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 modeled by a superlattice with a typical band-structure representation of energy levels, determining the confinement associated with a given band is highly nontrivial and no analytical method is known to date. Therefore, we propose a rigorous method to classify the dimensionality of wave confinement. Starting from the confinement energy and the mode volume, we use finite-size scaling to find that ratios of these quantities raised to certain powers yield the confinement dimensionality of each band. Our classification has negligible additional computational costs compared to a band structure calculation and is valid for any type of wave, both quantum and classical, and in any dimension. In the quantum regime, we illustrate our method on electronic confinement in 2D hexagonal boron nitride (BN) with a nitrogen vacancy, in agreement with previous results. In the classical case, we study a three-dimensional photonic band gap cavity superlattice, where we identify novel acceptorlike behavior. We briefly discuss the generalization to quasiperiodic lattices.

https://link.aps.org/doi/10.1103/PhysRevLett.129.176401

M. Kozoň, A. Lagendijk, M. Schlottbom, J. J. W. van der Vegt, and W. L. Vos

2022

10/2022

Phys. Rev. Lett.

129

176401: 1-6

10.1103/PhysRevLett.129.176401

band structure, confinement, defect, finite-size scaling, hexagonal BN, photonic crystal, superlattice