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Updated: Jun 3, 2026

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
Published on: August 5, 2013
Ince-Gaussian modes of the paraxial wave equation and stable resonators
Miguel A Bandres1, Julio C Gutiérrez-Vega
1Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey, México, 64849. mbandres@grad.physics.sunysb.edu
Abstract:
We present the Ince-Gaussian modes that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and that are transverse eigenmodes of stable resonators. The transverse shape of these modes is described by the Ince polynomials and is structurally stable under propagation. Ince-Gaussian modes constitute the exact and continuous transition modes between Laguerre- and Hermite-Gaussian modes. The expansions between the three families are derived and discussed. As with Laguerre-Gaussian modes, it is possible to construct helical Ince-Gaussian modes that exhibit rotating phase features whose intensity pattern is formed by elliptic rings and whose phase rotates elliptically.
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