Advances in Leaky-Wave Periodic Structures after Oliner’s Pioneering Research P. Lampariello 1 , F. Frezza 1 , A. Galli 1 , P. Baccarelli 1 , P. Burghignoli 1 , G. Lovat 1 , S. Paulotto 2 , G. Valerio 3 , and D. R. Jackson 4 1 Sapienza University of Rome, Rome, Italy {paolo.lampariello, fabrizio.frezza, alessandro.galli, paolo.baccarelli, paolo.burghignoli, giampiero.lovat}@uniroma1.it 2 Maxtena Inc., Rockville, MA, U.S.A. s.paulotto@gmail.com 3 Université de Rennes 1, Rennes, France guido.valerio@univ-rennes1.fr 4 University of Houston, Houston, TX, U.S.A. djackson@uh.edu Abstract—The research activity jointly developed during the last decade between the groups coordinated by P. Lampariello in Europe and by D. R. Jackson in the U.S.A. is reviewed, on the basis of the fruitful scientific interaction had with Prof. Oliner since the Eighties. The main focus here is on advances in leaky waves and leaky-wave antennas based on periodic structures. This involves topics of different nature, such as issues of numerical modeling in periodic Green’s functions, leakage features in metamaterials and other innovative media, and one- dimensional and two-dimensional configurations of printed and planar leaky-wave radiators. Keywords—periodic structures; leaky waves; numerical techniques; metamaterials; leaky-wave antennas I. INTRODUCTION It is widely known that one of the most significant parts of the research activity of Prof. Arthur A. Oliner, documented since the fifties, has dealt with leaky waves (LWs) and leaky- wave antennas (LWAs) [1]-[4]. After the dissemination of his fundamental contributions in the following decades, some research groups had the privilege to start fruitful collaborations with Prof. Oliner. Among them, since the early eighties, a main teamwork in Europe was activated by Prof. P. Lampariello and then by his group at Sapienza University of Rome [5]-[8]. Towards the end of eighties, Prof. D. R. Jackson and some American colleagues also had the opportunity to start productive scientific relationships with him on LWs [9],[10]. Having known and interacted with Prof. Oliner has been an unforgettable experience and an unsurpassed privilege for all of us. We feel deeply in debt to him both for the outstanding scientific guidance, always exceptionally clear, profound and rigorous, and for his very special personal qualities of humanity, kindness and congeniality. Most of the initial work in collaboration with Prof. Oliner was centered on LW radiators mainly derived by partially-open metallic guides and printed lines of uniform type [1]-[4]. Based on such fertile early work, the collaboration among “Oliner’s disciples” continued after the new millennium with a number of novel research topics, mainly focused on highly promising applications of LWs in periodic structures. Needless to say, Prof. Oliner provided also in this area pioneering insight, innovative perspectives and fundamental analyses, which are still landmarks for the scientific community [4]. A representative selection of our joint research developed on these topics, mainly during the last decade, is summarized in this contribution. Sec. II is devoted to the efficient numerical modeling of LWs structures through the development of ad-hoc acceleration techniques for periodic Green’s functions. Sec. III is focused on ‘small-scale’ (with respect to wavelength) periodic structures, with specific important applications involving metamaterials and other innovative media. Sec. IV is dedicated to modern one-dimensional (1D) periodic LWAs based on printed technology, for improved forward/backward scanning through broadside. Sec. V describes novel two- dimensional (2D) periodic planar LW radiators (Fabry-Pérot type etc.), for pencil-beam or conical radiation. Sec. VI outlines some conclusive remarks on these topics. II. PERIODIC GREEN’S FUNCTIONS As is well known [1]-[4], the efficient characterization of periodic LWAs is based on the computation of the phase and attenuation constants of the ‘dominant’ leaky wave describing the aperture field. For simple structures, such a result can be obtained through simplified circuit models (for which Oliner’s contribution was fundamental and extensive [1]-[4]) or through the analysis of truncated structures [11]. In more general cases, an accurate dispersive analysis of the periodic structure needs to be addressed. The electromagnetic problem can then be formulated, discretized and solved inside the unit cell with Floquet-periodic conditions at its boundary [12]. The method of moments (MoM) is often an advantageous discretization approach, thanks to the possibility of including the description of the periodic conditions and the background geometry in the periodic Green’s functions (PGF) of the problem [13]. Several kinds of Green’s functions can be defined: we refer here to a mixed-potential integral equation (MPIE) formulation, whose mild spatial singularity is helpful when implementing a spatial-domain MoM [14]. The PGF G p in a structure with periodic lattice vectors s 1 and s 2 can be expressed as a spatial series, i.e., a superposition of nonperiodic Green functions G, each one displaced by the vector 1 2 nm n m   s s s (n and m being integers) and shifted through the factor t00 nm j e   k s , where k t00 is the wavenumber in the plane of the periodicity [13]. Unfortunately, such a series does not converge for complex wavenumbers k t00 =  t00 – j t00 (as occurs in leaky waves), due to the factor t00 nm e   α s , which can give rise to amplification. 978-2-87487-035-4  2014 EuMA 6 -9 Oct 2014, Rome, Italy Proceedings of the 44th European Microwave Conference 433