Edge states on hexagonal array of resonators with complex coupling constants

Dmitry P. Fedchenko^ab, Daria V. Goryacheva^b, Ivan V. Timofeev<sup>ab

a</sup> Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Krasnoyarsk, Russian Federation
^b Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: A waveguide system consisting of a hexagonal array of resonators with the sixth-order symmetry is studied. Using deformations in the system obtained by permuting vertices on the coordination spheres and changing the constants of coupling between the resonators, the edge states have been obtained, the origin of which is explained by elementary means. The edge solutions are preserved for an array with the complex coupling constants.

Keywords: photonic edge states, graphene crystal lattice, tight binding approximation, complex coupling constants.

UDC: 519.174.7; 535.3

Received: 10.06.2025
Received in revised form: 05.10.2025
Accepted: 20.11.2025

Language: English