IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 5, MAY 2014 2361 Improved Bandwidth Formulas for Fabry-Pérot Cavity Antennas Formed by Using a Thin Partially-Reflective Surface Ali Hosseini, Student Member, IEEE, Filippo Capolino, Senior Member, IEEE, Franco De Flaviis, Fellow, IEEE, Paolo Burghignoli, Senior Member, IEEE, Giampiero Lovat, Member, IEEE, and David R. Jackson, Fellow, IEEE Abstract—The power bandwidth of Fabry-Pérot-cavity an- tennas comprised of a thin partially-reflective-surface (PRS) above a perfectly conducting ground plane, based on its trans- verse-equivalent-network model and the simple susceptance model of a thin PRS, is studied. Considering the frequency varia- tion of the PRS susceptance model, a new formula is proposed to estimate the power density bandwidth and thus (approximately) the gain bandwidth of such cavities. The application and accuracy of the proposed formula are investigated using both numerical (i.e., based on full-wave simulations) and analytical (i.e., based on a transmission-line model of the antenna) methods. Finally, the accuracy of the proposed formula is investigated for cavities formed using a finite versus infinite PRS. Index Terms—Fabry-Pérot cavity (FPC) antenna, leaky-wave antenna (LWA), thin metallic frequency-selective-surface (FSS), thin partially-reflective-surface (PRS). I. INTRODUCTION S INCE the seminal work of G. Von Trentini [1], the use of partially-reflecting surfaces (PRSs) as an effective way to enhance the directivity of simple sources placed above a ground plane has been extensively investigated. Realizations of PRSs in the form of single or multiple dielectric layers [2]–[4], or frequency-selective surfaces (FSSs) comprised of metal patches or slots cut in a metal plate [5]–[9] have been proposed and studied. The operating principle of the resulting antenna can be explained in different ways. With reference to its receiving mode, the strong enhancement of directivity at a prescribed angle (e.g., broadside, which is normal to the PRS plane) can be interpreted as due to the resonant response of the Fabry-Pérot-like cavity formed by the PRS and the ground Manuscript received December 11, 2012; revised November 11, 2013; ac- cepted February 05, 2014. Date of publication February 20, 2014; date of cur- rent version May 01, 2014. A. Hosseini, F. Capolino, and F. De Flaviis are with the Henry Samueli School of Engineering, University of California, Irvine, CA 92697 USA (e-mails: sahossei@uci.edu; f.capolino@uci; edu and franco@uci.edu). P. Burghignoli is with the Department of Information Engineering, Elec- tronics and Telecommunications, “La Sapienza” University of Rome, 00184 Rome, Italy (e-mail: burghignoli@ die.uniroma1.it). G. Lovat is with the Department of Astronautic, Electrical and Energetic En- gineering, “La Sapienza” University of Rome, 00184 Rome, Italy (e-mail: gi- ampiero.lovat@uniroma1.it). D. R. Jackson is with the Department of Electrical and Computer Engi- neering, University of Houston, Houston, TX 77204-4005 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2014.2307337 plane when excited by an impinging plane wave. Therefore, the structure can be classified as a Fabry-Pérot Cavity (FPC) antenna. Alternatively, with reference to the transmitting mode of the antenna, directivity enhancement can be related to the excitation of weakly-attenuated leaky modes, as first noted and then extensively studied by Jackson, Oliner, and their co-workers [10]–[14]. Such leaky modes dominate the aperture field of the antenna and give rise to strongly peaked patterns in the far field; the structure can thus be classified as a leaky-wave antenna (LWA). When excited by a localized source, such as a horizontal electric or magnetic dipole, the relevant leaky modes propagate radially as cylindrical waves in the transverse plane (i.e., the plane of the PRS). A critical aspect of FPC antennas is their operational bandwidth (BW), which may be defined in terms of either input impedance or radiated power density (or alternatively, gain). In particular, with reference to an FPC antenna designed to radiate at broadside, the relative 3 dB power density bandwidth, PBW, is defined as the frequency range over which the broadside power density of the antenna remains within 3 dB of its maximum value, divided by the frequency of maximum broadside radiated power density. A similar definition holds for the 3 dB gain bandwidth GBW, which uses the broadside gain instead of radiated power den- sity. The two bandwidths are approximately equal provided the total power radiated by the source is constant over the bandwidth of the structure, which is usually the case as seen in the results provided later. Whereas the impedance bandwidth is mainly determined by the feeding structure of the antenna (not considered in this work), the power or gain bandwidths are essentially determined by the cavity behavior and hence by the PRS features and the material filling the cavity. For highly-directive FPCs (i.e., cavities formed by a highly reflective FSSs), the frequency dependence of the FSS has a negligible impact on the power bandwidth of the antenna as discussed in [6], [7], [12]. It has to be noted that in this work, only FPCs formed by a ‘thin’ PRS (i.e., with a thickness much less than the wavelength at the operating frequency of the an- tenna that can be modeled as a susceptance) are considered. In [15], using rather simple analytical approximations, and ne- glecting the frequency-dependence of a thin FSS susceptance, a new power bandwidth formula was discussed with gives an im- proved accuracy for low/moderate-gain FPCs relative to the for- mula derived in [6], [7], [12] [presented here as formula (20)]. By considering simple LC models, the frequency dependence of the shunt susceptance representing a thin FSS was studied in 0018-926X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.