Nonlocal Microwave Engineering: Shaping Dispersion Relations and Enabling Frequency-Momentum Transformations via Time-Switched Long-Range Interactions

Abstract

Nonlocal metamaterials (MTMs) have recently attracted significant attention across different areas of wave physics, owing to their ability to translate long-range interactions among meta-atoms into a wide array of wavevector-dependent responses and functionalities. In this work, we introduce nonlocal transmission line metamaterials (TL MTMs) as a versatile platform to investigate and engineer nonlocality in the microwave frequency regime. We first establish a concise theoretical framework for nonlocal TL MTMs based on circuit and network theory, from which we derive the general dispersion relation for TL MTMs with arbitrarily complex nonlocal coupling configurations. Building upon this foundation, we demonstrate how such structures can be used to synthesize nearly arbitrary even-symmetric dispersion relations, effectively linking nonlocal circuit parameters to prescribed dispersion profiles. We then introduce time-switched nonlocal TL MTMs, a new class of metamaterials with time-varying nonlocality in which the nonlocal branches are dynamically activated as an electromagnetic pulse propagates through the structure. This platform enables complex, nearly arbitrary frequency-momentum transformations on a propagating pulse, as well as the excitation of modes with positive, negative, and zero group velocity. Finally, we experimentally validate our theoretical and numerical predictions with a proof-of-concept demonstration of a time-switched nonlocal TL MTM, observing a vertical transition in the dispersion diagram induced by abrupt time-switching. Our results provide new physical insights into the behavior of nonlocal MTMs, establish a versatile platform to investigate the interplay of frequency dispersion, spatial dispersion and time modulation, and, more broadly, lay a general foundation for the design of more advanced nonlocal and time-varying electromagnetic and photonic systems.