skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Theory of anisotropic whispering-gallery-mode resonators

Abstract

An analytic solution for a uniaxial spherical resonator is presented using the method of Debye potentials. This serves as a starting point for the calculation of whispering gallery modes (WGMs) in such a resonator. Suitable approximations for the radial functions are discussed in order to best characterize WGMs. The characteristic equation and its asymptotic expansion for the anisotropic case is also discussed, and an analytic formula with a precision of the order O[{nu}{sup -1}] is also given. Our careful treatment of both boundary conditions and asymptotic expansions makes the present work a particularly suitable platform for a quantum theory of whispering gallery resonators.

Authors:
 [1];  [1];  [2]
  1. Max Planck Institute for the Science of Light, Guenther-Scharowsky-Strasse 1/Bau24, D-91058 Erlangen (Germany)
  2. (Germany)
Publication Date:
OSTI Identifier:
22058787
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ANALYTICAL SOLUTION; ANISOTROPY; ASYMPTOTIC SOLUTIONS; BOUNDARY CONDITIONS; DEBYE LENGTH; EQUATIONS; OPTICAL SYSTEMS; OPTICS; POTENTIALS; RESONATORS; SPHERICAL CONFIGURATION

Citation Formats

Ornigotti, Marco, Aiello, Andrea, and Institute for Optics, Information and Photonics, University of Erlangen-Nuernberg, Staudtstrasse 7/B2, D-91058 Erlangen. Theory of anisotropic whispering-gallery-mode resonators. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.013828.
Ornigotti, Marco, Aiello, Andrea, & Institute for Optics, Information and Photonics, University of Erlangen-Nuernberg, Staudtstrasse 7/B2, D-91058 Erlangen. Theory of anisotropic whispering-gallery-mode resonators. United States. doi:10.1103/PHYSREVA.84.013828.
Ornigotti, Marco, Aiello, Andrea, and Institute for Optics, Information and Photonics, University of Erlangen-Nuernberg, Staudtstrasse 7/B2, D-91058 Erlangen. Fri . "Theory of anisotropic whispering-gallery-mode resonators". United States. doi:10.1103/PHYSREVA.84.013828.
@article{osti_22058787,
title = {Theory of anisotropic whispering-gallery-mode resonators},
author = {Ornigotti, Marco and Aiello, Andrea and Institute for Optics, Information and Photonics, University of Erlangen-Nuernberg, Staudtstrasse 7/B2, D-91058 Erlangen},
abstractNote = {An analytic solution for a uniaxial spherical resonator is presented using the method of Debye potentials. This serves as a starting point for the calculation of whispering gallery modes (WGMs) in such a resonator. Suitable approximations for the radial functions are discussed in order to best characterize WGMs. The characteristic equation and its asymptotic expansion for the anisotropic case is also discussed, and an analytic formula with a precision of the order O[{nu}{sup -1}] is also given. Our careful treatment of both boundary conditions and asymptotic expansions makes the present work a particularly suitable platform for a quantum theory of whispering gallery resonators.},
doi = {10.1103/PHYSREVA.84.013828},
journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 84,
place = {United States},
year = {2011},
month = {7}
}