The directionality and polarization of light show peculiar properties when the scattering by a dielectric sphere can be described exclusively by electric and magnetic dipolar modes. Particularly, when these modes oscillate in phase with equal amplitude, at the so-called first Kerker condition, the zero optical backscattering condition emerges for nondissipating spheres. However, the role of absorption and optical gain in the first Kerker condition remains unexplored. In this work, we demonstrate that either absorption or optical gain precludes the first Kerker condition and, hence, the absence of backscattered radiation light, regardless of the particle's size, incident wavelength, and incoming polarization. Finally, we derive the necessary prerequisites of the second Kerker condition of the zero forward light scattering, finding that optical gain is a compulsory requirement.

Increasing the sensitivity of chiral spectroscopic techniques such as circular dichroism (CD) spectroscopy is a current aspiration in the research field of nanophotonics. Enhancing CD spectroscopy depends on two complementary requirements: the enhancement of the electromagnetic fields perceived by the molecules under study and the conservation of the helicity of those fields, guaranteed by duality symmetry. In this work, we introduce a systematic method to design nanostructured dual periodic photonic systems capable of enhancing molecular CD spectroscopy resonantly. As an illustration, we engineer a dual 1D silicon nanoparticle array and show that its collective optical modes can be efficiently employed to resonantly enhance by 2 orders of magnitude the local density of optical chirality and, thus, the CD signal obtained from a given molecular sample on its vicinity.

High refractive index dielectric spheres present remarkable light-scattering properties in the spectral range dominated by dipolar modes. However, most of these properties are absent for larger spheres under plane wave illumination. Here, a proposal to unravel these dipolar regimes for larger particles under the illumination of a pure dipolar field is presented. This type of illumination ensures that the scattering response of the sphere is purely dipolar. In this scenario, it is shown that Kerker conditions are not only related to duality symmetry and a strong backward-to-forward asymmetric light-scattering, but also to the appearance of non-radiating sources: the so-called hybrid anapoles. Finally, it is shown that all the above-mentioned scattering features under dipolar illumination are reproducible with an experimentally accessible tightly-focused Gaussian beam.