We consider refractive index sensing with optical bounds states in the continuum (BICs) in dielectric gratings. Applying a perturbative approach we derived the differential sensitivity and the figure of merit of a sensor operating in the spectral vicinity of a BIC. Optimisation design approach for engineering an effective sensor is proposed. An analytic formula for the maximal sensitivity with an optical BIC is derived. The results are supplied with straightforward numerical simulations.

Collective lattice resonances (CLRs) in finite-sized $ 2D $ arrays of dielectric nanospheres have been studied via the coupled dipole approximation. We show that even for sufficiently large arrays, up to $ 100 \times 100 $ nanoparticles (NPs), electric or magnetic dipole CLRs may differ significantly from the ones calculated for infinite arrays with the same NP sizes and interparticle distances. The discrepancy is explained by the existence of a sufficiently strong cross-interaction between electric and magnetic dipoles induced at NPs in finite-sized lattices, which is ignored for infinite arrays. We support this claim numerically and propose an analytic model to estimate a spectral width of CLRs for finite-sized arrays. Given that most of the current theoretical and numerical researches on collective effects in arrays of dielectric NPs rely on modeling infinite structures, the reported findings may contribute to thoughtful and optimal design of inherently finite-sized photonic devices.

Regular arrays of plasmonic nanoparticles have brought significant attention over the last decade due to their ability to support localized surface plasmons (LSPs) and exhibit diffractive grating behavior simultaneously. For a specific set of parameters (i.e., period, particle shape, size, and material), it is possible to generate super-narrow surface lattice resonances (SLRs) that are caused by interference of the LSP and the grating Rayleigh anomaly. In this letter, we propose plasmonic structures based on regular 2D arrays of TiN nanodisks to generate high-Q SLRs in an important telecommunication range, which is quite difficult to achieve with conventional plasmonic materials. The position of the SLR peak can be tailored within the whole telecommunication bandwidth (from ≈ 1.26 μm to ≈ 1.62 μm) by varying the lattice period, while the Q-factor is controlled by changing nanodisk sizes. We show that the Q-factor of SLRs can reach a value of 2 × 10³, which is the highest reported Q-factor for SLRs at telecommunication wavelengths so far. Tunability of optical properties, refractory behavior, and low-cost fabrication of TiN nanoparticles paves the way for manufacturing cheap nanostructures with extremely stable and adjustable electromagnetic response at telecommunication wavelengths for a large number of applications.

We calculate the quasistatic electromagnetic density of states for aggregates of touching spheres, in particular, linear chains and computer-generated random fractal aggregates. Multipole moments with orders of up to $L=64$ are taken into account for random aggregates with the number of particles of up to $N=100$ and up to $L=8000$ for linear chains. Extensive comparisons with the dipole approximation and geometrical cluster renormalization method are performed. Extinction spectra are calculated for several metals and black carbon. Long wavelength electromagnetic properties of fractal aggregates are considered in details.

We have shown within quasistatic approximation that the giant fluctuations of a local electromagnetic field in random fractal aggregates of silver nanospheres are strongly correlated with a local anisotropy factor $S$ which is defined in this paper. The latter is a purely geometrical parameter which characterizes the deviation of local environment of a given nanosphere in an aggregate from spherical symmetry. Therefore, it is possible to predict the sites with anomalously large local fields in an aggregate without explicitly solving the electromagnetic problem. We have also demonstrated that the average (over nanospheres) value of $S$ does not depend noticeably on the fractal dimension $D$, except when $D$ approaches the trivial limit $D=3$. In this case, as one can expect, the average local environment becomes spherically symmetrical and $S$ approaches zero. This corresponds to the well-known fact that in trivial aggregates, fluctuations of local electromagnetic fields are much weaker than in fractal aggregates. Thus, we find that, within the quasistatics, the large-scale geometry does not have a significant impact on local electromagnetic responses in nanoaggregates in a wide range of fractal dimensions. However, this prediction is expected not to be correct in aggregates which are sufficiently large for the intermediate- and radiation-zone interaction of individual nanospheres to become important.