Related papers: Maxwell Optics: II. An Exact Formalism
We propose that the height-angle ray vector in matrix optics should be complex, based on a geometric algebra analysis. We also propose that the ray's 2x2 matrix operators should be right-acting, so that the matrix product succession would…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and $8\times 8$ real matrices (a…
A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different…
This note offers a conceptually straightforward and efficient way to formulate and solve problems in the electromagnetics of moving media based on a representation of Maxwell's equations in terms of differential forms on spacetime together…
The promise of perfect imaging in the optical domain, where light can be imaged without aberrations and with ultra-high resolution, could revolutionize technology and nanofabrication [1, 2, 3, 4, 5, 6]. Recently it has been shown…
I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely:…
Maxwell's equations in curved space-time are invariant under electromagnetic duality transformations. We exploit this property to constraint the design parameters of metamaterials used for transformations optics. We show that a general…
After having obtained previously an extended first approximation of Maxwell's equations in Fock's nonlinear relativity, we propose here the corresponding exact form. In order to achieve this goal, we were inspired mainly by the special…
In these lectures we discuss some basic aspects of Hamiltonian formalism, which usually do not appear in standard texbooks on classical mechanics for physicists. We pay special attention to the procedure of Hamiltonian reduction…
We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those…
Maxwellian approximations to linear general relativity are revisited in light of relatively recent results on the degrees of freedom in the linear gravitational field. The well-known Maxwellian formalism obtained in harmonic coordinates is…
We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton's characteristic functions and conservation of luminous flux, and briefly explain the connection with the…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
Chirality or handedness in condensed matter induces anomalous optical responses such as natural optical activity, rotation of the plane of light polarization, as a result of breaking of spatial-inversion symmetry. In this study, optical…
The traditional approach to accelerator optics, based mainly on classical mechanics, is working excellently from the practical point of view. However, from the point of view of curiosity, as well as with a view to explore quantitatively the…
We examine the optical properties of two different configurations of a cylindrical device made from a hyperbolic metamaterial with optical axis defined by circular and radial director fields. The hyperbolic metamaterial is an uniaxial…
Hamiltonian matrices appear in a variety or problems in physics and engineering, mostly related to the time evolution of linear dynamical systems as for instance in ion beam optics. The time evolution is given by symplectic transfer…
In this article we have illustrated how is possible to formulate Maxwell's equations in vacuum in an independent form of the usual systems of units. Maxwell's equations, are then specialized to the most commonly used systems of units:…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…