We present the theory of ray-optical transformation optics (RTO) with ideal thin lenses and show that ideal-thin-lens RTO devices are omnidirectional lenses. Key to designing such devices are two theorems, the loop-imaging theorem, and the edge-imaging theorem, which ensure that the interior physical space is distorted in the same way for all viewing directions. We discuss the possibility of realising such devices using lens holograms or Fresnel lenses, as both are in principle capable of changing the directions of rays incident from a specific point precisely like an ideal thin lens, thereby enabling macroscopic and broad-band RTO devices that work for at least one viewing position. Even when restricted in this way, our work opens up new possibilities in ray optics. Our devices have the potential to form the basis of new microscope objectives, virtual-reality headsets, and medical spectacles.
Recent observation of black hole and gravitational wave has stirred up great interest of Einstein's general relativity. In optical system, the "optical black hole" has also been a key topic in mimicking black holes. Another good way to study or mimic general relativity effects is based on transformation optics. In this paper, we propose a way by utilizing transformation optics theory to directly obtain the equivalent isotropic refractive index profiles which are the analogies of some static spaces of general relativity, such as de Sitter space, Anti de Sitter space, and Schwarzschild black hole. We find that, the analogue of de Sitter space is the Poincaré disk, while Anti de Sitter space is equivalent to Maxwell's fish eye lens. In particular, we prove that the "optical black hole" actually has infinite number of photon spheres, while our black hole only has a single one, which is closer to the real black hole. We study the effect from both geometric optics and wave optics. It can also be generalized to mimic any kind of metrics. Furthermore, with the isotropic refractivity index profile, we visualize the gravitational lensing effect of black hole from our software TIM. The image not only recovers the donut-liked halo of black hole, but also shows other phenomena.
Previously [Courtial et al., Opt. Express 26, 17872 (2018)] we presented the theory of transformation optics (TO) with ideal lenses and demonstrated an example, an omnidirectional lens. Here we interpret this omnidirectional lens in two different parameter regimes as ideal-lens cloaks that employ different cloaking strategies: a standard "shrink cloak" in which objects appear smaller (ideally zero) and a novel "abyss cloak" in which interior physical-space positions are mapped to the exterior and thus are visible only from certain directions. We proceed to combine two nested abyss cloaks into another novel, omnidirectional, "bi-abyss cloak." Our work significantly extends the arsenal of cloaking strategies.
We recently introduced the edge-imaging condition, a necessary condition for all generalized lenses (glenses) [J. Opt. Soc. Am. A 33, 962 (2016)JOAOD60740-323210.1364/JOSAA.33.000962] in a ray-optical transformation-optics (RTO) device that share a common edge [Opt. Express 26, 17872 (2018)OPEXFF1094-408710.1364/OE.26.017872]. The edge-imaging condition states that, in combination, such glenses must image every point to itself. Here we begin the process of building up a library of combinations of glenses that satisfy the edge-imaging condition, starting with all relevant combinations of up to three glenses. As it grows, this library should become increasingly useful when constructing lens-based RTO devices.
We study the ray optics of generalized lenses (glenses), which are ideal thin lenses generalized to have different object- and image-sided focal lengths, and the most general light-ray-direction-changing surfaces that stigmatically image any point in object space to a corresponding point in image space. Gabor superlenses [UK patent541,753 (1940); J. Opt. A1, 94 (1999)JOAOF81464-425810.1088/1464-4258/1/1/013] can be seen as pixelated realizations of glenses. Our analysis is centered on the nodal point. Whereas the nodal point of a thin lens always resides in the lens plane, that of a glens can reside anywhere on the optical axis. Utilizing the nodal point, we derive simple equations that describe the mapping between object and image space and the light-ray-direction change. We demonstrate our findings with the help of ray-tracing simulations. Glenses allow novel optical instruments to be realized, at least theoretically, and our results facilitate the design and analysis of such devices.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.