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Geometric representation of higher-order optical modes

Claire Cisowski

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Phys. Rev. A 113, 063530 – Published 26 June, 2026

DOI: https://doi.org/10.1103/gf21-tgcm

Abstract

An octant representation of higher-order optical modes that includes Laguerre-Gaussian and Hermite-Gaussian modes is presented. The octant picture captures the high-dimensional nature of three-state optical systems and beyond, with standard Poincaré spheres for orbital angular momentum forming subspaces of the entire state space. This representation enables intuitive manipulation of both classical modes and optical qudits and provides a framework for extending Berry phases and topological invariants to high dimensions.

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Phys. Rev. A 113, 063530– Published 26 June, 2026
  • Received 25 February 2026
  • Accepted 3 June 2026
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