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Physical Review

Relation between Absorption and Emission in the Region of the R Lines of Ruby

Donald F. Nelson, Michael D. Sturge

Published Feb 15, 1965• 257 citations
Publisher

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.

DOI
10.1103/physrev.137.a1117

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ASEE Northeast Section Meeting•May 9, 2025•1 citation
We have measured the radiative efficiency (ratio of RRR-line photons to the total number of photons emitted) and absorption cross sections for the RRR 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 RRR lines. This comparison shows that for the RRR 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 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1 was placed on any Stokes shift of the R1{R}_{1}R1​ line, confirming that it is a no-phonon line. Comparison of \ensuremathσ\ensuremath{\sigma}\ensuremathσ and \ensuremathα\ensuremath{\alpha}\ensuremathα spectra confirms that the RRR lines and their vibronic satellites are predominately electric-dipole in character. The radiative efficiency of the RRR 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 RRR 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 RRR 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.
Optical absorption cross sections and the fluorescent quantum efficiency in ruby have been determined. This data has been used to correlate calculations with the analysis of the preceding paper. Stimulated emission from ruby under pulsed excitation has been studied in some detail; the observations are found to depend strongly on the perfection of the particular crystal under study. A peak power output of approximately 5 kw, total output energy of near 1 joule, beam collimation of less than ${10}^{\ensuremath{-}2}$ rad, and a spectral width of individual components in the output radiation of about 6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$A at 6943 A have been measured. It is suggested that mode instabilities due to temperature shifts and a time-varying magnetic field are contributing to an oscillatory behavior of the output pulse.
The fluorescent decay of the 2E level of Cr3+ over the range of 77 to 300 K has been studied in experimental arrangements providing strong trapping of the O-phonon lines. At 300 K, rubies as large as 2.5-cm diameter by 33-cm length were used and were packed in highly reflective BaSO4 powder to provide adequate trapping of the O-phonon fluorescence. The measurements resulted in the determination explicitly of the lifetime vibronic transitions and the O-phonon decay rate. These studies of lifetime enhancement have potential application in the design of efficient solid-state lasers.
The absorption cross sections of the Cr3+{\mathrm{Cr}}^{3+}Cr3+ ion in the metastable states 2E(E‾and2A‾)^{2}E (\overline{E} \mathrm{and} 2\overline{A})2E(Eand2A) of lightly doped ruby (\ensuremath{\sim}0.01%) have been measured as a function of polarization at temperatures of 30, 105, and 296\ifmmode^\circ\else\textdegree\fi{}K in the region from 2300 to 7000 \AA{}. The lifetime of these states was measured by observing the decay rate of the excited-state absorption, and agreed with the value of the measured fluorescence decay rate at various temperatures. The population of the excited states was measured by the change of the area under the first two vibronic sidebands at low temperatures. At room temperature the population was measured by the change of transmitted intensity of a ruby laser.
Virtually simultaneous measurements of the emission and absorption profiles of the ruby R1 line show that no significant Stokes' shift is present. Observations were made on rubies of 0.0055% and 0.0186% Cr by weight with both crystallographic orientations and both polarizations in the temperature range from 77° to 153°K. The position of the peaks in the absorption line matched those of the emission line to within 0.002 cm−1. Shifts of this size or smaller cause no significant change in the operating characteristics of a laser.
Studies of the resonant interaction of radiation from a liquid-nitrogen-cooled ruby laser with a ruby crystal in the temperature range 4.2°–100°K are described. The interaction was measured by observation of the change which occurs in the Cr3+ ground state EPR absorption on laser irradiation. At low radiation intensities, the temperature dependence of this change is shown to be determined by the well-known thermal tuning behavior of the R lines. Precise measurement of the relative laser and ruby-sample absorption frequencies by this technique of double-resonance spectroscopy is described. Under optical saturation conditions, additional temperature-dependent pumping effects occur at low temperatures. In particular, as the ruby temperature is increased from 4.2° to 40°K, the laser-induced change in EPR absorption is observed to undergo a large increase. This increase cannot be explained by a relative thermal shift of the laser and absorption frequencies which is known to be very small in this temperature range. The phenomena are attributed in part to the temperature-dependent homogeneous linewidth which determines the widths of the holes burnt into the inhomogeneous strain-broadened R lines. Calculations indicate that the related temperature-dependent thermalization process which redistributes excited Cr3+ among the 2E levels quantitatively accounts for most of the increase.
The unique optical properties of the ruby crystal that make it effective as a lasing medium were measured using a simple optical setup.Ruby's absorption of visible light was shown to be strongest at 420 and 550 nm, corresponding to its physical appearance as transparent pink.While the ruby crystal was illuminated with a 532 nm green laser, the R-line fluorescence peaked at 693.5 ± 1.1 nm.Finally, the fluorescence lifetime of ruby was measured by pulsing the laser with a signal generator and capturing the decaying fluorescence on a digital oscilloscope using a photodiode.An exponential decay time-constant of 3.6 ± 0.1 ms was obtained, corresponding to the fluorescence lifetime.