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We present a framework, based on the null-surface formulation of general relativity, for discussing the dynamics of Fermat potentials for gravitational lensing in a generic situation without approximations of any kind. Additionally, we…
Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function…
In this paper, the optical properties and imaging performance of a non-ideal Pendry's negative index flat lens with a practical value for loss are studied. Analytical calculations of the optical properties of the lens are performed, and…
The influence of the medium on the gravitational deflection of light rays is widely discussed in literature for the simplest non-trivial case: cold non-magnetized plasma. In this article, we generalize these studies to the case of an…
In this work we introduced a new proposal to study the gravitational lensing theory by spherical lenses, starting from its surface mass density $\Sigma(x)$ written in terms of a decreasing function $f$ of a dimensionless coordinate $x$ on…
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…
The response of the ``perfect lens'', consisting of a slab of lossless material of thickness $d$ with $\epsilon=\mu=-1$ at one frequency $\omega_0$ is investigated. It is shown that as time progresses the lens becomes increasingly opaque to…
Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant…
The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…
We present a framework for studying gravitational lensing in spherically symmetric spacetimes using 1+1+2 covariant methods. A general formula for the deflection angle is derived and we show how this can be used to recover the standard…
In this paper, we present the proof of concept of a very fast adaptive glass membrane lens with a large aperture/diameter ratio, spherical aberration correction and integrated actuation. The membrane is directly deformed using two piezo…
The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our…
We present a novel approach of modelling surface light scattering in the context of freeform optical design. The model relies on energy conservation and optimal transport theory. For isotropic scattering in cylindrically or rotationally…
Leonhard and Philbin [Phys. Rev. A 81, 011804(R) (2010)] have recently constructed a mathematical proof that the Maxwell's fish-eye lens provides perfect imaging of electromagnetic waves without negative refraction. In this comment, we…
It has been shown that a slab of materials with refractive index = -1 behaves like a perfect lens focussing all light to an exact electromagnetic copy of an object. The original lens is limited to producing images the same size as the…
We introduce new linear mathematical formulations to calculate the focal length of a camera in an active platform. Through mathematical derivations, we show that the focal lengths in each direction can be estimated using only one point…
We report on a new concept of cloaking objects in diffusive light regime using the paradigm of the scattering cancellation and mantle cloaking techniques. We show numerically that an object can be made completely invisible to diffusive…
Achromatic combinations of a diffractive Phase Fresnel Lens and a refractive correcting element have been proposed for X-ray and gamma-ray astronomy and for microlithography, but considerations of absorption often dictate that the…
We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…
We present a framework that reformulates gravitational lensing as an optical phenomenon governed by an effective refractive index, enabling exploration of modified gravity theories using undergraduate-level mathematics and optics. After…