Related papers: Fractal Generalized Zone Plates
Lens design uses a calculation of the lens' surfaces that permit to obtain an image from a given object. A set of general rules and laws permits to calculate the essential points of the optical system such as distances, thickness, pupils,…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
The optical properties of dielectric plates coated with gapped graphene are investigated on the basis of first principles of quantum electrodynamics. The reflection coefficients and reflectivities of graphene-coated plates are expressed in…
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to…
New jet observables are defined which characterize both fractal and scale-dependent contributions to the distribution of hadrons in a jet. These infrared safe observables, named Extended Fractal Observables (EFOs), have been applied to…
We introduce a new product representation for general random binary fractal apertures defined by removing voids from Euclidean space, and use it to derive a simple closed-form expression for ensemble-averaged correlations. Power-law scaling…
The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
We demonstrate how the unusual mathematics of transfinite numbers, in particular a nearly perfect realization of Hilbert's famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a…
Limit periodic point sets are aperiodic structures with pure point diffraction supported on a countably, but not finitely generated Fourier module that is based on a lattice and certain integer multiples of it. Examples are cut and project…
Conventional light focusing, i. e. concentration of an extended optical field within a small area around a point, is a frequently used process in Optics. An important extension to conventional focusing is the generation of the annular focal…
It has recently been realized that fractals may be characterized by complex dimensions, arising from complex poles of the corresponding zeta function, and we show here that these lead to oscillatory behavior in various physical quantities.…
In these lecture notes we present connections between the theory of iterated function systems, in particular those attractors that are graphs of multivariate real-valued fractal functions, foldable figures and affine Weyl groups, and…
In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is a new framework that includes fractal fuzzy…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
In this paper, we explore some significant properties associated with a fractal operator on the space of all continuous functions defined on the Sierpi\'nski Gasket (SG). We also provide some results related to constrained approximation…
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
In this paper, we introduce fractal interpolation on complete semi-vector spaces. This approach is motivated by the requirements of preservation of positivity or monotonicity of functions for some models in approximation and interpolation…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…