A Topological View on Optical and Phononic Fabry–Perot Microcavities through the Su–Schrieffer–Heeger Model

Abstract

Advances in nanofabrication technologies have enabled the study of acoustic wave phenomena in the technologically relevant GHz-THz range. First steps towards applying concepts from topology in nanophononics were made with the proposal of a new topological acoustic resonator, based on the concept of band inversion. In topology, the Su-Schrieffer-Heeger (SSH) model is the paradigm that accounts for the topological properties of many one-dimensional structures. Both the classical Fabry-Perot resonator and the reported topological resonators are based on Distributed Bragg Reflectors (DBRs). A clear and detailed relation between the two systems, however, is still lacking. Here, we show how a parallelism between the standard DBR-based acoustic Fabry-Perot type cavity and the SSH model of polyacetylene can be established. We discuss the existence of surface modes in acoustic DBRs and interface modes in concatenated DBRs and show that these modes are equivalent to Fabry-Perot type cavity modes. Although it is not possible to assign topological invariants to both acoustic bands enclosing the considered minigap in the nanophononic Fabry-Perot case, the existence of the confined mode in a Fabry-Perot cavity can nevertheless be interpreted in terms of the symmetry inversion of the Bloch modes at the Brillouin zone edge.

Phonon engineering with superlattices: Generalized nanomechanical potentials

“…Another fundamental property of acoustic superlattices that has not been exploited here are the Bloch mode symmetries at the minigap edges. It has been shown [44] that an inversion of these symmetries can be achieved by closing and re-opening a minigap, inducing a topological phase transition and hence allowing the construction of topological interface states [23][24][25]45]. This approach could for example be combined with the adiabatic resonator presented in Fig.…”

“…Very recently, an acoustic cavity was reported based on the adiabatic periodicity breaking of a superlattice [5], in analogy to a potential well. Exploiting the symmetry properties in periodic superlattices, topological interface modes have also been recently reported [24,25].…”

Special Issue on Brillouin Scattering and Optomechanics

“…Topological protection can be obtained in certain passive structures based on symmetry considerations. Esmann and Lanzillotti-Kimura [3] considered nanofabricated Fabry-Perot resonators operating with phonons in the GHz-THz range. They drew a parallel between the Su-Schrieffer-Heeger (SSH) model, which is a paradigm that accounts for the topological properties of many one-dimensional structures, and the standard Distributed Bragg Reflector (DBR)-based acoustic Fabry-Perot interferometers.…”

Engineering of topological state transfer and topological beam splitter in an even-size Su-Schrieffer-Heeger chain

“…As one of the simplest topological insulator model, the Su-Schrieffer-Heeger (SSH) model [18,19] has also attracted more and more attention in recent years since it possesses the structural simplicity and the abundant physical insights concurrently [20][21][22]. The structural simplicity ensures that the SSH model can be mapped by dint of all kinds of different systems, such as the cold atoms trapped into the optical lattice [23][24][25][26], the waveguide arrays [27][28][29], the graphene nanoribbons [30][31][32][33], the superconducting resonators and qubits [34][35][36], the optomechanical array composed by multiple single optomechanical system [37][38][39][40], etc. Based on these platforms, various topological contexts in SSH model have been explored, including the edge state and the topological phase transition [25,[41][42][43], quantum walk [44][45][46], the non-Hermitian effect [42,[47][48][49], topological charge pumping [50][51][52][53], the observation and detection of the topological features [23,[54][55][56], etc.…”