Interference of electron trajectories and generation of high-order optical harmonics in a Coulomb system

The amplitudes of harmonics of the atomic response are determined as functions of the intensity of the pump light wave within the range of intensities of 4.9×10¹³ – 2.1×10¹⁴ W cm^-2 through the numerical solution of the Schrodinger equation for a hydrogen atom in an oscillating electric field. For the amplitudes of harmonics starting from the 5th up to at least the 55th order, these dependences display a deep modulation. Generation of high-order harmonics is analysed within the framework of semiclassical theory including several factors that were ignored in earlier studies. Relatively simple formulas for the amplitudes of high-order harmonics are derived. These formulas agree well with the results of numerical simulations in the range of tunnelling ionisation and provide a satisfactory agreement with numerical simulations in the range of barrier-suppression ionisation.