Related papers: Multidimensional optical singularities and their a…
We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$PT$ symmetry, i.e., symmetry with $(PT)^2=-1$. The scattering is characterized by a $4\times 4$ transfer…
We establish a general unified formulation which, using the optical theorem of electromagnetic helicity, shows that dichorism is a phenomenon arising in any scattering -or diffraction- process, elastic or not, of chiral electromagnetic…
Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
Exceptional points as branch singularities describe peculiar degeneracies of non-Hermitian systems that do not obey energy conservation. This work shows that exceptional points can emerge in a topological photonic system, for example, the…
Transformation optics aims to identify artificial materials and structures with desired electromagnetic properties by means of pertinent coordinate transformations. In general, such schemes are meant to appropriately tailor the constitutive…
We introduce an upper semi-continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic (over a perfect field). The blow-up along the maximum stratum defined by this function leads to a…
We present a progress overview focused on the recent theoretical and experimental advances in the area of soliton manipulation in optical lattices. Optical lattices offer the possibility to engineer and to control the diffraction of light…
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation.…
We study singularities and geometric properties of surfaces given by the singular loci of normal congruence of frontals with pure-frontal singular points. These surfaces consist of the normal ruled surface and focal surfaces of the initial…
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.
The structural versatility of light underpins an outstanding collection of optical phenomena where both geometrical and topological states of light can dictate how matter will respond or display. Light possesses multiple degrees of freedom…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…
Singular spectrum analysis is developed as a nonparametric spectral decomposition of a time series. It can be easily extended to the decomposition of multidimensional lattice-like data through the filtering interpretation. In this…
We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also…
The recent research of topological photonics has not only proposed and realized novel topological phenomena such as one-way broadband propagation and robust transport of light, but also designed and fabricated photonic devices with…
Optical microcavities have received much attention over the last decade from different research fields ranging from fundamental issues of cavity QED to specific applications such as microlasers and bio-sensors. A major issue in the latter…
We present a review and discussions on characterizations and quantifications of macroscopic quantum states as well as their implementations and applications in optical systems. We compare and criticize different measures proposed to define…
The paper introduces a number of new techniques to handle minimal hyersurface singularities. In particular, they allow to extend the obstruction theory for postive scalr curvature to any dimension.
The advent of visible-infrared laser pulses carrying a substantial fraction of their energy in a single field oscillation cycle has opened a new era in the experimental investigation of ultrafast processes in semiconductors and dielectrics…