Structural entropy and spatial decay of quasimodes in Vogel spirals

TL;DR

This study explores the decay and localization of quasimodes in Vogel spirals, revealing three decay types and identifying highly localized, long-lived modes with potential applications in optics and sensing.

Contribution

It introduces a comprehensive analysis of quasimode decay types in Vogel spirals, highlighting the coexistence of exponential, power-law, and Gaussian decays and their implications for optical functionalities.

Findings

Gaussian decay characterizes most localized quasimodes.

Critical quasimodes exhibit algebraic spatial decay.

Vogel spirals host long-lived, spatially localized quasimodes.

Abstract

We investigate the spatial decay and temporal localization properties of quasimodes (i.e., scattering resonances) of two-dimensional Vogel spirals, composed of deterministic, aperiodic arrays of electric dipoles. By determining the structural entropy and localization maps of Vogel spirals using the Green's matrix method, we show that three distinctive decay types of quasimodes coexist in Vogel spirals: exponential, power-law, and Gaussian. While the exponential and the power-law decays typically occur in disordered media and multifractal systems, respectively, the Gaussian decay is demonstrated to characterize, on average, the most localized quasimodes of Vogel spirals, both spatially (smallest participation ratios) and temporarily (longest lifetimes). These decay forms are demonstrated by a no-fitting analysis of the localization maps, independently corroborated by calculating the electric field in real space, which also provides a direct evidence of the algebraic spatial decay of critical quasimodes. Altogether our findings unveil a rich spectrum of both long-lived and spatially localized quasimodes that coexist in Vogel spirals and can be of direct relevance to novel optical functionalities for applications to light sources and sensing devices.