Transformation twinning to create isospectral cavities

TL;DR

This paper introduces a novel method to create isospectral cavities by applying transformation optics and inverse problem techniques, enabling different-shaped cavities to share identical spectral properties.

Contribution

It develops a general methodology for isospectral twinning of cavities using non-singular coordinate transforms and finite element analysis, combining physics concepts in a new way.

Findings

Successfully twin hexagonal drums with different shapes

Verified isospectrality through finite element analysis

Demonstrated practical application of transformation optics in cavity design

Abstract

Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide, is created by combining ideas from across physics including transformation optics, inverse problems and metamaterial cloaking. We twin a hexagonal drum with a deformed hexagonal drum using a non-singular coordinate transform that adjusts the deformed shape by mapping a near boundary domain to a zone of heterogeneous anisotropic medium. Splines define the mapping zone for twinning these two drums and we verify isospectrality by finite element analysis.