Novel Phenomena in Very-Low-Frequency Strong Fields

Atomic ionization by lasers of very low frequency, once thought to be a classical limit or a “tunneling limit”, presents unique spectral features unlike any tunneling phenomenon. The identity of the atom is the controlling factor, leading to photoelectron spectra with well-defined peaks and valleys that persist over wide ranges of field parameters. Such a spectrum was observed 20 years ago in ionization of xenon at $10.6\mu \mathrm{m}$.

Figure 1

This is a reproduction of a figure from Ref. 2, showing the photoelectron spectrum from the ionization of ground-state xenon by a ${\mathrm{CO}}_2$ laser operating at $10.6\mu \mathrm{m}$. Although the data were not abundant, they were still sufficient to allow a spectrum to be generated that shows the presence of two prominent peaks.

Figure 2

The momentum-dependent function $F(p)$ defined in Eq. (7) is shown for the noble gases that possess initial $p$ states. The $F(p)$ for argon, krypton, and xenon have a sharp peak at low energy. The exact location is difficult to discern in this figure, but the first peak occurs at about 12 eV for xenon, 18 eV for krypton, and 27 eV for argon.

Figure 3

The square of the generalized Bessel function modulates the $F(p)$ given in Fig. 2. (a) At 800 nm, small differences in intensity cause major changes in this modulation. The result is that the spatiotemporal distribution of intensity in the laser focus will mask the basic $F(p)$ form. (b) In contrast to the case of 800 nm in (a), the squared generalized Bessel function at $10.6\mu \mathrm{m}$ possesses a smoothly decreasing envelope.

Figure 4

(a) This figure shows the product of the $F(p)$ function for xenon in Fig. 2d and the $[J_n(u,v){]}^2$ envelope function for $10.6\mu \mathrm{m}$ in Fig. 3b. The result amounts to an isointensity spectrum for xenon at $10.6\mu \mathrm{m}$. The peak structure of Fig. 2d is retained, but with the relative peak amplitudes altered because of the decline of the envelope function. The localized gaps in Fig. 3b remain. The locations of these gaps have an intensity dependence that minimizes their effect when integrated over the spatiotemporal focal profile of the laser. The fundamental peak structure of the $F(p)$ for xenon is preserved. (b) In this figure, the spectrum obtained from a full treatment of the laser focal intensity profile is presented, including the effects of saturation. The basic $F(p)$ structure is maintained. The considerable depletion effects that are a consequence of the very long pulse length do not appreciably shift the locations of the peaks. The peak at 12 eV for xenon in Fig. 2d has been shifted to about 10 eV. (c) This figure is related to (b), except it is plotted on a logarithmic scale to make possible a comparison of spectra with and without depletion effects. The consequences of depletion for location of the peaks are minor. (d) An approximate correction for the effects of ponderomotive energy recovery from the long pulse is applied in this figure. See the text for further explanation. The two main xenon peaks remain, but an additional higher-energy peak appears in consequence of the recovery of ponderomotive energy. The maximum value of $U_p$ in the laser pulse is about 1 keV. This is responsible for shifting the far end of the spectrum to a higher energy, although the shift is less than the full $(U_p{)}_{\max }$. [The energy axis in (d) is more extensive than in (a)–(c).]