arXiv subjects

A. Zaidi

Publications and source records attributed to A. Zaidi.

3 recordsLinked to original sources

arXiv2023

Conformal pointwise slant Riemannian maps from or to Kähler manifolds

In this article, we study Conformal pointwise-slant Riemannian maps (\textit{CPSRM}) from or to Kähler manifolds to or from Riemannian manifolds. To check the existence of such maps, we provide some non-trivial examples. We derive some important results for these maps. We discuss the integrability and totally geodesicness of the distributions. Further, we investigate the conditions for homotheticity and harmonicity of these maps. Finally, we study some inequalities for these maps.

math.DG↗

arXiv2017

Achromatic Metalens in the Visible and Metalens with Reverse Chromatic Dispersion

In this letter, we experimentally report an achromatic metalens (AML) operating over a continuous bandwidth in the visible. This is accomplished via dispersion engineering of dielectric phase shifters: titanium dioxide nanopillars tiled on a dielectric spacer layer above a metallic mirror. The AML works in reflection mode with a focal length independent of wavelength from wavelength of 490 nm to 550 nm. We also design a metalens with reverse chromatic dispersion, where the focal length increases as the wavelength increases, contrary to conventional diffractive lenses. The ability to engineer the chromatic dispersion of metalenses at will enables a wide variety of applications that were not previously possible. In particular, for the AML design, we envision applications such as imaging under LED illumination, fluorescence, and photoluminescence spectroscopy.

physics.optics↗

arXiv2007

Rate Regions for the Partially-Cooperative Relay Broadcast Channel with Non-causal Side Information

In this work, we consider a partially cooperative relay broadcast channel (PC-RBC) controlled by random parameters. We provide rate regions for two different situations: 1) when side information (SI) S^n on the random parameters is non-causally known at both the source and the relay and, 2) when side information S^n is non-causally known at the source only. These achievable regions are derived for the general discrete memoryless case first and then extended to the case when the channel is degraded Gaussian and the SI is additive i.i.d. Gaussian. In this case, the source uses generalized dirty paper coding (GDPC), i.e., DPC combined with partial state cancellation, when only the source is informed, and DPC alone when both the source and the relay are informed. It appears that, even though it can not completely eliminate the effect of the SI (in contrast to the case of source and relay being informed), GDPC is particularly useful when only the source is informed.

cs.IT↗