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

• URL: http://arxiv.org/abs/2510.27205v1
• Date: Fri, 31 Oct 2025 05:56:23 GMT
• Title: Geometry-Driven Resonance and Localization of Light in Fractal Phase Spaces
• Authors: L. Yıldız, D. Kaykı, M. F. Ciappina,
• Abstract summary: We show that a fractal phase space endowed with a non-Euclidean, scale-dependent geometry can induce resonance quantization, spatial confinement, and tunable damping without the need for material boundaries or external potentials.<n>Our findings open a conceptually new and experimentally accessible paradigm for material-free control in photonic systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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