Abstract
Nothing can physically travel faster than light in vacuum. This is why it has been considered that there is no \v{C}erenkov radiation (\v{C}R) without an effective refractive index due to some background field. In this Letter, we theoretically predict \v{C}R in vacuum from a spatiotemporally modulated boundary. We consider the modulation of traveling wave type and apply a uniform electrostatic field on the boundary to generate electric dipoles. Since the induced dipoles stick to the interface, they travel at the modulation speed. When the grating travels faster than light, it emits \v{C}R. In order to quantitatively examine this argument, we need to calculate the field scattered at the boundary. We utilise a dynamical differential method, which we developed in the previous paper, to quantitatively evaluate the field distribution in such a situation. We can confirm that all scattered fields are evanescent if the modulation speed is slower than light while some become propagating if the modulation is faster than light.
Highlights
Cerenkov radiation (C R) is radiation from a charged particle moving faster than light in a medium, which was originally observed by Cerenkov in 1934 [1] and theoretically studied by Frank and Tamm [2]
There are many reports of C R in media as reviewed above; there is a limited number of studies on C R in vacuum
We propose a mechanism for C R in vacuum without introducing any effective index
Summary
Cerenkov radiation (C R) is radiation from a charged particle moving faster than light in a medium, which was originally observed by Cerenkov in 1934 [1] and theoretically studied by Frank and Tamm [2]. There are many reports of C R in media as reviewed above; there is a limited number of studies on C R in vacuum This is because nothing can physically move faster than light in vacuum. A moving light spot on a surface is one possibility to induce and mimic superluminal dipoles [14,15] Another way is to introduce some background such as external electromagnetic or Chern-Simons fields. Recent studies in the optics and photonics communities have shown that time-varying bulk media amplify source electromagnetic radiation [29,30,31] and generate light from vacuum fluctuation [32,33].
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