Related papers: Revisiting 2x2 matrix optics: Complex vectors, Fer…
We theoretically describe the optical computation of the divergence of a two-dimensional vector field, which is composed by the transverse electric field components of an incident light beam. The divergence is computed in reflection at…
It is shown that a light beam in free space is representable by an integral over a vectorial angular spectrum that is expressed in terms of an extension matrix, which describes the vectorial nature of the beam. A symmetry axis of the…
This paper is devoted to an intrinsic geometrical classification of three-mirror telescopes. The problem is formulated as the study of the connected components of a semi-algebraic set. Under first order approximation, we give the general…
The future generation of telescopes will be equipped with multi-conjugate adaptive optics (MCAO) systems in order to obtain high angular resolution over large fields of view. MCAO comes in two flavors: star- and layer-oriented. Existing…
We propose an approach for deriving a broad class of propagation models for inhomogeneously, linearly polarized ``vector'' beams. Our formulation leverages a complex scalar potential along with an appropriately constructed Lagrangian energy…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…
Aberration compensation with emphasis on the generalized spherical aberration components is discussed for plane-symmetric and anamorphic optical systems. A narrow field-of-view double-plane symmetric telescope objective containing…
A new formalism of beam-optics and polarization has been recently presented, based on an exact matrix representation of the Maxwell equations. This is described in Part-I and Part-II. In this Part, we present the application of the above…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
We study and classify systems of certain screening operators arising in a generalized vertex operator algebra, or more generally an abelian intertwining algebra with an associated vertex operator (super)algebra. Screening pairs arising from…
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately…
We used Geometric Algebra to compute the paths of skew rays in a cylindrical, step-index multimode optical fiber. To do this, we used the vector addition form for the law of propagation, the exponential of an imaginary vector form for the…
In this paper, we describe the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…
We present an extension of the string-inspired technique suitable to the calculation of amplitudes and effective Lagrangians involving both vector and axial vector gauge fields. The technique is easily adaptable to problems involving…
Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…
In this paper we propose a very effective method for constructing matrix commuting differential operators of rank 2 and vector rank (2,2). We find new matrix commuting differential operators L, M of orders 2 and 2g respectively.
To obtain a light mode in two-dimensional staggered fermions, we introduce four new local operators keeping the rotational invariance for a staggered Dirac operator. To split masses of tastes, three cases are considered. The mass matrix and…
We develop a linear algebraic framework for the shape-from-shading problem, because tensors arise when scalar (e.g. image) and vector (e.g. surface normal) fields are differentiated multiple times. Using this framework, we first investigate…
Recently, sum rules were derived for the inverse eigenvalues of the Dirac operator. They were obtained in two different ways: i) starting from the low-energy effective Lagrangian and ii) starting from a random matrix theory with 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…