Exploiting space-time duality in the synthesis of impedance transformers via temporal metamaterials

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.