Related papers: Generalized Fibonacci zone plates
The construction of fractal generalized zone plates (FraGZPs) from a set of periodic diffractive optical elements with circular symmetry is proposed. This allows us to increase the number of foci of a conventional fractal zone plate…
We present a new kind of photon sieves on the basis of the generalized Fibonacci sequences. The required numbers and locations of axial foci can be designed by generalized Fibonacci photon sieves (GFiPS). Furthermore, the three-dimensional…
Thin structured surfaces allow flexible control over propagation of electromagnetic waves. Focusing and polarization state analysis are among functions, required for effective manipulation of radiation. Here a polarization sensitive Fresnel…
Fresnel zone plates (FZPs), with patterns of $1\,\mu$m resolution, allow the formation of clean, diffraction-limited foci -- but have a static phase profile. Spatial light modulators (SLMs) allow dynamic control of spatial beam intensity…
Fresnel zone plates are diffractive elements that are essential to form images in many scientific and technological areas, especially where refractive optics is not available. One of the main shortcomings of Fresnel zone plates, which limit…
The new type of multilevel Fresnel zone plate, consisting of stacked layers with bi-level zone profile has been investigated. The conditions of layers acting as single multilevel Fresnel zone plate have been discussed by numerical…
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…
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 investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the…
We have studied several generalizations of Fibonacci sequences as the sequences with arbitrary initial values, the addition of two and more Fibonacci subsequences and Fibonacci polynomials with arbitrary bases. For Fibonacci numbers with…
We present a new family of diffractive lenses whose structure is based on the combination of two concepts: photon sieve and fractal zone plates with variable lacunarity. The focusing properties of different members of this family are…
Extraordinary optical transmission and good focusing properties of a two-dimensional scattering structure is presented. The structure is made of Fresnel zone plates periodically arranged along two orthogonal directions. Each plate consists…
Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of…
Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.
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…
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…
In this paper we study how to accelerate the convergence of the ratios (x_n) of generalized Fibonacci sequences. In particular, we provide recurrent formulas in order to generate subsequences (x_{g_n}) for every linear recurrent sequence…
In this paper, we study the linear space of all two-sided generalized Fibonacci sequences $\{F_n\}_{n \in \mathbb{Z}}$ that satisfy the recurrence equation of order $k$: $F_n = F_{n-1} + F_{n-2} + \dots + F_{n-k}$. We give two types of…
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.
Diffractive lenses fabricated by lithographic methods are one of the most popular image forming optics in the x-ray regime. Most commonly, binary diffractive optics, such as Fresnel zone plates are used due to their ability to focus at high…