Wavelength Scaling of High-Harmonic Yield: Threshold Phenomena and Bound State Symmetry Dependence

Describing harmonic generation (HG) in terms of a system’s complex quasienergy, the harmonic power $P_{\Delta E}(\lambda )$ (over a fixed interval, $\Delta E$, of harmonic energies) is shown to reproduce the wavelength scaling predicted recently by two groups of authors based on solutions of the time-dependent Schrödinger equation: $P_{\Delta E}(\lambda )\sim {\lambda }^{-x}$, where $x\approx 5–6$. Oscillations of $P_{\Delta E}(\lambda )$ on a fine $\lambda$ scale are then shown to have a quantum origin, involving threshold phenomena within a system of interacting ionization and HG channels, and to be sensitive to the bound state wave function’s symmetry.

Figure 1

Wavelength dependence of $P_{\Delta E}(\lambda )$ for H (circles), He (squares), and Ar (triangles) for $\Delta E=20–50\mathrm{eV}$ and $I=$ (a) $1.6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ or (b) $3.2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. Lines are fits of the scaling law (4) to the data, with $x$ given in Table .

Figure 2

Threshold phenomena in $P_{\Delta E}(\lambda )$ (upper panel) and in the yields of the individual harmonics in the interval 20–50 eV (bottom panel) for the H atom, with $I=1.6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. (cf. Fig. 2 in Ref. 6).

Figure 3

The same as in Fig. 2, but for Ar over a different range of $\lambda$. In the upper panel, our results (solid line) are compared with the TDSE results [6] (dotted line).

Figure 4

Dependence of $\delta \lambda$ on $\lambda$ [cf. Eq. (6)] for intensities $I=1.6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ (thick lines) and $I=3.2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ (thin lines). Dash-dot-dot lines: Eq. (7).