Related papers: Maxwell Optics: II. An Exact Formalism
General guidelines for constructing a quantum theory of charged-particle beam optics starting ab initio from the basic equations of quantum mechanics, appropriate to the situation under study. In the context of spin-1/2 particles, these…
We demonstrate the possibility of using time-space crystalline structures to simulate eight-dimensional systems based on only two physical dimensions. A suitable choice of system parameters allows us to obtain a gapped energy spectrum,…
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…
Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor {\mu} \neq 1 are studied. 4x4 matrix formalism is employed to produce general solutions for the complex reflection coefficients…
These notes, intended to be self contained and tutorial, present a direct, macroscopic approach to quantizing light inside a linear-response dielectric material when both spectral dispersion and spatial nonuniformity are present, but the…
A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to…
A Poisson structure on the time-extended space R x M is shown to be appropriate for a Hamiltonian formalism in which time is no more a privileged variable and no a priori geometry is assumed on the space M of motions. Possible geometries…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…
Metamaterials are beginning to transform optics and microwave technology thanks to their versatile properties that, in many cases, can be tailored according to practical needs and desires. Although metamaterials are surely not the answer to…
An asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions;…
The various non-linear transformations incurred by the rays in an optical system can be modelled by matrix products up to any desired order of approximation. Mathematica software has been used to find the appropriate matrix coefficients for…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real…
In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
We develop a differential-form approach to systematically derive the Newman-Penrose null-tetrad equations for Lorentz-violating extensions of Maxwell electrodynamics. The coordinate-independent nature of differential forms allows the…
For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is…
The constrained structure of the duality invariant form of Maxwell theory is considered in the Hamiltonian formulation of Dirac as well as from the symplectic viewpoint. Compared to the former the latter approach is found to be more…
Previous formulations of transformation optics have generally been restricted to transformations from relatively simple initial media, such as the vacuum, because of limitations due to their non-covariance. I show that a completely…