We present a theory of high-order harmonic generation by arbitrary polyatomic molecules based on the molecular strong-field approximation (MSFA) in the framework of the S-matrix theory. A polyatomic molecule is modeled by an (N + 1)-particle system, which consists of N heavy atomic (ionic) centers and an electron. We derived various versions (with or without the dressing of the initial and/or final molecular state) of the MSFA. The general expression for the T-matrix element takes a simple form for neutral polyatomic molecules. We show the existence of the interference minima in the harmonic spectrum and explain these minima as a multiple-slit type of interference. This is illustrated by numerical examples for the nitrous oxide (N2O) molecule exposed to strong linearly polarized laser field.

We investigate high-order above-threshold ionization (HATI) of krypton atoms by a bicircular laser field, which consists of two coplanar co- or counter-rotating circularly polarized fields of frequencies rw and sw. We show that the photoelectron spectra in the HATI process, presented in the momentum plane, exhibit the same discrete rotational symmetry as the driving field. We also analyze HATI spectra for various combinations of the intensities of two field components for co- and counter-rotating fields. We find that the appearance of high-energy plateau for the counter-rotating case is vary sensitive to the laser intensity ratio, while the plateau is always absent for the co-rotating bicircular field.

We investigate laser-assisted electron-ion recombination (LAR), high-order harmonic generation (HHG) and above-threshold ionization (ATI) of argon atoms by a bicircular laser field, which consists of two coplanar counter-rotating circularly polarized fields of frequencies rω and sω. The energy of soft x rays generated in the LAR process is analyzed as a function of the incident electron angle and numerical results of direct recombination of electrons with Ar+ ions are presented. We also present the results of HHG by a bicircular field and confirm the selection rules derived earlier for inert-gas atoms in a p ground state. We show that the photoelectron spectra in the ATI process, presented in the momentum plane, as well as the LAR spectra exhibit the same discrete rotational symmetry as the applied field.

We consider high-order above-threshold ionization (HATI) of polyatomic molecules ionized by a strong linearly polarized laser field. Improved molecular strong-field approximation by which the HATI process on polyatomic molecular species can be described is developed. Using this theory we calculate photoelectron angular-energy spectra for different triatomic molecules. Special attention is devoted to the minima that are observed in the calculated high-energy electron spectra of the ozone and carbon dioxide molecules. A key difference between these minima and minima that are observed in the corresponding spectra of diatomic molecules are presented.