Spatio-temporal optical vortices: principles of description and basic properties

Abstract: This compilation represents a summary of the main physical foundations underlying the structure and properties of spatio-temporal optical vortices (STOV). The general approach to the STOV description and characterization is based on the model of scalar paraxial Gaussian wave packet. On this ground, the STOV structures of arbitrary orders are considered as superpositions of spatio-temporal Hermite-Gaussian modes. This approach enables a systematic characterization of the main STOV properties in an explicit and physically transparent form. In particular, we analyze the STOV amplitude and phase distributions, their evolution upon free propagation and in optical systems, internal energy flows and the orbital angular momentum. The topologically determined inherent asymmetry of the STOVs and the difference between the "energy center" and "probability center" [Phys. Rev. A 107, L031501 (2023)] are discussed and qualitatively interpreted. Methods for the STOV generation and diagnostics are outlined, and the main properties of non-Gaussian (Bessel-type) STOVs are briefly described. Finally, limitations of the scalar Gaussian model, accepted throughout the whole text, are considered, and possible generalizations are exposed. The whole presentation may be useful as initial introduction to the STOV-associated ideas and their extraordinary properties.