相关论文: Light propagation in local and linear media: Fresn…

The propagation of light through bianisotropic materials is studied in the geometrical optics approximation. For that purpose, we use the quartic general dispersion equation specified by the Tamm-Rubilar tensor, which is cubic in the…

Geometrical optics describes, with good accuracy, the propagation of high-frequency plane waves through an electromagnetic medium. Under such approximation, the behaviour of the electromagnetic fields is characterised by just three…

We show, in this first part, that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic $2$ is at most $16$. We produce examples with…

We study the dispersion of electromagnetic waves in a spatially dispersive metamaterial with Lorentz-like dependence of principal permittivity tensor components on the respective components of the wave vector performing the analysis of…

In this paper we first show that each Kummer quartic surface (a quartic surface $X$ with 16 singular points) is, in canonical coordinates, equal to its dual surface, and that the Gauss map induces a fixpoint free involution $\gamma$ on the…

Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…

Anisotropic, Tellegen, chiral, moving-medium-type, omega, gyrotropic, hyperbolic, and multi-hyperbolic materials form an important class of isotropy-broken photonic media in which wave propagation can no longer be characterized by the…

We show that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic $2$ is at most $20$, and that if equality is attained, then the…

We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable (2,2)-tensor on the 4-manifold N. Moreover, in each…

We show, in this second part, that the maximal number of singular points of a quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic 2 is at most 14, and that, if we have 14…

We reveal extraordinary electromagnetic properties for a general class of uniaxially polarizable media. Depending on parameters, such metamaterials may have wide range of nontrivial shapes of isofrequency contours including lemniscate,…

In some anisotropic bulk media (for example, biaxial weakly absorbing crystals) there are special directions along which the plane wave field distribution has a singular profile of the form $\propto (\mathbf{n} \mathbf{r}) \exp(i q…

In this paper we describe the propagation of smooth (C^\infty) and Sobolev singularities for the wave equation on smooth manifolds with corners M equipped with a Riemannian metric g. That is, for X=MxR, P=D_t^2-\Delta_M, and u locally in…

We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their…

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is modelled by an antisymmetric (2, 2)-tensor kappa with real coefficients. In this setting the Fresnel surface is a fourth order polynomial surface in each…

We study the interference and diffraction of light when it propagates through a metamaterial medium mimicking the spacetime of a cosmic string, -- a topological defect with curvature singularity. The phenomenon may look like a gravitational…

We enumerate the singular algebraic curves in a complete linear system on a smooth projective surface. The system must be suitably ample in a rather precise sense. The curves may have up to eight nodes, or a triple point of a given type and…

In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…

We show show that the singularities of the Fresnel surface for Maxwell's equation on an anisotrpic material can be accounted from purely topological considerations. The importance of these singularities is that they explain the phenomenon…

It is classically known that a real cubic surface in the real projective 3-space cannot have more than one solitary point (locally given by x^2+y^2+z^2=0) whereas it can have up to four nodes (x^2+y^2-z^2=0). We show that on any surface of…