Theory for generation of high harmonics in the electron exit process

Experiments manifested that plasma interacting with a strong laser field can produce both even and odd high harmonics. Applying a nonperturbative quantum electrodynamics theory, we treat plasma states in a laser field as Volkov states. Our study shows when charged particles exit the single-mode laser field, spontaneous emissions as high harmonics with both even and odd orders occur due to the energy-momentum conservation. In multiphoton ionization (MPI) Volkov states play a role as intermediate states subject to a subsequent transition to plane waves according to the scattering theory of Guo, Aberg, and Crasemann (GAC). We identify the intermediate Volkov states in MPI as plasma states. By applying Gao et al.'s recent formula for MPI, derived from GAC theory with the inclusion of spontaneous emissions, we obtain spectra for high harmonics with both even and odd orders generated in the photoelectron exit process