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  • Open Access

Unified framework for photon dynamics in non-Euclidean polygonal cavities

Yechun Ding1, Yongsheng Wang1,2, Peng Li3, Yaxin Guo1, Yanpeng Zhang1, Feng Yun1,4, Ce Shang5,*, Run-Qiu Yang6,†, Caigui Jiang7,‡ et al.

Feng Li1,4,§

  • *Contact author: shangce@aircas.ac.cn
  • †Contact author: aqiu@tju.edu.cn
  • ‡Contact author: cgjiang@xjtu.edu.cn
  • §Contact author: felix831204@xjtu.edu.cn
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Phys. Rev. Research 8, 033334 – Published 18 September, 2026

DOI: https://doi.org/10.1103/hmxc-ltdl

Abstract

We extend the concept of polygonal resonators to curved spaces through a unified model governed by a joint curvature parameter. This framework uncovers unique dynamics, including dissipative states defined by hyperbolic fixed points that yield phase diagrams in the curvature space. We find that stability transitions across geometric boundaries are characterized by sharp declines in the quality factor, a manifestation of chaotic instability that is overcome in the wave regime, highlighting the wave nature of wave chaos. A key discovery is the symmetry-driven asymptotic behavior in geodesic-sided cavities, revealing a profound connection between physical dynamics and underlying geometry. We also introduce a “non-Euclidean unit circle” as a general shape-invariant platform for optical simulation. These findings provide a robust framework for studying non-Euclidean wave chaos and point to strategies for designing integrated photonics with enhanced degrees of freedom.

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Phys. Rev. Research 8, 033334– Published 18 September, 2026
  • Received 30 April 2025
  • Revised 3 June 2026
  • Accepted 1 September 2026
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