The tunneling model of laser-induced ionization and its failure at low frequencies

Abstract

The tunneling model of ionization applies only to longitudinal fields: quasistatic electric fields that do not propagate. Laser fields are transverse: plane wave fields that possess the ability to propagate. Although there is an approximate connection between the effects of longitudinal and transverse fields in a useful range of frequencies, that equivalence fails completely at very low frequencies. Insight into this breakdown is given by an examination of radiation pressure, which is a unique transverse-field effect whose relative importance increases rapidly as the frequency declines. Radiation pressure can be ascribed to photon momentum, which does not exist for longitudinal fields. Two major consequences are that the near-universal acceptance of a static electric field as the zero frequency limit of a laser field is not correct; and that the numerical solution of the dipole-approximate Schr\"{o}dinger equation for laser effects is inapplicable as the frequency declines. These problems occur because the magnetic component of the laser field is very important at low frequencies, and hence the dipole approximation is not valid. Some experiments already exist that demonstrate the failure of tunneling concepts at low frequencies.