Related papers: Maxwell Optics: II. An Exact Formalism
The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
Using the worldline formalism of the Dirac field with a non-Abelian gauge symmetry we show how to describe the matter field transforming in an arbitrary representation of the gauge group. Colour degrees of freedom are carried on the…
We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point purely in terms of the original Hamiltonian, avoiding the normalization procedure.…
We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the…
This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory.…
In this paper, we report two new kinds of absolute optical instruments that can make stigmatically images for geometric optics in two dimensional space. One is called the duplex Mikaelian lens, which is made by splicing two half Mikaelian…
In the first part of this paper we review several formalisms which give alternative ways for describing the light. They are: the formalism `baroque' and the Majorana-Oppenheimer form of electrodynamics, the Sachs' theory of Elementary…
We present a matrix formalism, inspired by the Minkowski four-vectors of special relativity, useful to solve classical physics problems related to both mechanics and thermodynamics. The formalism turns out to be convenient to deal with…
Illumination is the deliberate utilization of light to realize practical or aesthetic effects. The designers combine with the environmental considerations, energy-saving goals, and technology advances with fundamental physics to develop…
A new set of mathematical morphology (MM) operators adaptive to illumination changes caused by variation of exposure time or light intensity is defined thanks to the Logarithmic Image Processing (LIP) model. This model based on the physics…
Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical…
In this work we study the so-called ModMax nonlinear electrodynamics, which is a novel model designed to preserve duality rotations and conformal transformations, such as the Maxwell's equations do. This model allows to study diverse…
Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior…
A phenomenological theory of luminescence properties of one-dimensional resonant photonic crystals is developed within the framework of classical Maxwell equations with fluctuating polarization terms representing non-coherent sources of…
Optical forces in dielectric structures are typically analyzed by utilizing either the Maxwell stress tensor or energy-based methods from which they can be derived by means of the eigenfrequencies and the effective refractive indices…
Light propagation in distributed feedback optical structures with gain/loss regions is shown to provide an accessible laboratory tool to visualize in optics the spectral properties of the one-dimensional Dirac equation with non-Hermitian…
We consider optical systems where propagation of light can be described by a Dirac-like equation with $PT$-symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…