Geometry-Driven Resonance and Localization of Light in Fractal Phase Spaces
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918180337745920 |
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| author | Yıldız, L. Kaykı, D. Ciappina, M. F. |
| author_facet | Yıldız, L. Kaykı, D. Ciappina, M. F. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry-Driven Resonance and Localization of Light in Fractal Phase Spaces Yıldız, L. Kaykı, D. Ciappina, M. F. Optics Quantum Physics 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. |
| title | Geometry-Driven Resonance and Localization of Light in Fractal Phase Spaces |
| topic | Optics Quantum Physics |
| url | https://arxiv.org/abs/2510.27205 |