Theoretical and experimental investigations are made of two-photon absorption spectra of trivalent rare-earth ions in crystals. Effective cross-sections, selection rules, and relative intensities of the components are found. The most intensive two-photon transitions are established. Two-photon excitation spectra of luminescence of Er3+ and Ho3+ ions in CaF, are obtained and effective excitation cross-sections are measured using a tunable dye laser (715 to 850 nm). It is shown that the spectra have a peculiar structure which differs considerably from that of the one-photon absorption spectra. The experimental results agree with theory. It is established that one of the levels in Hos+ is the level 5G, rather than sK, usually assumed.
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