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.

Bound states in the continuum (BICs) have been thoroughly investigated due to their formally divergent Q‐factor, especially those emerging in all‐dielectric, nanostructured metasurfaces from symmetry protection at the Γ point (in‐plane wavevector k_|| = 0). Less attention has been paid to accidental BICs that may appear at any other in the band structure of supported modes, being in turn difficult to predict. Here, a coupled electric/magnetic dipole model is used to determine analytical conditions for the emergence of accidental BICs, valid for any planar array of meta‐atoms that can be described by dipolar resonances, which is the case of many nanostructures in the optical domain. This is explored for all‐dielectric nanospheres through explicit analytical conditions that allow in turn to predict accidental BIC positions in the parameter space (ω, k_||). Finally, such conditions are exploited to determine not only single, but also double (for both linear polarizations) accidental BICs occurring at the same position in the dispersion relation ω − k_|| for realistic semiconductor nanodisk meta‐atoms. This might pave the way to a variety of BIC‐enhanced light–matter interaction phenomena at the nanoscale such as lasing or nonlinear conversion, that benefit from emerging at wavevectors away from the Γ point (off‐normal incidence) overlapping for both linear polarizations.

The optical properties of infinite planar array of scattering particles, metasurfaces and metagratings, are attracting special attention lately for their rich phenomenology, including both plasmonic and high-refractive-index dielectric meta-atoms with a variety of electric and magnetic resonant responses. Herein we derive a coupled electric and magnetic dipole analytical formulation to describe the reflection and transmission of such periodic arrays, including specular and diffractive orders, valid in the spectral regimes where only dipolar multipoles are needed. The two-dimensional lattice Green function is rewritten in terms of a one-dimensional (chain) version that fully converges in the complex frequency plane and can be easily calculated. Modes emerging as poles of such lattice Green function can be extracted, as evidenced by calculating resonances and bound states in the continuum for an array of Si spheres. This formulation can be applied to investigate a wealth of plasmonic, all-dielectric, and hybrid metasurfaces and metagratings of interest throughout the electromagnetic spectrum.

Optical trapping is a well-established, decades old technology with applications in several fields of research. The most common scenario deals with particles that tend to be centered on the brightest part of the optical trap. Consequently, the optical forces keep the particle away from the dark zones of the beam. However, this is not the case when a focused doughnut-shaped beam generates on-axis trapping. In this system, the particle is centered on the intensity minima of the laser beam and the bright annular part lies on the periphery of the particle. Researchers have shown great interest in this phenomenon due to its advantage of reducing light interaction with trapped particles and the intriguing increase in the trapping strength. This work presents experimental and theoretical results that extend the analysis of on-axis trapping with light vortex beams. Specifically, in our experiments, we trap micron-sized spherical silica (SiO₂) particles in water and we measure, through the power spectrum density method, the trap stiffness constant κ generated by vortex beams with different topological charge orders. The optical forces are calculated from the exact solutions of the electromagnetic fields provided by the generalized Lorentz-Mie theory. We show a remarkable agreement between the theoretical prediction and the experimental measurements of κ. Moreover, our numerical model gives us information about the electromagnetic fields inside the particle, offering valuable insights into the influence of the electromagnetic fields present in the vortex beam trapping scenario.

The near-zero forward intensity condition for light scattering by a dielectric dipolar sphere is usually associated with the generalized second Kerker condition, at which equal amplitude electric and magnetic dipolar responses are phase-shifted by $\pi$. As we show, this condition does lead to optimal backward light scattering for a given scattering cross section. However, it is clearly insufficient to give rise to the nearly zero optical forward scattering, in striking contrast to the actual view of the problem. In fact, we show that the generalized second Kerker condition leads to an energy radiation pattern that ranges all possible optical scattering diagrams depending on the total scattering cross section. Interestingly, we demonstrate that optimization of backward intensity, near the electric and magnetic dipolar resonances, leads to the counterintuitive result of a far-field energy radiation pattern with nearly zero backscattering.