On the cutoff law of laser induced high harmonic spectra

摘要

The currently well accepted cutoff law for laser induced high harmonic spectra predicts the cutoff energy as a linear combination of two interaction energies, the ponderomotive energy U_p and the atomic biding energy I_p, with coefficients 3.17 and 1.32, respectively. Even though, this law has been there for twenty years or so, the background information for these two constants, such as how they relate to fundamental physics and mathematics constants, is still unknown. This simple fact, keeps this cutoff law remaining as an empirical one. Based on the cutoff property of Bessel functions and the Einstein photoelectric law in the multiphoton case, we show these two coefficients are algebraic constants, 9 - 42~(1/2) ≈ 3.34 and 22~(1/2) - 1 ≈ 1.83, respectively. A recent spectra calculation and an experimental measurement support the new cutoff law.