Dihedral beams
arXiv:2412.15566 · doi:10.1088/2040-8986/ad8802
Abstract
In this work, a group theory-based formulation that introduces new classes of dihedral-symmetric beams is presented. Our framework leverages the algebraic properties of the dihedral group of rotations and reflections to transform input beams into closed-form families of dihedral-invariant wavefields, which will be referred to as dihedral beams. Each transformation is associated with a specific dihedral group in such a way that each family of dihedral beams exhibits the symmetries of its corresponding group. Our approach is inspired by one of the outcomes of this work: elegant Hermite-Gauss beams can be described as a dihedral interference pattern of elegant traveling waves, a new set of solutions to the paraxial equation also developed in this paper. Particularly, when taking elegant traveling waves as input beams, they transform into elegant dihedral beams possessing quasi-crystalline properties and including features like phase singularities, self-healing, and pseudo-nondiffracting propagation, as well as containing elegant Hermite and Laguerre-Gauss beams as special cases. Our approach can be applied to arbitrary scalar and vector input beams and constitutes a general group-theory formulation that can be extended beyond the dihedral group.
Published as an invited article to the Journal of Optics Emerging Leaders collection 2024 (IOP Publishing). The Final Published Version is available online at https://iopscience.iop.org/article/10.1088/2040-8986/ad8802 For the Emerging Leaders collection website, see https://iopscience.iop.org/collections/jopt-230424-206