Diffraction-induced transformation of near-cycle and subcycle pulses

Abstract

An analytical approach to the theory of diffraction transformation of pulses with superbroad spectra and arbitrary time dependence, in particular half-cycle (unipolar), single-cycle, and multicycle pulses, was developed. Closed-form solutions were found for on-axis propagation of half-cycle pulses with initially Gaussian spatial profiles that have either cosh-1-like or Gaussian time dependence, for single-cycle pulses based on higher modes of these functions, and for multicycle pulses. The far-field propagation demonstrates common patterns of time-derivative behavior regardless of the initial spatiotemporal profile. It is also shown that the time width of an off-axis pulse increases with the angle of observation. Owing to time–space reciprocity, the pulse transformation that is due to diffraction can be reversed, e.g., by reflection of a pulse from a spherical concave mirror.