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Proceedings Paper

Geometric phases in higher-order transverse optical modes
Author(s): Steven J. M. Habraken; Gerard Nienhuis
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Paper Abstract

We study the geometric origin of generalized Gouy phases in paraxial optical modes of arbitrary order. We focus on the specific case of cyclic beam transformations of non-astigmatic vortex beams, thereby, generalizing the well-known geometric phase shift for first-order beams with orbital angular momentum to modes of arbitrary order. Our method involves two pairs of bosonic ladder operators, which, analogous to the algebraic description of the quantum-mechanical harmonic oscillator in two dimensions, connect transverse modes of different order. Rather than studying the geometry of the infinite-dimensional space of higher-order modes, we focus on the space underlying the ladder operators. We identify overall phases of the ladder operators, thereby obtaining the phases of all higher-order modes, and show that the variation of these phases under optical elements and transformations has a geometric interpretation in terms of the other parameters involved.

Paper Details

Date Published: 8 February 2010
PDF: 8 pages
Proc. SPIE 7613, Complex Light and Optical Forces IV, 76130F (8 February 2010); doi: 10.1117/12.840024
Show Author Affiliations
Steven J. M. Habraken, Leiden Univ. (Netherlands)
Gerard Nienhuis, Leiden Univ. (Netherlands)


Published in SPIE Proceedings Vol. 7613:
Complex Light and Optical Forces IV
Enrique J. Galvez; David L. Andrews; Jesper Glückstad, Editor(s)

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