arXiv subjects

Riccardo Borghi

Publications and source records attributed to Riccardo Borghi.

23 records · Page 2Linked to original sources

arXiv2009

Resampling and requantization of band-limited Gaussian stochastic signals with flat power spectrum

A theoretical analysis, aimed at characterizing the degradation induced by the resampling and requantization processes applied to band-limited Gaussian signals with flat power spectrum, available through their digitized samples, is presented. The analysis provides an efficient algorithm for computing the complete {joint} bivariate discrete probability distribution associated to the true quantized version of the Gaussian signal and to the quantity estimated after resampling and requantization of the input digitized sequence. The use of Fourier transform techniques allows deriving {approximate} analytical expressions for the quantities of interest, as well as implementing their efficient computation. Numerical experiments are found to be in good agreement with the theoretical results, and confirm the validity of the whole approach.

cs.IT↗

arXiv2009

Joint use of the Weniger transformation and hyperasymptotics for accurate asymptotic evaluations of a class of saddle-point integrals. II. Higher-order transformations

The use of hyperasymptotics and the Weniger transformation has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals {evaluated across Stokes sets} [R. Borghi, Phys. Rev. E {\bf 78,} 026703 (2008)]. In the present sequel, the full development of the H-WT up to the second order in H is derived. Numerical experiments, carried out on several classes of saddle-point integrals, including the swallowtail diffraction catastrophe, show the effectiveness of the 2nd-level H-WT, in particular when the integrals are evaluated beyond the asymptotic realm.

physics.comp-ph↗

arXiv2009

Non-quantum entanglement and a complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism which governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could demand of a $4\times 4$ real matrix $M$ in order that it qualifies to be the Mueller matrix of some physical system is that $M$ should map $Ω^{({\rm pol})}$, the positive cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability or non-quantum entanglement brings in additional constraints that a pre-Mueller matrix $M$ mapping $Ω^{({\rm pol})}$ into itself needs to meet in order that it is an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized.

quant-ph↗

arXiv2009

Non-quantum entanglement resolves a fundamental issue in Polarization optics

The issue raised in this paper is classical in the sense of being ancient: which subset of 4X4 matrices should be accepted as physical Mueller matrices in polarization optics? Non-quantum entanglement between the polarization and spatial degrees of freedom of an electromagnetic beam is shown to provide the physical basis to resolve this issue in a definitive manner.

quant-ph↗

arXiv2007

Optical asymptotics via Weniger transformation

Starting from the resurgence equation discovered by Berry and Howls [M. V. Berry and C. Howls "Hyperasymptotics for integrals with saddles," Proc. R. Soc. Lond. A 434, 657-675 (1991)], the Weniger transformation is here proposed as a natural, efficient, and straightforwardly implementable scheme for the efficient asymptotics evaluation of a class of integrals occurring in several areas of physics and, in particular, of optics. Preliminary numerical tests, carried out on the Pearcey function, provide a direct comparison between the performances of Weniger transformation and those of Hyperasymptotics, which seems to corroborate the theoretical predictions. We believe that Weniger transformation would be a very useful computational tool for the asymptotic treatment of several optical problems.

physics.optics↗