Classical Emergence of Intrinsic Spin-Orbit Interaction of Light at the Nanoscale

Traditionally, in macroscopic geometrical optics intrinsic polarization and spatial degrees of freedom of light can be treated independently. However, at the subwavelength scale these properties appear to be coupled together, giving rise to the spin-orbit interaction (SOI) of light. In this work we address theoretically the classical emergence of the optical SOI at the nanoscale. By means of a full-vector analysis involving spherical vector waves we show that the spin-orbit factorizability condition, accounting the mutual influence between the amplitude (spin) and phase (orbit), is fulfilled only in the far-field limit. On the other side, in the near-field region, an additional relative phase introduces an extra term that hinders the factorization and reveals an intricate dynamical behavior according to the SOI regime. As a result, we find a suitable theoretical framework able to capture analytically the main features of intrinsic SOI of light. Besides allowing for a better understanding into the mechanism leading to its classical emergence at the nanoscale, our approach may be useful in order to design experimental setups that enhance the response of SOI-based effects.Comment: 10 pages, 5 figure

Near-Field Directionality Beyond the Dipole Approximation: Electric Quadrupole and Higher-Order Multipole Angular Spectra

Within the context of spin-related optical phenomena, the near-field directionality is generally understood from the quantum spin Hall effect of light, according to which the transverse spin of surface or guided modes is locked to the propagation direction. So far, most previous works have been focused on the spin properties of circularly polarized dipolar sources. However, in near-field optics, higher-order multipole sources (e.g., quadrupole, octupole, and so on) might become relevant, so a more in-depth formulation would be highly valuable. Building on the angular spectrum representation, we provide a general, analytical, and ready-to-use treatment in order to address the near-field directionality of any multipole field, particularizing to the electric quadrupole case. Besides underpinning and upgrading the current framework on spin-dependent directionality, our results may open up new perspectives for engineering light-matter coupling at the nanoscale.Comment: 7 pages, 2 figures. Supplemental Material (19 pages). Supplemental tools (calculator of angular spectra and animation) available at https://doi.org/10.5281/zenodo.267790

Robust beamforming for interference rejection in mobile communications

The problem of robust beamformer design in the presence of moving sources is considered. A new technique based on a generalization of the constrained minimum variance beamformer is proposed. The method explicitly takes into account changes in the scenario due to the movement of the desired and interfering sources, requiring only estimation of the desired DOA. Computer simulations show that the resulting performance constitutes a compromise between interference and noise rejection, computational complexity, and sensitivity to source movement.Peer ReviewedPostprint (published version

Hodge polynomials of the moduli spaces of pairs

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic pair on $X$ is a couple $(E,\phi)$, where $E$ is a holomorphic bundle over $X$ of rank $n$ and degree $d$, and $\phi\in H^0(E)$ is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which $E$ has fixed determinant.Comment: 23 pages, typos added, minor change