Electrodynamics of Space-filling Curves and their Antenna and Metamaterial Applications
The concept of space-filling curves has been studied in mathematics since the late 19th century.
These curves are, in general, continuous mappings from a normalized one-dimensional interval [0,1] to a
normalized two-dimensional region, [0,1] × [0,1]. In each case the curve passes through every point in the
2-D region in the limit of infinite iteration order. The most widely known of these curves are the ones
proposed by G. Peano and David Hilbert in 1890 and 1891, respectively. From an electromagnetics,
scattering, and antenna perspective, space-filling curves are particularly attractive as they offer resonant
structures with very small footprints when the step-order of iterative filling increases. However, these
curves are a subset of a broader class of curves in graph theory known as Grid-Graph Hamiltonian Paths
(GG-HP) and Grid-Graph Hamiltonian Cycles (GG-HC).
In this lecture, we will explore the fundamental electrodynamics of space-filling curves and Grid-Graph
Hamiltonian Paths, focusing on their scattering properties, polarizability, and multiband functionality, and
their roles in the development of electrically small and reconfigurable antennas, metamaterials, and
metasurfaces. Specifically, we will examine the use of space-filling curve and Hamiltonian Path fractal
elements in designing wideband yet miniaturized top-loaded monopoles, ultra-passive RFID tags,
polarization-insensitive high-impedance surfaces, electrically-thin microwave absorbers, single-negative
(SNG) and double-negative (DNG) metamaterials, and metasurfaces with non-uniformly spaced
inclusions for printed antenna beam shaping. We will highlight the key features of these novel structures
and provide physical insights into both theoretical and experimental results.
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- Campina Grande, Paraiba
- Brazil
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Biography:
Ahmad Hoorfar is a professor of electrical and computer engineering, the ECE department’s graduate chair, and the founder and director of Antenna Research Laboratory at Villanova University. He received his B.S. in electronics engineering from the University of Tehran and the M.S. and Ph.D. degrees in electrical
engineering from the University of Colorado Boulder, His research contributions over the years have covered areas in electromagnetic field theory, numerical electromagnetics, printed and low-profile antennas, metamaterial media and surfaces, inverse scattering, microwave sensing and imaging, and stochastic optimization methods.
Dr. Hoorfar was the recipient of Villanova University’s Outstanding Faculty Research Scholar Award in
2007, and the recipient of Philadelphia section’s ‘IEEE chapter of the year award' for his leadership in
chairing the AP/MTT joint chapter in 1995. He has served on the review board of various IEEE and other
technical publications and has also been on the technical program committees of numerous international
symposia and conferences on antennas, microwaves, radar, and remote sensing in the last thirty years. He
spent his sabbatical leaves in 2002 and 2009 at NASA’s Jet Propulsion Laboratory (JPL) in Pasadena,
California, where he contributed to the design and development of antenna systems for NASA’s deep-
space communication network.
Dr. Hoorfar is a Life Fellow member of IEEE, a member of International Radio Science Commission B,
and an elected member of the Franklin Institute Committee on Science and the Arts. He is a Distinguished
Lecturer of the IEEE Antennas and Propagation Society (AP-S) for 2023-2025 and has also been serving
as the chair of the IEEE AP-S paper awards committee since 2023.