Geometry-Driven Resonance and Localization of Light in Fractal Phase Spaces

TL;DR

This paper shows how fractal, non-Euclidean geometries can intrinsically induce light resonance, localization, and damping without materials or external potentials, revealing a new paradigm for controlling light through geometry.

Contribution

It introduces a novel mechanism where fractal phase space geometry alone causes resonance and localization of light, independent of material boundaries.

Findings

Fractal geometry enforces resonance quantization via closed-loop geodesics.

Light can be localized and dissipated purely through geometric effects.

Numerical simulations confirm geometry-driven wave confinement and damping.

Abstract

Geometry can fundamentally govern the propagation of light, independent of material constraints. Here, we demonstrate that a fractal phase space, endowed with a non-Euclidean, scale-dependent geometry, can intrinsically induce resonance quantization, spatial confinement, and tunable damping without the need for material boundaries or external potentials. Employing a fractional formalism with a fixed scaling exponent, we reveal how closed-loop geodesics enforce constructive interference, leading to discrete resonance modes that arise purely from geometric considerations. This mechanism enables light to localize and dissipate in a controllable fashion within free space, with geometry acting as an effective quantizing and confining agent. Numerical simulations confirm these predictions, establishing geometry itself as a powerful architect of wave dynamics. Our findings open a conceptually new and experimentally accessible paradigm for material-free control in photonic systems, highlighting the profound role of geometry in shaping fundamental aspects of light propagation.