V. Barrera-Figueroa

Spectral parameter power series analysis of isotropic planarly layered waveguides

This work addresses the analysis of an isotropic planarly layered waveguide consisting of an inhomogeneous core that is enclosed between two homogeneous layers forming the cladding. The analysis relies on an auxiliary one-dimensional spectral problem that is intimately linked with the scalar wave equation for planarly layered media. We construct the Green function of the waveguide as an expansion involving the eigenfunctions of the continuous and the discrete spectrum of the auxiliary problem. From the eigenvalues of the discrete spectrum, we calculate the allowed propagation constants of the guided modes. The Spectral Parameter Power Series (SPPS) method [Math. Method Appl. Sci. 2010;33: 459–468] leads us to analytic expressions for the eigenfunctions of the auxiliary problem in the form of power series of the spectral parameter. In addition, we obtain an SPPS representation for the dispersion relation without making any kind of approximation or discretisation to the core of the waveguide. The SPPS analysis here presented is well suited for its numerical implementation, since all these series can be truncated due to their uniform convergence.

Equidistant and Non-Equidistant Sampling for Method of Moments Applied to Pocklington Equation

We present a non-equidistant sampling for the method of moments in the solution of Pocklington equation operator, to prove the reduction of segments junctions and conductor far end discontinuities. Comparison of equidistant and non-equidistant sampling is presented, obtaining E field over the surface of a lambda/2 dipole.

Numerical estimates of the essential spectra of quantum graphs with delta-interactions at vertices

ABSTRACT In this paper, we consider periodic metric graphs embedded in , equipped by Schrödinger operators with bounded potentials q, and -type vertex conditions. Graphs are periodic with respect to a group isomorphic to . Applying the limit operators method, we give a formula for the essential spectra of associated unbounded operators consisting of a union of the spectra of the limit operators defined by the potential q. We apply this formula and the spectral parameter power series (SPPS) method for the analysis of the essential spectral of Schrödinger operators with potentials q of the form , where is a periodic potential and is a slowly oscillating at infinity potential. The conjunction of both methods lead to an effective technique that can be used for performing numerical analysis as well. Several numerical examples demonstrate the effectiveness of our approach.

On the importance of the vertical radiation pattern on simulations of WSNs

Applications of wireless sensor networks have nowadays expanded their technical requirements. One of them is the form how nodes are distributed, from random positions to a predetermined location of nodes. In this concern, those applications that require a specific planning of position of nodes usually consider simple characteristics of the antenna radiation pattern (an isotropic pattern, for instance). Depending on the particular application, nodes can be located not only at different distances from each other, but also at different heights, which could introduce less gain due to the vertical pattern of the antenna. Thus, this paper addresses the importance of considering the vertical radiation pattern of antennas on simulations of wireless sensor networks, when nodes have a fixed position. By taking a commercial antenna and its measured radiation pattern, an evaluation of the achieved gain and its impact on a link budget is presented.

Numerical approach to King’s analytical study for circular loop antenna

Abstract We exhibit a numerical technique based on the Pocklington equation and the method of moments for the study of circular loop antennas, and we show that the current distributions thus obtained are in total harmony with the corresponding analytical results of King [1].