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Gravitational lens models, some of which might act as if a concave lens, have been recently investigated by using a static and spherically symmetric modified spacetime metric that depends on the inverse distance to the $n$-th power…
Flatness of discrete-time systems can be characterized by two simple properties. There exists a map, a submersion, from the flat coordinates and their forward shifts to the state and the input of the discrete-time system, such that the…
We assume that the Universe has a non trivial topology whose compact spatial sections have a volume significantly smaller than the horizon volume. By a topological lens effect, such a "folded" space configuration generates multiple images…
As an important optical component, lens is widely used in scientific inquiry and production. At present, lens manufacturing mainly relies on grinding, polishing and other methods. However, these methods often require expensive equipment and…
We revisit the gravitational lensing phenomenon using a new visualization technique. It consists in projecting the observers sky into the source plane, what gives rise to a folded and stretched surface. This provides a clear graphical tool…
The basic equations and geometry of gravitational lensing are described, as well as the most important contexts in which it is observed in astronomy: strong lensing, weak lensing and microlensing.
We design freeform lenses refracting an arbitrarily given incident field into a given fixed direction. In the near field case, we study the existence of lenses refracting a given bright object into a predefined image. We also analyze the…
The study of light lensed by cosmic matter has yielded much information about astrophysical questions. Observations are explained using geometrical optics following a ray-based description of light. After deflection the lensed light…
Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first…
Gravitational lensing has been identified as a powerful tool to address fundamental problems in astrophysics at different scales, ranging from exoplanet identification to dark energy and dark matter characterization in cosmology. Image…
Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from…
The so-called "flat optics" that shapes the phase of an incident wave in free space through subwavelength structures has a venerable history. In that domain, achieving high efficiency at large deflection angles requires a low absorption…
It is known that spherically symmetric spacetimes admit flat spacelike foliations. We point out a simple method of seeing this result via the Hamiltonian constraints of general relativity. The method yields explicit formulas for the…
We consider a class of stationary and axisymmetric wormhole spacetimes that is closely related to, but not identical with, the class of Teo wormholes. We fix a point $p$ (observation event) and a timelike curve $\gamma$ (worldline of a…
The optical medium analogy of a radiation field generated by either an exact gravitational plane wave or an exact electromagnetic wave in the framework of general relativity is developed. The equivalent medium of the associated background…
Geometric optics effectively describes the propagation of electromagnetic waves when the wavelength is much smaller than the characteristic length scale of the medium, making wave phenomena like diffraction negligible. As a result, light…
The deflection and gravitational lensing of light and massive particles in arbitrary static, spherically symmetric and asymptotically (anti-)de Sitter spacetimes are considered in this work. We first proved that for spacetimes whose metric…
We investigate gravitational microlensing of point-like lenses surrounded by diffuse gas clouds. Besides gravitational bending, one must also consider refraction and absorption phenomena. According to the cloud density, the light curves may…
Spatial filtering is a commonly deployed technique to improve the quality of laser beams by optically filtering the noise. In the "textbook" example, the noise is usually assumed to be high frequency and the laser beam, Gaussian. In this…
Invisibility cloaking in acoustic scattering via the approach of transformation optics is considered. The near-cloaks of both passive medium and active/radiating object are investigated. From a practical viewpoint, we are especially…