Collimation and focusing of initially single-cycle paraxial optical beams

The paper reports theoretical results of collimation and focusing of spatio-temporal field structure that is forming due to far-field (Fraunhofer) diffraction of paraxial wave packet emitted by single-cycle radiation source. A spatial collimation of such waves results in a peculiar shape of spatio-temporal structure with the central part moving faster than its outlying areas. During the focusing of collimated beam, a transformation from 1.5-cycle to single-cycle and again to 1.5-cycle wave occurs along a path from collimating to focusing mirrors with equal focal lengths.