Engineering Nonreciprocal Responses in Travelling-Wave Spacetime Crystals via Clausius-Mossotti Homogenization

TL;DR

This paper develops an analytical homogenization method for three-dimensional spacetime crystals with spherical scatterers, enabling the engineering of nonreciprocal electromagnetic responses, including isotropic Tellegen effects and Lorentz-invariant properties.

Contribution

It extends the Clausius-Mossotti formula to time-varying platforms and introduces a formalism for designing nonreciprocal and Lorentz-invariant spacetime crystals.

Findings

Engineered nonreciprocal bianisotropic couplings in spacetime crystals.

Realized isotropic Tellegen response in modulated scatterer lattices.

Identified Lorentz-invariant generalized Minkowskian crystals.

Abstract

Here, we investigate the effective response of three-dimensional spacetime crystals formed by spherical scatterers under a travelling-wave modulation. We develop an analytical formalism to homogenize the spacetime crystals that extends the renowned Clausius-Mossotti formula to time-varying platforms. Our formalism shows that travelling-wave spacetime crystals can be used to engineer a wide range of classes of nonreciprocal bianisotropic couplings in the long wavelength limit. In particular, our theory reveals the possibility of realizing a purely isotropic Tellegen response in crystals formed by interlaced sub-lattices of scatterers subjected to different modulation velocities. Furthermore, we introduce a class of generalized Minkowskian crystals that displays invariance under arbitrary Lorentz boosts aligned with a fixed spatial direction. We prove that such systems are formed by pseudo-uniaxial materials with the principal axis aligned parallel to the modulation velocity. The electromagnetic response of such generalized Minkowskian crystals is indistinguishable from that of moving photonic crystals.