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Nonlinear transmission measurements of silicon are used to determine the two- and three-photon absorption coefficients for photon energies above the indirect band gap of Si in the range of 1.14–2.07 eV. By careful characterization of the temporal and spatial profiles of the ultrashort optical pulses, the nonlinear transmission as a function of peak optical intensity can be determined. Two- and three-photon absorption coefficients are acquired by fitting both an analytical and numerical model to the transmission traces, from which two distinct spectral regimes emerge with a clear threshold at 1.7 eV—this corresponds to half the direct band gap in Si. At photon energies above the threshold, the nonlinear transmission traces are dominated by two-photon absorption, whereas below the threshold three-photon absorption is dominant with a nondetectable contribution from indirect two-photon absorption. This result is at variance with the current understanding of above-band-gap nonlinear absorption in Si, which is exclusively attributed to two-photon absorption processes.
Aagaard et al. (Mon,) studied this question.