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

Martin Esmann,Norberto Lanzillotti-Kimura

doi:10.3390/app8040527

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.

Highlights

Optical semiconductor microcavities are widely used in nanophotonic applications
Similar to optical distributed Bragg reflectors (DBRs), these resonant structures can control the propagation of acoustic phonons in the technologically relevant GHz–THz range by making use of minigaps in their band structure at the center and the edge of the Brillouin zone
We study the role of the composition (x) in a Alx Ga1−x As/Al1−x Gax As superlattice and how to directly map an acoustic Fabry–Perot type structure to a polyacetylene chain described by the Su–Schrieffer–Heeger (SSH) model [32,33]

Summary

Introduction

Optical semiconductor microcavities are widely used in nanophotonic applications. Based on the concept of a Fabry–Perot resonator, the metallic mirrors are replaced by distributed Bragg reflectors (DBRs), where two materials with contrasting indices of refraction are arranged in a periodic stack. It was recently realized that an optimized optical cavity in the near infrared is at the same time an optimized acoustic cavity in the 20 GHz range [11] This concept was extended into GaAs/AlAs micropillars showing unprecedented quality factors at room temperature and high vacuum optomechanical couplings [2,26]. In a previous work [27], we introduced the concept of topological invariants to nanophononics and experimentally implemented a nanophononic system supporting a robust topological interface state at 350 GHz. The confined nanophononic state was constructed through band inversion, i.e., by concatenating two semiconductor superlattices with inverted spatial mode symmetries at the Brillouin zone center. The confined nanophononic state was constructed through band inversion, i.e., by concatenating two semiconductor superlattices with inverted spatial mode symmetries at the Brillouin zone center This led to the generation of robust interface states between two topologically different superlattices. The same analogies, hold in the optical domain

Interface Modes through Material Composition Tuning

Discussion and Conclusions