Relation between Absorption and Emission in the Region of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>Lines of Ruby

TLDR

The study discusses how the measured absorption and emission properties of ruby R lines impact laser performance. The authors measured radiative efficiency, absorption cross sections, and fluorescent lifetimes of ruby R lines across 20–373 K, then compared reciprocal lifetimes in thin and thick crystals using Einstein relations to relate to integrated absorption. The measurements confirm detailed balance for ruby R lines to within 5 % at 20 and 77 K, set a 0.002 cm⁻¹ upper limit on Stokes shift, show the lines are mainly electric‑dipole, reveal strong polarization dependence of radiative efficiency, and find that absorption increases ~20 % from 20 to 373 K while 10–30 % of decay is nonradiative or outside the observed range.

Abstract

We have measured the radiative efficiency (ratio of $R$-line photons to the total number of photons emitted) and absorption cross sections for the $R$ lines of dilute ruby, as a function of polarization and temperature between 20 and 373\ifmmode^\circ\else\textdegree\fi{}K. We have also measured the fluorescent lifetime from 20 to 373\ifmmode^\circ\else\textdegree\fi{}K in optically thin crystals, and from 20 to 273\ifmmode^\circ\else\textdegree\fi{}K in optically thick crystals. The difference between the reciprocal lifetimes in thin and thick crystals is directly comparable (via the Einstein relations) with the integrated absorption in the $R$ lines. This comparison shows that for the $R$ lines at 20 and 77\ifmmode^\circ\else\textdegree\fi{}K detailed balance holds to well within the experimental error of 5%, a precision never to our knowledge previously approached in solids. An upper limit of 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ was placed on any Stokes shift of the ${R}_{1}$ line, confirming that it is a no-phonon line. Comparison of $\ensuremath{\sigma}$ and $\ensuremath{\alpha}$ spectra confirms that the $R$ lines and their vibronic satellites are predominately electric-dipole in character. The radiative efficiency of the $R$ lines is strongly polarization dependent, a result which differs from that of previous workers. Its temperature dependence agrees well with that calculated from the observed vibronic spectrum at 77\ifmmode^\circ\else\textdegree\fi{}K. The integrated absorption in the $R$ lines increases by about 20% between 20 and 373\ifmmode^\circ\else\textdegree\fi{}K. The absorption in the vibronic satellites on the high-frequency side of the $R$ lines appears to be weaker than the corresponding emission on the low-frequency side. The temperature variation of the lifetime agrees well with that calculated from the absorption and radiative efficiency, but about 10% of the decay at 77\ifmmode^\circ\else\textdegree\fi{}K and 30% at 373\ifmmode^\circ\else\textdegree\fi{}K is either nonradiative or by emission at wavelengths outside the range of observation. The implications of our results for laser work are discussed.