Min, Bumki and Yang, Lan and Vahala, Kerry (2007) Perturbative analytic theory of an ultrahigh-Q toroidal microcavity. Physical Review A, 76 (1). Art. No. 013823. ISSN 1050-2947. doi:10.1103/PhysRevA.76.013823. https://resolver.caltech.edu/CaltechAUTHORS:MINpra07
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Abstract
A perturbation theoretic approach is proposed as an efficient characterization tool for a tapered fiber coupled ultrahigh-quality factor (Q) toroidal microcavity with a small inverse aspect ratio. The Helmholtz equation with an assumption of quasi-TE/TM modes in local toroidal coordinates is solved via a power series expansion in terms of the inverse aspect ratio and the expanded eigenmode solutions are further manipulated iteratively to generate various characteristic metrics of the ultrahigh-Q toroidal microcavity coupled to a tapered fiber waveguide. Resonance wavelengths, free spectral ranges, cavity mode volumes, phase-matching conditions, and radiative Q factors are derived along with a mode characterization given by a characteristic equation. Calculated results are in excellent agreement with full vectorial finite-element simulations. The results are useful as a shortcut to avoid full numerical simulation, and also render intuitive insight into the modal properties of toroidal microcavities.
Item Type: | Article | ||||||
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Additional Information: | ©2007 The American Physical Society (Received 13 February 2007; published 20 July 2007) This work was supported by DARPA, NSF, Caltech Lee Center, and the plasmonic MURI. | ||||||
Subject Keywords: | perturbation theory; laser cavity resonators; Helmholtz equations; optical fibre theory; optical phase matching; Q-factor; finite element analysis | ||||||
Issue or Number: | 1 | ||||||
DOI: | 10.1103/PhysRevA.76.013823 | ||||||
Record Number: | CaltechAUTHORS:MINpra07 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:MINpra07 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 8180 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Archive Administrator | ||||||
Deposited On: | 31 Jul 2007 | ||||||
Last Modified: | 08 Nov 2021 20:48 |
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