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 to a normalized two-dimensional region, × . 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.
Please join us at 5:30PM for networking and light refreshments!
[] [] [] Co-sponsored by: Syracuse University EECS Department
Speaker(s): IEEE AP-S Distinguished Lecturer and IEEE Life Fellow Prof. Ahmad Hoorfar
Agenda:
5:30pm: Networking and light refreshments;
6:00pm: Presentation;
7:00pm: Q&A and discussion;
Room: Lundgren Room (LSB 106), Bldg: FREE PARKING is available! Indicate interest in registration form., Life Sciences Complex at Syracuse University, 107 College Pl, Syracuse, New York, United States, 13210