相关论文: Refracting profiles and generalized holodiagrams
We propose an original method for determining suitable refracting profiles between two media to solve two related problems: to produce a given wave front from a single point source after refraction at the refracting profile, and to focus a…
A generalization of the notion of a (pseudo-) Riemannian space is proposed in a framework of noncommutative geometry. In particular, there are parametrized families of generalized Riemannian spaces which are deformations of classical…
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained.…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development…
This expository paper is concerned with the properties of proper holomorphic mappings between domains in complex affine spaces. We discuss some of the main geometric methods of this theory, such as the Reflection Principle, the scaling…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
An exact formulation of the propagation of a monochromatic wave packet impinging upon a transparent, homogeneous, isotropic and parallel slab at oblique incidence is presented. Approximate formulas are derived for low divergence Gaussian…
A formula for the wavefront of a wave reflected from a diffraction grating with an arbitrary surface profile, as well as with arbitrary non-equidistant and non-parallel grooves was obtained. It was shown that the wavefront of the reflected…
We introduce a new class of quantum and classical correlation measures by generalizing the reflected entropy to multipartite states. We define the new measures for quantum systems in one spatial dimension. For quantum systems having gravity…
Digital holography numerically restores three-dimensional image information using optically captured diffractive waves. The required bandwidth is larger than that of hologram pixel at a closer distance in the Fresnel diffraction regime,…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
Metagratings have been shown to form an agile and efficient platform for extreme wavefront manipulation, going beyond the limitations of gradient metasurfaces. Previous approaches for transmissive metagratings have resorted on compound…
Based on transformation optics, we introduce another set of generalized laws of reflection and refraction (differs from that of [Science 334, 333 (2011)]), through which a transformation media slab is derived as a meta-surface, producing…
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…