any dimension. In the quantum case, we illustrate our method on electronic confinement in 2D hexagonal BN with a nitrogen vacancy, which confirms the previous results. In the classical case, we study a three-dimensional photonic band gap cavity superlattice, where we identify novel acceptor-like behavior.

arXiv comment6 pages and 5 figures main text, 6 pages and 4 figures supplemental material

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Cited by in corpus (5)

• Observation of light propagation through a three-dimensional cavity superlattice in a 3D photonic band gap
• Non-utopian optical properties computed of a tomographically reconstructed real photonic nanostructure
• Optical and thermal effects in the neighborhood of the spherical layered nanoparticle of the "metallic core -- J-aggregate shell'' structure
• Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures
• Symmetries and Wavefunctions of Photons Confined in 3D Photonic Band Gap Superlattices