Attosecond electromagnetic pulses: generation, measurement, and application. Generation of high-order harmonics of an intense laser field for attosecond pulse production

This review presents the current state of research on the generation and application of subfemtosecond (or attosecond, where $1$ as${}=10^{-18}$ s) ultraviolet and X-ray pulses. Emission of attosec„ond pulses is closely related to the generation of high-order harmonics in a laser field: the interaction of intense femtosec„ond laser pulses with matter causes the generation of high-order harmonics whose highest orders range from dozens to thousands and which produce attosecond pulses when they are phase-locked in a sufficiently broad spectral region. Two ways of attosecond pulse generation, the interaction of an intense laser radiation with a gaseous medium and with the edge of a solid state plasma, are discussed. The theory of the microscopic high-frequency response of a gaseous medium to an intense low-frequency laser field is presented together with numerical results based on the solution of the time-dependent Schr$\ddot {\rm o}$dinger equation for an atom in the external field. The review describes the methodology for calculating the macroscopic response and for analyzing the phase-matching in high-order harmonic generation. For the generation of coherent XUV radiation at the edge of a dense plasma, different generation scenarios are discussed, a simple model is proposed, and a comparison of model predictions with numerical results obtained from particle-in-cell (PIC) simulations is given.