Damian P. San Roman Alerigi

arXiv2023

A high-order finite volume method for Maxwell's equations in heterogeneous and time-varying media

We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately resolve fine structures that develop due to the varying material properties. Numerical examples demonstrate the effectiveness of the proposed method in handling temporal variation and its efficiency relative to traditional 2nd-order FDTD.

physics.comp-ph↗

arXiv2012

Generation of J0-Bessel-Gauss Beam by an heterogeneous refractive index map

In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of such device by solving the inverse electromagnetic problem. The computed conversion efficiency is 90%. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction; demonstrate that a 2D graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping which is fully integrable in silicon photonics based planar lightwave circuits (PLC). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and non-linear beam diode lasers.

physics.optics↗