Dihedral beams
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915072963510272 |
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| author | Jaimes-Nájera, Alfonso |
| author_facet | Jaimes-Nájera, Alfonso |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15566 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dihedral beams Jaimes-Nájera, Alfonso Optics Mathematical Physics 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. |
| title | Dihedral beams |
| topic | Optics Mathematical Physics |
| url | https://arxiv.org/abs/2412.15566 |