Ultrahigh-order harmonic generation in the subnanometer wavelength range: the role of finite atomic size

Abstract

As shown by recent theoretical studies, intense ultrafast laser sources of long-wave infrared range are capable, in principle, of generating ultrahigh-order harmonics in the wavelength range of the atomic or even subatomic scale. Under these conditions the atom as an elementary emitter can no longer be considered within the framework of the point dipole model generally accepted in the theory of high-order harmonic generation. It can be expected that the non-pointness of an atomic dipole will lead to a change in both the power of the radiation emitted by it and its directivity pattern. In this paper, we study these effects in detail using the example of the hydrogen atom. The analysis was carried out within the widely used recollision model, according to which the high-frequency dipole moment responsible for the generation of high harmonics by an atomic system is induced as a result of the interference of the de Broglie wave of the recolliding electron with the wave function of the atomic bound state. Taking into account the non-pointness of the induced dipole, the dependences of the power and directivity pattern of its radiation on the wavelength of the emitted photon are found. In particular, a universal atomic dipole non-pointness factor is obtained in an explicit form, which depends on the wavelength and emission angle of the harmonic photon and makes it possible to calculate the frequency and angular characteristics of the emitted harmonics based on the results obtained in the point dipole approximation.