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Evolution of the transverse photoelectron momentum distribution for atomic ionization driven by a laser pulse with varying ellipticity

We consider the process of atomic ionization driven by a laser pulse with varying ellipticity. We study distribution of the momenta of the photoelectrons, ionized by a strong laser field, emitted in the direction perpendicular to the polarization plane (transverse distribution). We show, that with changing laser pulse ellipticity, the transverse distribution evolves from the singular cusp-like distribution for the close to linear polarization to the smooth gaussian-like structure for the close to circular polarization. In the latter case, when the ellipticity parameter $ε\to 1$ the strong-field approximation formula for the transverse momentum distribution becomes quantitatively correct.