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All naturally found and technologically fabricated solid microparticles possess surface roughness. Upon optical wave scattering from such particles, in addition to its geometric shape, the surface relief becomes an important morphological factor determining the optical properties of the scatterer. We present results of the numerical 3D-simulations of focusing an optical wave with a dielectric microsphere with randomly distributed surface roughness. We address different cases of azimuthally symmetric and asymmetric distortions of the particle surface. We show that the key parameters of the near-field focal region (intensity, longitudinal and transverse dimensions) referred to as a photonic nanojet (PNJ) are sensitive to changes in the microsphere surface texture. Two important PNJ parameters, the peak intensity and the longitudinal length, are subject to more prominent changes. The influence of the optical contrast (relative refractive index) of the microsphere on PNJ parameters is investigated in detail. The possibility of reducing the influence of surface roughness on the near-field focusing strength by microsphere watering (water-uptake) is demonstrated.

Using a finite-difference time-domain method, it has been shown that focal spots generated when tightly focusing a linearly polarized Gaussian beam by a Fresnel zone plate (FZP) and when focusing a Gaussian beam with an embedded optical vortex by a spiral zone plate (SZP) have different patterns of the intensity and energy flux. The most significant differences are observed when the value of the topological charge (TC) is equal to three. The energy flux has an annular distribution when the Gaussian beam is focused by the FZP, while the SZP produces a field whose patterns of intensity and energy flux have three local maxima. The number of local maxima corresponds to the order of the SZP. At a certain distance from the focus, the petal structure of the intensity (and energy flux) changes to a ring distribution.

Focusing of a linearly polarized laser beam of wavelength 633 nm with two-layer dielectric microcylinders of a circular cross-section and 2-um diameter was simulated using a finite-difference time-domain (FDTD) method, implemented using the FullWAVE software. It was shown that using a cladding whose refractive index (1.8 or 1.9) is higher than that of the core (1.45), it is possible to increase the depth of focus by a factor of 2.57 multiplied by the incident wavelength and shift the focal spot position along the optical axis away from the microcylinder boundary. It was also shown that parameters of the microcylinder could be chosen in such a way that a tighter focal spot was generated, with its full width at half maximum of intensity being 2.27 of the incident wavelength. The intensity at this focus was shown to be 1.4 times higher than that at the focus generated with a homogeneous microcylinder.

Using the finite difference method implemented in the COMSOL Multiphysics software package, the focusing of laser radiation by dielectric prisms with a triangular profile was numerically investigated. It was shown that two-dimensional triangular prisms make it possible to focus light in free space into spots with dimensions smaller than the scalar diffraction limit. In particular, a silica glass prism with a base width of 60 μm and a height of 28.5 μm forms a photonic nanojet with a maximum intensity of 6 times the intensity of the incident radiation and a width of FWHM=0.38λ. A prism from barium titanate with a base width of 60 μm and a height of 20 μm allows to obtain a photonic nanojet with the same width (0.38λ) and a maximum intensity 5 times the intensity of the incident radiation. The size of the focal spot can be reduced further if the height of the prism is selected so that the maximum intensity is located inside the material of the prism. For example, a barium titanate prism with a height of 21 μm and a base width of 60 μm forms a focal spot with a width of FWHM=0.25λ.