Elliptical beams

A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the EB are the standard, elegant, and generalized Ince-Gauss beams, Mathieu-Gauss beams, among others

Normalization of the Mathieu-Gauss optical beams

A series scheme is discussed for the determination of the normalization constants of the even and odd Mathieu-Gauss (MG) optical beams. We apply a suitable expansion in terms of Bessel-Gauss (BG) beams and also answer the question of how many BG beams should be used to synthesize a MG beam within a tolerance. The structure of the normalization factors ensures that MG beams will always be normalized independently of the particular normalization adopted for the Mathieu functions. In this scheme, the normalization constants are expressed as rapidly convergent series that can be calculated to an arbitrary precision

Comment on 'Exact solution of resonant modes in a rectangular resonator'

We comment on the recent Letter by J. Wu and A. Liu [Opt. Lett. 31, 1720 (2006)] in which an exact scalar solution to the resonant modes and the resonant frequencies in a two-dimensional rectangular microcavity were presented. The analysis is incorrect because (a) the field solutions were imposed to satisfy simultaneously both Dirichlet and Neumann boundary conditions at the four sides of the rectangle, leading to an overdetermined problem, and (b) the modes in the cavity were expanded using an incorrect series ansatz, leading to an expression for the mode fields that does not satisfy the Helmholtz equation

Airy-Gauss beams and their transformation by paraxial optical systems

We introduce the generalized Airy-Gauss (AiG) beams and analyze their propagation through optical systems described by ABCD matrices with complex elements in general. The transverse mathematical structure of the AiG beams is form-invariant under paraxial transformations. The conditions for square integrability of the beams are studied in detail. The model of the AiG beam describes in a more realistic way the propagation of the Airy wave packets because AiG beams carry finite power, retain the nondiffracting propagation properties within a finite propagation distance, and can be realized experimentally to a very good approximation

Lorenz-Mie scattering of focused light via complex focus fields: an analytic treatment

The Lorenz-Mie scattering of a wide class of focused electromagnetic fields off spherical particles is studied. The focused fields in question are constructed through complex focal displacements, leading to closed-form expressions that can exhibit several interesting physical properties, such as orbital and/or spin angular momentum, spatially-varying polarization, and a controllable degree of focusing. These fields constitute complete bases that can be considered as nonparaxial extensions of the standard Laguerre-Gauss beams and the recently proposed polynomials-of-Gaussians beams. Their analytic form turns out to lead also to closed-form expressions for their multipolar expansion. Such expansion can be used to compute the field scattered by a spherical particle and the resulting forces and torques exerted on it, for any relative position between the field's focus and the particle.Comment: 11 pages, 7 figure

Logic Negation with Spiking Neural P Systems

Nowadays, the success of neural networks as reasoning systems is doubtless. Nonetheless, one of the drawbacks of such reasoning systems is that they work as black-boxes and the acquired knowledge is not human readable. In this paper, we present a new step in order to close the gap between connectionist and logic based reasoning systems. We show that two of the most used inference rules for obtaining negative information in rule based reasoning systems, the so-called Closed World Assumption and Negation as Finite Failure can be characterized by means of spiking neural P systems, a formal model of the third generation of neural networks born in the framework of membrane computing.Comment: 25 pages, 1 figur

Higher-order moments and overlaps of Cartesian beams

We introduce a closed-form expression for the overlap between two different Cartesian beams. In the course of obtaining this expression, we establish a linear relation between the overlap of circular beams with azimuthal symmetry and the overlap of Cartesian beams such that the knowledge of the former allows the latter to be calculated very easily. Our formalism can be easily applied to calculate relevant beam parameters such as the normalization constants, the M2 factors, the kurtosis parameters, the expansion coefficients of Cartesian beams, and therefore of all their relevant special cases, including the standard, elegant, and generalized Hermite–Gaussian beams, cosh-Gaussian beams, Lorentz beams, and Airy beams, among others

El administrador educativo como líder académico

The author analyzes the dilemma facing educational administrators when they try to clarify their on beliefs and expectations regarding the role they are to perform. By and large, when these individuals become principals, they assume the role of administrators per se rather than that of academic leaders. This situation has serious implications for the improvement of the quality of education. To overcome this weakness, the author proposes the renewal of the academic offer of the universities with a new conceptual framework that holistically prepares the new generations of academic leaders.El autor analiza el dilema que enfrentan los administradores educativos cuando tratan de clarificar sus propias concepciones y expectativas sobre el papel que deben desempeñar. Según su criterio, estas personas al asumir posiciones de dirección se caracterizan, en la práctica diaria, más por su papel de administradores que por el de líderes académicos, lo cual tiene serias implicaciones para el mejoramiento cualitativo de la educación. Como respuesta a esta problemática, propone actualizar la oferta académica de las universidades mediante la puesta en ejecución de una visión conceptual renovada que forme integralmente a las nuevas generaciones de líderes académicos