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


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. C. Fabry and A. Pérot, “Théorie et applications d’une nouvelle méthodes de spectroscopie interférentielle,” Ann. Chim. Phys. 16, 115–144 (1899).
  2. L. V. Ahlfors, Complex Analysis, 3rd ed. (McGraw-Hill, Inc., 1979), Chap. 5, pp. 187–190, Sec. 2.
  3. G. H. Song, “Mathematical modeling of Fabry–Perot resonators: II. Uniformly converging multimode equivalent-circuit models,” J. Opt. Soc. Am. A.31, 411–420 (2014).
  4. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984). Fig. 9.9.
  5. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999). [CrossRef]
  6. A. I. Markushevich, Theory of Functions of a Complex Variable (AMS Chelsea Publishing, 2005), Vol. II, Chap. II.10, pp. 299–304, Sec. 51.
  7. L. Euler, Introduction to the Analysis of Infinite, Book I (Springer-Verlag, 1989). Translated by J. D. Bantom in 1840 from L. Euler, Introduction in Analysin Infinitorum (1748).
  8. L. V. Ahlfors, Complex Analysis, 3rd ed. (McGraw-Hill, 1979), Chap. 5, pp. 197, Sec. 2.3, Eq. (24).
  9. S. Lang, Complex Analysis, 4th ed. (Springer-Verlag, 1999), Chap. XIII, pp. 382.
  10. T. W. Gamelin, Complex Analysis (Springer-Verlag, 2001), pp. 356. Eq. (3.3).
  11. T. W. Gamelin, Complex Analysis (Springer-Verlag, 2001), pp. 351. Sec. XIII.2, Exer. 1.
  12. T. W. Gamelin, Complex Analysis (Springer Verlag, 2001), pp. 350. Sec. XIII.2, Example of Eq. (2.1).
  13. T. W. Gamelin, Complex Analysis (Springer-Verlag, 2001), pp. 118. Sec. IV.5.
  14. T. W. Gamelin, Complex Analysis (Springer Verlag, 2001), pp. 357. Sec. XIII.3, Exer. 12.
  15. L. V. Ahlfors, Complex Analysis, 3rd ed. (McGraw-Hill, 1979), Chap. 5, pp. 208–212, Sec. 3.2.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited