Related papers: Fractal Generalized Zone Plates
Fractal concepts have been introduced in the accretion disc as a new feature. Due to the fractal nature of the flow, its continuity condition undergoes modifications. The conserved stationary fractal flow admits only saddle points and…
Light from any physical source diffracts over space, as spherical wavefronts grow and energy density is spread out. Diffractive effects pose fundamental limits to light-based technologies, including communications, spectroscopy, and…
The theoretical description for the reflectivity properties of dielectric, metal and semiconductor plates coated with graphene is developed in the framework of the Dirac model. Graphene is described by the polarization tensor allowing the…
In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate such data sets, an interpolation function…
This paper describes the design of near-field focusing plates, which are grating-like structures that can focus electromagnetic radiation to spots or lines of arbitrarily small subwavelength dimension. A general procedure is outlined for…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
Line-doubled Fresnel zone plates provide nanoscale, high aspect ratio structures required for efficient high resolution imaging in the multi-keV x-ray range. For the fabrication of such optics a high aspect ratio HSQ resist template is…
Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
Surface topography dictates the deterministic functionality of diffraction by a surface. In order to maximize the efficiency with which a diffractive optical component, such as a grating or a diffractive lens, directs light into a chosen…
In this work, the properties of the radiation emitted by a corner reflector with an electric dipole feeder are analyzed in the optical domain where the distance between the dipole and the corner apex can be large in terms of the optical…
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
In principle, diffractive optics, particularly Phase Fresnel Lenses (PFLs), offer the ability to construct large, diffraction-limited, and highly efficient X-ray/$\gamma$-ray telescopes, leading to dramatic improvement in angular resolution…
Closed formulas are derived for the field in the focal region of a diffraction limited lens, such that the electric field component in a given direction at the focal point is larger than that of all other focused fields with the same power…
Diffractive zone plate optics uses a thin micro-structure pattern to alter the propagation direction of the incoming light wave. It has found important applications in extreme-wavelength imaging where conventional refractive lenses do not…
Assuming fractality of hadronic constituents, we introduce elements of special realization of the relativity principle applied to physical quantities expressed with respect to various fractal structures. The construction is inspired by the…
The theory of optical effects in hydrogenated graphene (graphane) in terahertz and infrared range is developed, including the analysis of complex conductivity, reflection coefficient for graphane on a substrate and dispersion of surface…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals.…