Identifying regions of minimal backscattering by a relativistically moving sphere

The far-field backscattering amplitude of an electric field from a relativistically moving sphere is analyzed. Contrary to prior research, we do so by expressing the fields in the helicity basis and we highlight here its advantages when compared to the commonly considered parity basis. With the purpose of exploring specific scattering phenomena considering relativistic effects, we identify conditions that minimize the backscattered field, leading to a relativistic formulation of the first Kerker condition. The requirements to be satisfied by the sphere are expressed in terms of Mie angles, which constitute an effective parametrization of any possible optical response a sphere might have. By considering different speeds of the sphere and angles of incidence, we are able to identify multiple combinations of Mie angles up to octupolar order via gradient-based optimization that satisfy our relativistic Kerker condition, that is, where the backscattered energy is at most 0.1% of the average scattered energy. Our results can be extended to involve multiple particles forming a metasurface, potentially having direct implications on the design of light sails as considered by the Breakthrough Starshot Initiative. © 2023 American Physical Society.