Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals

TL;DR

This paper investigates the non-orthogonality of modes in optical micro-spirals, revealing broad parameter regimes with significant asymmetry and non-orthogonality due to asymmetric scattering, supported by numerical and ray dynamics simulations.

Contribution

It demonstrates that non-orthogonality in optical micro-spirals is more prevalent than previously thought, linked to asymmetric scattering effects, using a non-Hermitian model and numerical simulations.

Findings

Significant non-orthogonality occurs over broad parameter ranges.

Asymmetric scattering causes near-degenerate, highly non-orthogonal modes.

Ray-wave correspondence confirms the scattering effects in micro-spirals.

Abstract

Quasi-bound states in an open system do in general not form an orthogonal and complete basis. It is, however, expected that the non-orthogonality is weak in the case of well-confined states except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the non-orthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly non-orthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenomenon is related to the asymmetric scattering between clockwise and counterclockwise propagating waves in the spiral geometry. Numerical simulations of ray dynamics reveal a clear ray-wave correspondence.