Related papers: The Initial Approximations for Achromatic Doublets…
Zoom metalens doublet exhibits unprecedented advantages over the traditional zoom lens in many aspects, like ultra-compactness, CMOS compatibility, and miniaturization. However, most of them can only work in a narrow band due to chromatic…
The English optician John Dollond (1706-1761) performed a number of experiments with prisms of various transparent materials and concluded that an achromatic lens could exist. At that time, the dominant opinion about light refraction denied…
Colour symmetries with ten colours are presented for different tilings. In many cases, the existence of these colourings were predicted by group theoretical methods. Only in a few cases explicit constructions were known, sometimes using…
Using the group-theoretical point of view we study in this paper second and third order repetitive achromats with a mirror symmetric or mirror antisymmetric basic cell and compare these achromats with repetitive achromats designed without…
In this article we introduce a group-theoretical point of view for the design of magnetic optical achromats based on symmetry. As examples we use two-cell repetitive achromats and four-cell achromats employing mirror symmetry.
A plethora of metalenses and diffractive lenses (flat lenses) have been demonstrated over the years. Recently, attempts have been made to stretch their performance envelope, particularly in the direction of wide-band achromatic performance.…
Over the recent years, there have been many reports of achromatic metalenses and diffractive lenses. However, very few (if any) practical applications of such achromatic flat lenses have been demonstrated, which raises questions about the…
We study the colour changes induced by blending in a wormhole-like microlensing scenario with extended sources. The results are compared with those obtained for limb darkening. We assess the possibility of an actual detection of the colour…
It has been claimed [1-6] that fractal analysis can be applied to unambiguously characterize works of art such as the drip paintings of Jackson Pollock. This academic issue has become of more general interest following the recent discovery…
This is the first of several monographs to be devoted to the optics of accelerated systems. They are being published for the benefit of those who may wish to have another way of looking at kineoptical problems, and also to demonstrate that…
We introduce a class of pairs of graphs consisting of two cliques joined by an arbitrary number of edges. The members of a pair have the property that the clique-bridging edge-set of one graph is the complement of that of the other. We…
The chromatic number related to a colouring of facets of certain classes of generalised associahedra is studied. The exact values are obtained for permutohedra, associahedra and simple permutoassociahedra, while lower and upper bounds are…
The investigation of colour symmetries for periodic and aperiodic systems consists of two steps. The first concerns the computation of the possible numbers of colours and is mainly combinatorial in nature. The second is algebraic and…
The chromatic polynomials are studied by several authors and have important applications in different frameworks, specially, in graph theory and enumerative combinatorics. The aim of this work is to establish some properties of the…
Efficiently collecting light emitted or scattered from nanoscale systems, which can be embedded in a high-index medium, is a challenge for fundamental spectroscopic studies and commercial applications of quantum dots, color centers, single…
Complete colorings have the property that any two color classes has at least an edge between them. Parameters such as the Grundy, achromatic and pseudoachromatic numbers comes from complete colorings, with some additional requirement. In…
It is known (Bollob\'{a}s (1978); Kostochka and Mazurova (1977)) that there exist graphs of maximum degree $\Delta$ and of arbitrarily large girth whose chromatic number is at least $c \Delta / \log \Delta$. We show an analogous result for…
The main focus of this paper is on models of quartic surfaces, especially so-called complex surfaces. These are special fourth-degree surfaces that Julius Pl\"ucker introduced in the 1860s for visualizing the local structure of a quadratic…
Flat lenses have shown promising applications in miniaturized and ultracompact lightweight optical systems. However, it has been a great challenge in simultaneously achieving broadband achromatism and high numerical aperture. Here, we…
The dichromatic number of a graph $G$ is the maximum integer $k$ such that there exists an orientation of the edges of $G$ such that for every partition of the vertices into fewer than $k$ parts, at least one of the parts must contain a…