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Perturbative analytic theory of an ultrahigh-Q toroidal microcavity

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.

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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.

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Vahala, Kerry0000-0003-1783-1380
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
Record Number:CaltechAUTHORS:MINpra07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8180
Deposited By: Archive Administrator
Deposited On:31 Jul 2007
Last Modified:08 Nov 2021 20:48

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