On the Validity of the Judd-Ofelt Theory for Two-Photon Absorption in the Rare-Earths

Abstract

The one-photon absorption theory of JUDD and OFELT^[1] has been rather succesfui in describing the oscillator strength of many forced electric-dipole f-f transitions in the trivalent rare-earths.^[2,3] Such a success has very often been taken as a vindication of all the assumptions behind the Judd-Ofelt theory when really it shows only that the formalism of representing the intensity of an f-f transition by the sum of phenomenological parameters multiplied by the squares of tabulated reduced matrix elements U^(λ)(λ = 2, 4, 6) is valid. There are cases where the Judd-Ofelt theory of one-photon absorption does not lead to accurate prediction Some well-known examples are given by the hypersensitive transitions.^[2] These transitions are characterized by large values of U⁽²⁾ matrix elements and are in general rather sensitive to the environment of the lanthanide ions. Since the Judd-Ofelt theory has also its weak points, it is very important to design new experiments to pinpoint its limitations. We would like to report here on a completely new test of the Judd-Ofelt theory. It is based on a theoretical calculation of AXE^[4]on two-photon absorption in the rare-earths. His work is a direct extension of the Judd-Ofelt theory for one-photon absorption to two-photon absorption. The theoretical predictions on relative two-photon absorption cross-sections are even simpler and involve only the U⁽²⁾ reduced matrix elements. It should be noted here that both the Axe and the Judd-Ofelt theories ignore the band character of the 5d states. In our work, we have observed direct two-photon f-f transitions in the Gd³⁺ ions in a LaF₃ host, using a CW linearly polarized laser beam of about 100 mW power.

On leave from Physikalisches Institut, D-6900 Heidelberg, Fed. Rep, of Germany