Frequency Upconversion in Y<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Yb</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Tm</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>

The stepwise conversion of infrared ($\ensuremath{\approx}0.97\ensuremath{\mu}$) radiation to near infrared (0.81 \ensuremath{\mu}) and visible (0.475 \ensuremath{\mu}) light in Y${\mathrm{F}}_{3}$ sensitized with ${\mathrm{Yb}}^{3+}$ and activated with ${\mathrm{Tm}}^{3+}$ has been studied in detail. The lifetimes and fluorescence intensities of the important manifolds ($\mathrm{Yb}^{2}F_{\frac{5}{2}}$, $\mathrm{Tm}^{3}H_{4}$, $\mathrm{Tm}^{3}F_{4}$, and $\mathrm{Tm}^{1}G_{4}$), as well as the Yb-to-Tm transfer probability coefficients for the three steps of the process, have been measured as functions of concentration. A saturation effect previously observed in the Tm emission versus infrared excitation intensity has been shown to result from the rate of depopulation of $\mathrm{Tm}^{3}H_{4}$ by the second Yb-to-Tm transfer exceeding the $\mathrm{Tm}^{3}H_{4}$ decay rate. This was used to determine the second transfer probability coefficient. The first transfer probability coefficient was found to be 1.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{3}$${\mathrm{sec}}^{\ensuremath{-}1}$ independent of Tm concentration and for Yb concentration of the order of 10 at.% and greater. The second transfer probability coefficient was found to be approximately ${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{3}$${\mathrm{sec}}^{\ensuremath{-}1}$ for Yb concentrations of 25 at.% and greater. The third transfer probability coefficient was found to be 2.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{3}$${\mathrm{sec}}^{\ensuremath{-}1}$. The dependence on Yb concentration of the relative efficiency of conversion to 0.475-\ensuremath{\mu} light agrees well with the values calculated from a rate-equation model using the measured lifetimes and transfer probability coefficients.