Nonlocal microwave engineering: Shaping dispersion relations and enabling pulse transformations via time-switched long-range couplings.

Nonlocal metamaterials have recently attracted considerable attention across different areas of wave physics, owing to their ability to translate long-range interactions among meta-atoms into a wide array of wave vector-dependent responses and functionalities. Here, 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 on 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 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 transformations on a propagating pulse, as well as the excitation of modes with positive, negative, and zero group velocity. Last, 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 key 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 lay a general foundation for the design of more advanced nonlocal and time-varying electromagnetic and photonic systems.