Related papers: Fractal Generalized Zone Plates
When plane waves diffract through fractal-patterned apertures, the resulting far-field profiles or diffractals also exhibit iterated, self-similar features. Here we show that this specific architecture enables robust signal processing and…
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and…
Combination of Fresnel Zone Plates (FZP) can make excellent telescopes for imaging in X-rays. We present the results of our experiments with such telescopes with an X-ray source kept at a distance of 45 feet. We compare the patterns…
A telescope with Fresnel Zone Plates has been contemplated to be an excellent imaging mask in X-rays and gamma-rays for quite some time. With a proper choice of zone plate material, spacing and an appropriate readout system it is possible…
The article concerns an investigation of the Fresnel diffraction characteristics of two types of phase optical elements, under Gaussian laser beam illumination. Both elements provide an azimuthal periodicity of the phase retardation. The…
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…
Self-similar sets with open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles. Examples…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
Cabrelli, Forte, Molter and Vrscay in 1992 considered a {fuzzy} version of the theory of iterated function systems (IFSs in short) and their fractals%The idea was to extend the classical Hutchinson-Barnsley operator to selfmaps of a metric…
We present the results of simulations of shadows cast by a zone plate telescope which may have one to four pairs of zone plates. From the shadows we reconstruct the images under various circumstances. We discuss physical basis of the…
A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces…
Phase Fresnel lenses have the same imaging properties as zone plates, but with the possibility of concentrating all of the incident power into the primary focus, increasing the maximum theoretical efficiency from 11% to close to 100%. For…
In optical devices like diffraction gratings and Fresnel lenses, light wavefront is engineered through the structuring of device surface morphology, within thicknesses comparable to the light wavelength. Fabrication of such diffractive…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
We propose a novel fractal based interpolation scheme termed Rational Cubic Trigonometric Zipper Fractal Interpolation Functions (RCTZFIFs) designed to model and preserve the inherent geometric property, positivity, in given datasets. The…
We show that a metallic plate with fractal-shaped slits can be homogenitized as a plasmonic metamaterial with plasmon frequency dictated by the fractal geometry. Owing to the all-dimensional subwavelength nature of the fractal pattern, our…
We propose a method for designing multifocal diffractive lenses generating prescribed sets of foci with fixed positions at several different wavelengths. The method is based on minimizing the difference between the complex amplitudes of the…
We have simulated the optical properties of micro-fabricated Fresnel zone plates (FZPs) as an alternative to spatial light modulators (SLMs) for producing non-trivial light potentials to trap atoms within a lensless Fresnel arrangement. We…
When focusing a light beam at high numerical aperture, the resulting electric field profile in the focal plane depends on the transverse polarisation profile, as interference between different parts of the beam needs to be taken into…
In view of promising applications of fractal nanostructures, we analyze the spectra of quantum particles in the Sierpinski carpet and study the non-correlated electron gas in this geometry. We show that the spectrum exhibits scale…