Homogenization of dispersive space-time crystals: Anomalous dispersion and negative stored energy

We introduce a homogenization approach to characterize the dynamical response of a generic dispersive space-time crystal in the long-wavelength limit. The theory is applied to dispersive space-time platforms with a traveling-wave modulation. It is shown that for long wavelengths the effective response may be described by a frequency-dependent permittivity. Due to the active nature of space-time systems, the permittivity is not bound by the same constraints as in standard time-invariant metamaterials. In particular, we find that dispersive space-time crystals can exhibit rather peculiar physics, such as an anomalous (non-Foster) permittivity dispersion with a negative stored energy density, alternate between gain and loss regimes, and present multiple resonances in the quasistatic regime. Furthermore, it is verified with numerical simulations that the effective theory captures faithfully the exact dispersion of the first few photonic bands.

Automated summary

We introduce a homogenization approach to characterize the dynamical response of a generic dispersive space-time crystal in the long-wavelength limit. The theory is applied to dispersive space-time platforms with a traveling-wave modulation, and it is shown that for long wavelengths the effective response may be described by a frequency-dependent permittivity. The article discusses the peculiar physics exhibited by dispersive space-time crystals, such as anomalous permittivity dispersion, alternate gain and loss regimes, and multiple resonances in the quasistatic regime.