Emergence of collective spectral features in finite arrays of dielectric rods

Periodic optical structures, such as diffraction grating and numerous photonic crystals, are one of the staples of modern nanophotonics for the manipulation of electromagnetic radiation. The array of subwavelength dielectric rods is one of the simplest platforms, which, despite its simplicity exhibits extraordinary wave phenomena, such as diffraction anomalies and narrow reflective resonances. Despite the well-documented properties of infinite periodic systems, the behavior of these diffractive effects in systems incorporating a finite number of elements is studied to a far lesser extent. Here we study theoretically and numerically the evolution of collective spectral features in finite arrays of dielectric rods. We develop an analytical model of light scattering by a finite array of circular rods based on the coupled dipoles approximation and analyze the spectral features of finite arrays within the developed model. Finally, we validate the results of the analytical model using full-wave numerical simulations.