Introduction to macroscopic power scaling principles for high-order harmonic generation

Abstract

This tutorial presents an introduction to power scaling concepts for high-order harmonic generation (HHG) and attosecond pulse production. We present an overview of state-of-the-art HHG-based extreme ultraviolet (XUV) sources, followed by a brief introduction to basic principles underlying HHG and a detailed discussion of macroscopic effects and scaling principles. Particular emphasis is put on a general scaling model that allows the invariant scaling of the HHG process both, to μJ-level driving laser pulses and thus to multi-MHz repetition rates as well as to 100 mJ-or even Joule-level laser pulses, allowing new intensity regimes with attosecond XUV pulses.

How can attosecond pulse train interferometry interrogate electron dynamics?

“…the ratio of the energy of the attosecond pulse train or single attosecond pulse to the energy of the driving laser pulse, is about 10 -5 at best (usually lower for single attosecond pulses and for photon energies larger than 50 eV), determined both by the single-atom response and by phase-matching in the generation gas. Still, modern attosecond pulse sources can have average powers in the range of µW to mW [10].…”

Macroscopic scaling of high-order harmonics generated by two-color optimized waveforms in a hollow waveguide

“…High-order harmonic generation (HHG) is a highly nonlinear process which is sensitive to the driving laser and the gas target [8][9][10][11]. Therefore, there is a wide range of macroscopic parameters that affects the generation of harmonics in an experiment, thus making it difficult to locate the needed phase-matching conditions for the efficient buildup of macroscopic harmonic fields in a gas medium [12][13][14].…”

“…For applications HHG sources in different spectral or intensity regions may be needed. It is advantageous to investigate the scaling of harmonic generation processes to extend existing macroscopic parameter space for reaching phase-matching conditions in new regimes [14,15]. One of the well studied examples is the scaling of HHG yield with the driving laser wavelength.…”

“…However, their designed scaling was not achieved due to the limitation in pulse energy. Recently, a general scaling rule has been proposed [14,27,28], * Corresponding author: cjin@njust.edu.cn which identifies the invariance of HHG processes from the μJ-level multi-MHz high-repetition-rate lasers with tightly focused geometry to the loosely focused 100 mJ or Joule level pulses [29]. To obtain such scaling for nonlinear optical phenomena in gases [30], several macroscopic parameters, such as the medium length, beam diameter, focal length, and gas density, need to be appropriately scaled with input pulse energy.…”

“…Thus it is desirable to search for the scaling rule of high harmonics generated in a guided geometry [42][43][44]. So far the scaling of macroscopic parameters has been studied for one-color laser pulses in the free geometry only [14,[26][27][28]30]. Whether or not such scaling will work for multicolor laser pulses in a hollow waveguide has not been examined yet.…”