In the last decade, the interest in the optical properties of structures of high-index semiconductor nanoparticles with low losses (for example, Si, TiO2) increased incrementally. Their response in a continuous irradiation mode was studied in detail, and many new optical effects were obtained, arising primarily due to the ability to excite both electrical and magnetic multipole moments in such particles and the almost complete absence of absorption. Based on the detected phenomena, several ultra-thin optical systems (about a few tens of nanometers thick) have been developed. These systems have functionality that is unattainable for the conventional ones. Despite the large number of groups in the world carrying out these studies, the field still is far from exhaustion, being regularly replenished with new discoveries. It seems most interesting to consider the temporal dynamics of states that in the stationary mode are non-scattering (dark modes) and, accordingly, the metasurfaces of such particles are almost completely transparent. In this regard, nanoparticles and metasurfaces in the anapole and hybrid-anapole states (the recently discovered state protected in a stationary regime from both the environment and the substrate, the femtosecond response of which, in turn, strongly depends on the environment and substrate) will be investigated theoretically and experimentally. These states, similar in stationary mode, have completely different mode compositions and will allow realizing different time dynamics and effects. The combination of the completely different properties in continuous and pulse regimes will provide an opportunity to subsequently develop new optical elements with dual functionality (for example, new ultrathin repetition rate multipliers, light filters, modulators, polarizers, etc.), which presently do not exist. The planned Thesis lies in a new and extremely rapidly developing field of nanophotonics. For example, according to the Scopus database, more than 1,500 articles are published annually in this area. The applications of dielectric nanophotonics are very diverse; for example, waveguides, modulators, directional radiation sources and nanoantennas, detectors, masking and invisibility devices, phase metasurfaces, etc. The development of dielectric nanophotonics has already made it possible to create various metasurfaces, materials, and meta-devices that realize the control of optical beams with almost no loss. However, there is now a need for new, ultra-thin photonic elements capable of effectively controlling ultrashort laser pulses, which the aforementioned nanophotonic devices, with few exceptions, do not allow. The PhD Thesis is complex and includes a full cycle of work, starting with a theoretical (analytical and numerical) study of the tasks, carried out in close cooperation with the experimental testing, which will make it possible to verify the correctness of the theory and, if necessary, make adjustments to it, and ending with the testing of prototypes that most fully demonstrate new phenomena, this project is devoted to. Specifically, the Thesis is investigating both theoretically and experimentally new effects due to the action of ultrashort laser pulses on high-index semiconductor nanoparticles (e.g., Si, Ge) with low absorption in the visible range. Currently, this area remains poorly explored. The study of transient dynamics in interaction with the pulses of nanoparticles in states that are non-scattering relative to continuous radiation, characterized by non-trivial mode structure in the near field, is of special interest. In particular, the project will focus on the study of the temporal dynamics of the anapole and hybrid-anapole states, as well as the interaction of metasurfaces of such nanoparticles with femtosecond pulses. Note that it is, for the first time, found that at the steady-state, the mentioned new hybrid anapole may correspond to the realization at the same frequency of the anapole states simultaneously for all contributing multipoles. Therefore, the irradiated particles occur in a completely nonscattering state (the usual anapole state makes it possible to extinguish only the radiation from a single, usually electric-dipolar, mode). Remarkably, a hybrid anapole state is accompanied by a strong concentration of the electromagnetic field in the near field zone and the excitation of a large set of resonant and nonresonant eigenmodes with different Q-factors. At the action of a short (femtosecond) laser pulse, it may result in a strong and non-trivial modulation of its envelope. In the case of the irradiation of an array of such nanoparticles and/or the corresponding metasurfaces, the modulation will depend on the metasurface’s symmetry as well as on the geometrical and optical properties of the substrate. Note that in the CW irradiation the optical response in the hybrid-anapole state does not depend on the environment and the substrate. Because of that, the metasurfaces made of such nanoparticles, while remaining completely transparent to a CW (though controlling its phase!), should strongly modulate femtosecond pulses. These properties will be used in the project to realize various dual-performance optical systems and devices whose response to the action of femtosecond and long laser pulses will be qualitatively different. The focus is on the study of new optical effects in the challenging subfield of ultrafast subwavelength optics. However, the specific subfield, namely transient optics of the nonscattering regimes, practically has not been developed yet and represents a vast field of activity. The Thesis is aimed at fundamental research in a new area and the implementation of fundamental models of new devices based on the results obtained. Within the Thesis framework, models have been developed, and prototypes of new ultra-thin planar photonic elements such as ultra-thin repetition rate multipliers, light filters, beam modulators, etc., have been implemented. These elements are designed for femtosecond optics and have dual-use applications for both short pulses and continuous irradiation.