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

Using our recent description of harmonic generation (HG) in terms of a system's complex quasienergy [1], we analyze the harmonic power $P_{\Delta E}(\lambda)$ (over a fixed interval, $\Delta E$, of harmonic energies) as a function of wavelength and show that it reproduces the wavelength scaling predicted recently by two groups of authors [2, 3] based on solutions of the time-dependent Schr\"{o}dinger equation: $P_{\Delta E}(\lambda)\sim \lambda^{-x}$, where $x \approx 5-6$. Furthermore, the oscillations of $P_{\Delta E}(\lambda)$ on a fine $\lambda$ scale found in Ref. [3] are then shown to have a quantum origin, involving threshold phenomena within a system of interacting ionization and HG channels. Our results are also shown to be sensitive to the bound state wave function's symmetry. [1] M.V. Frolov, A.V. Flegel, N.L. Manakov, and A.F. Starace, Phys. Rev. A {\bf 75}, 063407 (2007). [2] J. Tate, T. Auguste, H.G. Muller, P. Sali\`{e}res, P. Agostini, and L.F. DiMauro, Phys. Rev. Lett.{\bf 98}, 013901 (2007). [3] K. Schiessl, K.L. Ishikava, E. Persson, and J. Burgd\"{o}rfer, Phys. Rev. Lett.{\bf 99}, 253903 (2007).