Year: 2024
Type: article
Abstract: . This paper deals with the existence of guided waves and edge states, in particular two-dimensional media obtained by perturbing a reference periodic medium with honeycomb symmetry. This reference medium is a thin periodic domain (the thickness is denoted [Formula: see text]) with a hexagonal structure, which is close to a honeycomb quantum graph. In a first step, we show the existence of Dirac points (conical crossings) at arbitrarily large frequencies if [Formula: see text] is chosen small enough. We then perturb the domain by cutting the perfectly periodic medium along the so-called zigzag direction, and we consider either Dirichlet or Neumann boundary conditions on the cut edge. In the two cases, we prove the existence of edge modes as well as their robustness with respect to some perturbations, namely, the location of the cut and the thickness of the perturbed edge. In particular, we show that different locations of the cut lead to almost-nondispersive edge states, the number of locations increasing with the frequency. All the results are obtained via asymptotic analysis and semiexplicit computations done on the limit quantum graph. Numerical simulations illustrate the theoretical results.
DOI: 10.1137/23m1600177
Authors: Bérangère Delourme, Sonia Fliss
Institutions: Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, École Nationale Supérieure de Techniques Avancées, Institut Polytechnique de Paris, POEMS: Propagation des Ondes : Etude Mathématique et Simulationan, École Nationale Supérieure de Techniques Avancées Paris
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402689060