Diffraction of hollow beams by dielectric microparticles and microsphere assisted microscopy

One of the main tasks of nano-optics is to produce nanostructured light that has spatial features well below the wavelength of visible light. In the present work, we theoretically reveal and study the nanostructured light resulting from the diffraction by a dielectric sphere or cylinder. The peculiarity of our nanostructured light is its location in free space at a substantial distance from the particle. We analyze the electromagnetic fields inside and behind a dielectric sphere's rear edge, illuminated by a hollow Bessel wave beam. We theoretically reveal a new kind of resonance called the spatial Fano resonance. The main minimum of the electromagnetic field is strongly subwavelength and noticeably distanced from the sphere's rear edge. A similar result we also obtained for the incidence of a 2D hollow wave beam called the cosine beam onto the microcylinder. We prove that this resonance can be utilized for a submicron optical trap. We also found the regime of subwavelength field concentration outside the microparticle, which could have applications such as cavity-enhanced fluorescence and cavity-enhanced all-dielectric Raman scattering. Results of this study are presented in the first part of this thesis. The second part of this thesis corresponds to the excitation of a dielectric microsphere or a microcylinder by point-wise dipoles. Capability of a simple dielectric sphere to offer label-free, far-field real-time subwavelength imaging of planar objects was experimentally revealed a decade ago. However, since then, the scientific community has yet to find a suitable explanation for this effect for a non-resonant microparticle. We have suggested a non-resonant mechanism for this superresolution and estimated the bounds of the ultimate resolution for the 2D case (imaging microcylinder). Our imaging mechanism does not involve evanescent waves. Instead, we exploit the property of a dipole scatterer that does not radiate along its direction.