Abstract
As invisibility cloaking has recently become experimental reality, it is interesting to explore ways to reveal remaining imperfections. In essence, the idea of most invisibility cloaks is to recover the optical path lengths without an object (to be made invisible) by a suitable arrangement around that object. Optical path length is proportional to the time of flight of a light ray or to the optical phase accumulated by a light wave. Thus, time-of-flight images provide a direct and intuitive tool for probing imperfections. Indeed, recent phase-sensitive experiments on the carpet cloak have already made early steps in this direction. In the macroscopic world, time-of-flight images could be measured directly by light detection and ranging (LIDAR). Here, we show calculated time-of-flight images of the conformal Gaussian carpet cloak, the conformal grating cloak, the cylindrical free-space cloak, and of the invisible sphere. All results are obtained by using a ray-velocity equation of motion derived from Fermat's principle.
Highlights
Transformation optics connects geometry of curved space and propagation of light in inhomogeneous anisotropic optical media via mapping physical path length onto optical path length [1,2,3,4]
Optical phase is proportional to optical path length and proportional to the time of flight (TOF) of a light ray. These quantities are at the heart of transformation optics
Measuring TOF images via light detection and ranging (LIDAR) is a well-established technology that could be used to reveal objects that may appear barely visible at first sight in mere amplitude imaging of some scenery
Summary
Transformation optics connects geometry of curved space and propagation of light in inhomogeneous anisotropic optical media via mapping physical path length onto optical path length [1,2,3,4]. This concept has, for example, provided various blueprints for macroscopic invisibility-cloaking structures in free space [1,2,3,4,5] as well as for the simplified carpet-cloak (or ground-plane) geometry [6]. As the TOF is directly proportional to the optical path length in Fermat’s principle, we chose to derive the ray equation of motion directly from Fermat’s principle in this paper
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