" Flat band induced topological photonic Tamm states in stubbed structures: Theory and experiment".

By

Madiha AMRANI

Mohamed 1er University, Oujda, Morocco

19 December 2024 at 10.30 a.m. P5 room 002

ABSTRACT

We provide theoretical and experimental evidence for the existence of topological Tamm states at the interface between two photonic crystals (PCs) as a function of period and stub length. Several works have addressed these states in the well-known Su-Schrieffer-Heeger model, a dimerised chain based on two resonators per unit cell where the opening of a gap at a Dirac cone leads to a symmetry inversion of the mass bands between two topologically different crystals. We present here a detailed theoretical analysis of a mechanism based on the inversion of the band edge symmetry around a flat band, i.e. when the bandwidth disappears, while using a single resonator (stub) per unit cell. We then propose a simple and versatile experimental platform for observing these interface states, based on coaxial cables operating in the radio frequency domain. The study of these states was carried out using different approaches: (i) band topology based on Zak phase and band edge mode symmetry, (ii) the sign of the reflection phase between each PC and a waveguide, and (iii) dips or peaks in the reflection and transmission spectra when two finite photonic crystals are connected together either horizontally or vertically along a waveguide. In addition, we give a general rule on the existence of interface states when two PCs have two common vacancies with a flat band in their middle and different bulk edge symmetries. We also provide closed expressions for the geometrical parameters and the frequency for which the interface state becomes a continuum bound state (BIC). We show that these topological BIC states are stationary states of the cavity between the two PCs, and that they are very robust to any perturbation on either side of the cavity. Finally, we demonstrate the impossibility of the existence of interface states between two PCs with identical periods and different stubs. Theoretical and experimental results are discussed for the Neumann and Dirichlet boundary conditions at the end of the stubs.

Abstract:

We provide theoretical and experimental evidence for the existence of topological Tamm states at the interface between two stubbed photonic crystals (PCs) as a function of the period and length of the stubs. Several works have addressed these states in the well-known Su-Schrieffer-Heeger model, a dimerized chain based on two resonators per unit cell where the opening of a gap at a Dirac cone results in a symmetry inversion of bulk bands between two topologically different crystals. Here, we give a detailed theoretical analysis of a mechanism based on band-edge symmetry inversion around a flat band, i.e., when the width of the pass band vanishes, while using only one resonator (stub) per unit cell. Then, we propose a simple versatile experimental platform to observe such interface states, which is based on coaxial cables operating in the radio-frequency domain. The investigation of these states was performed by using different approaches: (i) the topology of the bands based on the Zak phase and the symmetry of the band-edge modes, (ii) the sign of the reflection phase between each PC and a waveguide, and (iii) the dips or peaks in the reflection and transmission spectra when two finite photonic crystals are connected together either horizontally or vertically along a waveguide. Furthermore, we give a general rule about the existence of interface states when two PCs exhibit two common gaps with a flat band in their middle and different bulk-edge symmetries. Also, we provide closed-form expressions of the geometrical parameters and the frequency for which the interface state becomes bound state in the continuum (BIC). We show that these topological BIC states are stationary states of the cavity between the two PCs, and are very robust to any perturbation on both sides of the cavity. Finally, we show the impossibility of existence of interface states between two PCs with identical periods and different stubs. The theoretical and experimental results are discussed for both Neumann and Dirichlet boundary conditions at the end of the stubs.