Analytic formulae for high harmonic generation

Analytic formulae for high harmonic generation

Analytic formulae describing harmonic generation by a weakly bound electron are derived quantum mechanically in the tunneling limit. The formulae confirm the classical three-step model and provide an analytic explanation for oscillatory structures on the harmonic generation plateau.

Analytic scaling analysis of high harmonic generation conversion efficiency.

Closed form expressions for the high harmonic generation (HHG) conversion efficiency are obtained for the plateau and cutoff regions. The presented formulas eliminate most of the computational complexity related to HHG simulations, and enable a detailed scaling analysis of HHG efficiency as a function of drive laser parameters and material properties. Moreover, in the total absence of any fitti...

Analytic surgery and gluing formulae for determinants

Generalized quadrature formulae for analytic functions

A kind of generalized quadrature formulae of maximal degree of precision for numerical integration of analytic functions is considered. Precisely, a general weighted quadrature of Birkhoff-Young type with 4n+3 nodes and degree of precision 6n+5 is studied. Its nodes are characterized by an orthogonality relation and a general numerical method for their computation is given. Special cases and nu...

Summation formulae involving harmonic numbers

Several summation formulae for finite and infinite series involving the classical harmonic numbers are presented. The classical harmonic numbers are defined by