Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities

TL;DR

This paper demonstrates that deformed microdisk cavities without mirror symmetry naturally support nonorthogonal copropagating optical modes with a preferred rotation sense, expanding understanding of mode behavior in asymmetric optical resonators.

Contribution

It reveals that nonorthogonal mode pairs are common in deformed microdisks lacking mirror symmetry, without requiring boundary discontinuities, and establishes a quantitative relation between nonorthogonality and chirality.

Findings

Nonorthogonal mode pairs are prevalent in deformed microdisks.

A quantitative relation between nonorthogonality and chirality is established.

Ray-tracing simulations support the numerical results.

Abstract

Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes which agrees well with the predictions from an effective non-Hermitian Hamiltonian. A comparison to ray-tracing simulations is given.