OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 2 — Feb. 1, 2014
  • pp: 404–410

Mathematical modeling of Fabry–Perot resonators: I. Complex-variable analysis by uniformly convergent partial-fraction expansion

G. Hugh Song  »View Author Affiliations


JOSA A, Vol. 31, Issue 2, pp. 404-410 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000404


View Full Text Article

Acrobat PDF (422 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In the first part of a two-part study on the equivalent-circuit representation of any given Fabry–Perot resonator (FPR) that supports, by nature, infinitely many resonance modes, the complex-variable pole-zero structure of its scattering coefficients is extensively analyzed in general terms through partial-fraction expansion based on a corollary to Mittag-Leffler’s theorem for meromorphic functions. By finding the right offset constant in the expansion from the theory, we present two sets of uniformly converging series of partial fractions for the two scattering coefficients. We compare quality of convergence between the two series sets and find that a set obtained by the fraction-reciprocated reflection coefficient for the FPR is relatively better than the other one, which is fortunate for the subsequent work in the second part.

© 2014 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.2230) Diffraction and gratings : Fabry-Perot
(070.4790) Fourier optics and signal processing : Spectrum analysis

ToC Category:
Diffraction and Gratings

History
Original Manuscript: September 17, 2013
Manuscript Accepted: December 12, 2013
Published: January 29, 2014

Citation
G. Hugh Song, "Mathematical modeling of Fabry–Perot resonators: I. Complex-variable analysis by uniformly convergent partial-fraction expansion," J. Opt. Soc. Am. A 31, 404-410 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-2-404

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited