Analysis of the lowest4f→5dtwo-photon transition inCe3+:CaF2

A theoretical estimate of the two-photon absorption (TPA) cross section for the lowest 4f→5d zero-phonon transition in ${\mathrm{Ce}}^{3+}$:${\mathrm{CaF}}_2$ is presented. A point-charge crystal-field model is used to calculate the odd component of the $C_{4v}$ crystal field which mixes states of opposite parity into the initial and final states participating in the transition. The sum over intermediate states is evaluated by assuming a constant energy denominator and using a closure approximation. The calculated magnitude and polarization anisotropy of the TPA cross section are compared with the experimentally measured values and methods to improve the calculation are discussed.