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Theoretical framework demonstrates pseudounitary Floquet scattering matrix formulation in time-periodic photonic media, suggesting new approaches for spatio-temporal light micromanipulation.
The physics of waves in time-varying media provides numerous opportunities for wave control that are unattainable with static media. In particular, Floquet systems with a periodic time modulation are currently of considerable interest. Here we demonstrate how the scattering properties of a finite Floquet medium can be correctly described by a static Floquet scattering matrix, which satisfies a pseudounitary relation. This algebraic property is a consequence of the conservation of wave action for which we formulate here a continuity equation. Using this Floquet scattering matrix, we further demonstrate how it can be used to transfer concepts for wave-front-shaping based on the Wigner-Smith operator from static to Floquet systems. The eigenstates of the corresponding Floquet Wigner-Smith matrix are shown to be light pulses that are optimally shaped in both their spatial and temporal degrees of freedom for the optical micromanipulation of time-varying media.
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Globosits et al. (2024) studied this question.
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