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The mathematically correct computation of the spin glasses free energy in the infinite range limit crowns 25 years of mathematic efforts in solving this model. The exact solution of the model was found many years ago by using a heuristic…
We obtain the geodesics for the simplest possible stealth defect which has a flat spacetime. We, then, discuss the lensing properties of such a defect, and the corresponding image formation. Similar lensing properties can be expected to…
The joint design of the optical system and the downstream algorithm is a challenging and promising task. Due to the demand for balancing the global optimal of imaging systems and the computational cost of physical simulation, existing…
Flat lenses have shown promising applications in miniaturized and ultracompact lightweight optical systems. However, it has been a great challenge in simultaneously achieving broadband achromatism and high numerical aperture. Here, we…
The concept of optical phase discontinuities is applied to the design and demonstration of aberration-free planar lenses and axicons, comprising a phased array of ultrathin subwavelength spaced optical antennas. The lenses and axicons…
The super-oscillation lens (SOL) can achieve super-resolution focusing but have to trade-off with weaker hotspots and higher sidebands. We propose a single compound SOL to achieve reflective confocal imaging in principle without additional…
For given convex set $K$ in the plane (not necessarily bounded), we can construct the curve $C$ for which the visibility (aperture) angle of this set has the same, prescribed value. We give the implicit formula for $C$, discuss some issues…
We introduce a synthetic aperture imaging framework that takes into consideration directional dependence of the reflectivity that is to be imaged, as well as its frequency dependence. We use an $\ell_1$ minimization approach that is…
As a lens capable of sending images of deep sub-wavelength objects to the far field, the hyperlens has garnered significant attention for its super-resolution and magnification capabilities. However, traditional hyperlenses require extreme…
We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes…
Conceptual studies and numerical simulations are performed for imaging devices that transform a near-field pattern into magnified far-zone images and are based on high-order spatial transformation in cylindrical domains. A lens translating…
In this paper we show that a negative index of refraction is not a direct implication of transformation optics with orientation-reversing diffeomorphisms. Rather a negative index appears due to a specific choice of sign freedom.…
We obtain a construction of the total spherical perspective with ruler, compass, and nail. This is a generalization of the spherical perspective of Barre and Flocon to a 360 degree field of view. Since the 1960s, several generalizations of…
Negative index of refraction has become an accepted part of transformation optics, which is encountered in transformations that change the orientation of the manifold. Based on this concept, various designs of perfect lenses have been…
In this paper, we study closed-form optimal solutions to two-view triangulation with known internal calibration and pose. By formulating the triangulation problem as $L_1$ and $L_\infty$ minimization of angular reprojection errors, we…
In the last decades nanostructures have unlocked myriads of functionalities in nanophotonics by engineering light-matter interaction beyond what is possible with conventional bulk optics. The space of parameters available for design is…
In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct…
The advent of 4$^\text{th}$ generation high-energy synchrotron facilities (ESRF-EBS and the planned APS-U, PETRA-IV and SPring-8 II) and free-electron lasers (Eu-XFEL and SLAC) allied with the recent demonstration of high-quality free-form…
We show that there is no need to modify the Parisi replica symmetry breaking ansatz, by working with $R$ steps of breaking and solving {\it exactly} the discrete stationarity equations generated by the standard ``truncated Hamiltonian" of…
In this work, we present a detailed procedure of computer implementation of the laws of refraction and reflection on an arbitrary surface with rotational symmetry with respect to the propagation axis. The goal is to facilitate the…