Virtual Fresnel drag in spatiotemporal transformation medium.

A moving dielectric medium can modify the propagation of light by adding an extra velocity in the direction of the medium's motion, a phenomenon commonly referred to as Fresnel drag. However, moving dielectric slabs typically result in boundary reflections and cannot drag light when their refractive index approaches unity. In this study, we use a more intuitive geometrical method to explore the drag effect within the conceptual framework of a virtual moving geometry-a space with impedance matched to the air, thereby precluding the occurrence of boundary reflections. Subsequently, we demonstrate that the virtual moving geometry can be realized by a stationary bianisotropic spatiotemporal transformation medium utilizing transformation optics. This medium incorporates both spatial and temporal degrees of freedom, providing it with enhanced flexibility and functionality for the manipulation of electromagnetic waves, such as arbitrary reflectionless bending (achieving a virtual Fresnel drag effect), nonreciprocal transmission, and the induction of a virtual Doppler effect. Ultimately, we apply the spatiotemporal transformation medium to design a nonreciprocal reflectionless field shifter and a nonreciprocal invisibility cloak. The introduction of a virtual moving geometry to design the spatiotemporal transformation medium can serve as theoretical support for the rapidly evolving field of time-varying metamaterials.