This thesis presents the working principle of dielectric optical metasurfaces: arrays of optical scatterers smaller than the wavelength of light, which, due to their geometrical properties, can locally change the amplitude, phase or polarization of the incident wavefront. They can be utilized to create optical elements that are significantly thinner than conventional ones, while at the same time achieving functionalities that are impossible with a single conventional optical element. The theory of individual scatterers is described at the beginning of the thesis, where the effect on the polarization of light is discussed and described using the Jones formalism. Then the procedures for determining the phase shift profile of a thin surface are presented, which makes the surface function as a lens. The topology optimisation of the dielectric profile by means of adjoint optimisation, which is applicable to arbitrary functionalities of the metasurface is also described. The finite-difference time-domain simulation method is briefly presented, and then the results of simulations of individual scatterers and several types of metalenses are shown (ideal, parabolic, bifocal and RGB). The aim of this thesis is to understand the basics of metasurface operation.
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