Adiabatic theory of high-order harmonic generation: One-dimensional zero-range-potential model

The adiabatic theory of ionization of atoms by intense few-cycle laser pulses, whose development was initiated recently [Tolstikhin et al., Phys. Rev. A 81, 033415 (2010)], is applied to the study of high-order harmonic generation (HHG). The same one-dimensional zero-range-potential model is considered. The asymptotic formula for the HHG spectrum in this model is obtained in the leading-order adiabatic approximation. This asymptotics is uniform in terms of the photon energy in the cutoff region. It is shown that the factorization formula for the HHG spectrum, first proposed by Morishita et al. [Phys. Rev. Lett. 100, 013903 (2008)] on the basis of numerical solution of the time-dependent Schrödinger equation, results from the adiabatic theory, and the structure of the rescattering photoelectron wave-packet factor is clarified. The theory is illustrated by calculations.

Figure 1

HHG spectrum produced by a one-cycle pulse, Eqs. (93) and (94), with $F_0=0.1$ and $T=50$. Solid (black) lines: exact TDSE results. Dotted (green) lines: uniform asymptotic formula (77). Dash-dotted (blue) line: simple asymptotic formula (83). Dashed (red) line: cutoff asymptotic formula (87). Vertical dotted and dash-dotted lines show the cutoff photon energies defined by Eq. (73) calculated with and without the correction term $d{t}_i\left(t\right)/dt$, respectively. The total ionization probability for this pulse is $0.030$.

Figure 2

Energy of an emitted photon $\omega$ as a function of the moment of recombination $t$ for the same one-cycle pulse with $F_0=0.1$ and $T=50$ as in Fig. 1. Solid (black) and dashed (red) lines show the results obtained from Eq. (70) with and without the term $d{t}_i\left(t\right)/dt$, respectively. Horizontal dotted lines indicate the corresponding cutoff photon energies, Eq. (73).

Figure 3

Same as Fig. 1, but for a one-cycle pulse with $F_0=0.1$ and $T=100$. The total ionization probability for this pulse is $0.050$.

Figure 4

HHG spectrum produced by a few-cycle pulse, Eqs. (93) and (95), with $F_0=0.1$, $n_{\text{oc}}=3$, and $T=331$ ($\text{FWHM}=6.7$ fs and $\lambda =800$ nm). Solid (black) line: exact TDSE results. Dotted (green) line: uniform asymptotic formula (77). The total ionization probability for this pulse is $0.041$.

Figure 5

Same as Fig. 4, but for a few-cycle pulse with $F_0=0.1$, $n_{\text{oc}}=3$, and $T=662$ ($\text{FWHM}=13.4$ fs and $\lambda =1600$ nm). (b) and (c): magnified views of the corresponding regions indicated in (a). The total ionization probability for this pulse is $0.083$.