Abstract
Abstract Multisection quarter-wave impedance transformers are widely applied in microwave engineering and optics to attain impedance-matching networks and antireflection coatings. These structures are mostly designed in the spatial domain (time harmonic) by using geometries of different materials. Here, we exploit such concepts in the time domain by using time-varying metamaterials. We derive a formal analogy between the spectral responses of these structures and their temporal analogs, i.e., time-varying stepped refractive-index profiles. We show that such space-time duality grants access to the vast arsenal of synthesis approaches available in microwave engineering and optics. This allows, for instance, the synthesis of temporal impedance transformers for broadband impedance matching with maximally flat or equi-ripple responses, which extend and generalize the recently proposed quarter-wave design as an antireflection temporal coating. Our results, validated via full-wave numerical simulations, provide new insights and deeper understanding of the wave dynamics in time-varying media, and may find important applications in space-time metastructures for broadband frequency conversion and analog signal processing.
Highlights
The study of wave interactions with time-varying media and structures is a subject of a longstanding interest in electromagnetics [1,2,3], which has recently gained new momentum in the emerging field of space-time metamaterials and metasurfaces [4,5,6,7]
As a proof of concept, here we show that the general synthesis approach developed by Riblet in the 1950s [43] for the spatial case can be seamlessly applied to the synthesis of broadband temporal impedance-matching transformers
Our theory ensures that this result holds in the presence of generic spatial and temporal multisteps, under the argument mapping θ ↔ φ. We show how this formal analogy can be leveraged to exploit the wealth of synthesis tools and approaches developed in microwave engineering for impedance transformers using time-varying media
Summary
The study of wave interactions with time-varying media and structures is a subject of a longstanding interest in electromagnetics [1,2,3], which has recently gained new momentum in the emerging field of space-time metamaterials and metasurfaces [4,5,6,7] In these artificial materials, the conventional spatial modulation of the constitutive parameters is synergistically coupled with temporal modulation, thereby enabling a wealth of intriguing field-manipulation effects and anomalous wave-matter interactions. Castaldi et al.: Exploiting space-time duality in impedance synthesis [36], effective-medium theory [37], and higher-order homogenization schemes [38] were proposed to model “temporal multilayers” or “temporal multisteps” These scenarios can be considered as the temporal equivalent of spatial multi-layered media [39] with the difference that in the former case time-varying media with stepped permittivity profiles are implemented for the whole spatially unbounded medium where the wave travels. Our results, which include the temporal quarter-wave design [41] as a special case, provide new insights and deeper understanding of the role and possible applications of temporal boundaries by exploiting the space-time duality in the study of wave propagation in temporal metamaterials and pave the way to novel exciting developments in this emerging field
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