Generation of harmonic radiation during electron scattering from a piecewise-constant potential in an intense electromagnetic field

In a previous study [Phys. Rev. A 40, 5614 (1989)] we presented and discussed an exact solution for the scattering of electrons by a piecewise-constant potential in the presence of a strong electromagnetic field. An intimate connection with the physics of multiphoton ionization was demonstrated. Here we extend that study and present what we believe is the first accurate evaluation of power radiated at harmonics of the applied field frequency during electron scattering from a potential in a strong electromagnetic field. The results are nonperturbative and manifestly gauge invariant. We observe the production of multiple-order harmonics whose relative intensities as a function of harmonic number are similar to those of the above-threshold ionization peaks. No plateau in radiated intensity as a function of harmonic number is seen. Suppression of even harmonics in a symmetric potential is seen if the incoming state is strictly single parity (even or odd), but this suppression is found to be exceedingly sensitive to admixture of a small component of the opposite parity. In scattering from a well with two bound states, we observe a striking minimum in the third-harmonic intensity for incident electron energy close to resonance.