Laser Transition Cross Section and Fluorescence Branching Ratio for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Nd</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>in Yttrium Aluminum Garnet

The emission cross section at the laser line peak of YA1G: ${\mathrm{Nd}}^{3+}$ was measured at room temperature by two independent methods. The effective cross section for the ion in the upper (${R}_{2}$) level of the $^{4}F_{\frac{3}{2}}$ manifold was found to be (8.8\ifmmode\pm\else\textpm\fi{}1.0) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}19}$ ${\mathrm{cm}}^{2}$. The values determined by the two different methods agreed with each other within experimental error. The result indicates that nonradiative transitions from the emitting state are negligible compared with the radiative transitions. The measured fluorescence branching ratios are also presented.