Related papers: Geometrical aspects of first-order optical systems
We consider a nonlinear optical system in general, and a broad aperture laser in particular in a resonator where the diffraction coefficients are of opposite signs along two transverse directions. The system is described by the hyperbolic…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Circular and hyperbolic fractional-order Fourier transformations are actually Weyl pseudo-differential operators. Their associated kernels and symbols are written explicitly. Products of fractional-order Fourier transformations are obtained…
We study the multiplicity sets of first order symbols associated with differential operators on two dimensional surfaces. This work is inspired by the phenomenon of conical refraction explained by the existence of singularities in the…
We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic…
The aim of this paper is fourfold. Firstly, we introduce and study the f-ultra-harmonic maps. Secondly, we recall the geometric dynamics generated by a first order normal PDE system and we give original results regarding the geometric…
We report on the linear and nonlinear optical response of metamaterials evoked by first and second order multipoles. The analytical ground on which our approach bases permits for new insights into the functionality of metamaterials. For the…
The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and equations is broken resulting the appearance of a scalar field. We find the…
We study the geometrical optics generated by a refractive index of the form $n(x,y)=1/y$ $(y>0)$, where $y$ is the coordinate of the vertical axis in an orthogonal reference frame in $\R^2$. We thus obtain what we call "hyperbolic…
The scalar field theory with higher derivatives is considered in the first order formalism. The field equation of the forth order describes scalar particles possessing two mass states. The first order relativistic wave equation in the…
Optical resonators are structures that utilize wave interference and feedback to confine light in all three dimensions. Depending on the feedback mechanism, resonators can support either standing- or traveling-wave modes. Over the years,…
A light ray in space is characterized by two vectors: (i) a transverse spatial-vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation.…
Paraxial lens optics is discussed to study the continuity properties of the $ABCD$ beam transfer matrix. The two-by-two matrix for the one-lens camera-like system can be converted to an equi-diagonal form by a scale transformation, leaving…
The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting…
In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the…
In this paper we explore how light propagates from thin elements into a volume for viewing. In particular, devices that are typically connected with geometric optics, like parallax barriers, differ in treatment with those that obey physical…
We construct a semiclassical theory for propagation of an optical wavepacket in non-conducting media with periodic structures of dielectric permittivity and magnetic permeability, i.e., non-conducting photonic crystals. We employ a…
We require decomposition methods for the ABCD-matrix formulation in rotationally symmetric paraxial geometric optics when designing a multi-component optical system from a given single paraxial specification (represented by an ABCD matrix)…
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…
It is shown that the one-lens system in para-axial optics can serve as an optical computer for contraction of Wigner's little groups and an analogue computer which transforms analytically computations on a spherical surface to those on a…