Coulomb phase in high harmonic generation

We derive a regularized expression for the Coulomb term in the phase of high order harmonics emitted in the interaction of intense laser pulses with atoms. The calculation is based on the formalism of quantum orbits and on the imaginary time method and allows one to match the initially divergent Coulomb integral with the phases of the atomic wave function at the instants of ionization and recombination, leading to a finite and closed analytic formula. This complex-valued Coulomb phase can considerably modify both the yield and the interference structure of high harmonic spectra. Its possible implications for numerical calculations of the high harmonic signal are discussed. (paper)