Related papers: Fractal Generalized Zone Plates
The fractional Fourier transform (FrFT), which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its applications in electrical engineering and optics. In this paper, we…
The collective response of closely spaced metal particles in non-periodic arrangements has the potential to provide a beneficial angular and frequency dependence in sensing applications. In this paper, we investigate the optical response of…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
The permutation associated with the decimal expression of the binary reflected Gray code with $N$ bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
Fractals with different levels of self-similarity and magnification are defined as reduced fractals. It is shown that spectra of these reduced fractals can be constructed and used to describe levels of complexity of natural phenomena.…
The breakup of glass and alumina plates due to planar impacts on one of their lateral sides is studied. Particular attention is given to investigating the spatial location of the cracks within the plates. Analysis based on a…
The evolution from classical to quantum matter wave optics has been influenced by transformative optical devices. Fresnel zone plates (FZP), initially designed for light manipulation, have now found expanded applications in matter waves. In…
Influence of material anisotropy and gyrotropy on optical properties of fractal multilayer nanostructures is theoretically investigated. Gyrotropy is found to uniformly rotate the output polarization for bi-isotropic multilayers of…
Diffractive/refractive optics, such as Phase Fresnel Lenses (PFL's), offer the potential to achieve excellent imaging performance in the x-ray and gamma-ray photon regimes. In principle, the angular resolution obtained with these devices…
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting…
Fresnel lens has a long history in optics. This concept at non-optical wavelengths is also applicable. In this paper we report design and fabrication of a half and quarter wave dielectric Fresnel lens made of Plexiglas, and a Fresnel…
Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions…
We present a theoretical study of a spectral filter, which consists of a diffraction grating, a coupling lens, and an optical fiber. As the diffracted beam is highly dispersed spatially, coupling into an optical fiber naturally creates a…
The basic principle of astronomical interferometry is to derive the angular distribution of radiation in the sky from the Fourier transform of the electric field on the ground. What is so special about the Fourier transform? Nothing, it…
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
The art of light engineering unveils a world of possibilities through the meticulous manipulation of photonic properties such as intensity, phase, and polarization. The precise control over these optical properties under various conditions…
We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we address is to find the structure which uses the least…
The eigenmodes of unstable canonical optical resonators possess fractal structure in their transverse intensity cross-sections [Karman et al., Nature 402, 138 (1999)]. In one particular plane, the magnified self-conjugate plane, this…