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
Diffraction and Gratings
Original Manuscript: September 17, 2013
Manuscript Accepted: December 12, 2013
Published: January 29, 2014
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)