Optical maser action at the R2 line in ruby has been observed. Because of a fast thermal relaxation between the two 2E levels, it is not usually possible to satisfy the maser conditions at the R2 line when stimulated emission is occurring at the R1 line. However, if maser action can be suppressed at the R1 line, even at high inversion, it can be made to occur at the R2 line by the appropriate selection of operating conditions. This has been accomplished by using, for end reflectors, multilayer dielectric interference filters which have high transmission at the R1 line and low transmission at the R2 line. The selection of the operating conditions requires a correction of the absorption coefficients for the R1 and R2 lines based on the Boltzmann distribution between the two excited states. When the Boltzmann correction is made, the calculations show reasonable requirements on pumping threshold and reflectivities.
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
R1 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.
Small differences between the emission and absorption spectra of three-level maser centers can have a pronounced effect on maser operation. This paper considers the effects of a Stokes shift, the simplest and most probable difference. If there is a Stokes shift which is large compared to the linewidth, the operation of the maser will be essentially four level. If there is a small Stokes shift (some fraction of the linewidth) the operation will still be three level, but the Stokes shift will significantly affect the operation of the maser. The principal effects will be a shift of the maser line from the peak in the fluorescent emission line (away from the absorption peak) and a reduction in the upper level population required to reach the threshold of oscillation. The evidence is not conclusive as to whether there is a Stokes shift in the ruby R1 line, but if there is a shift it is at most a small fraction of the fluorescent linewidth at room temperature. Shifts of the ruby maser line to the red have been observed by D'Haenens and Asawa and have been attributed to large temperature changes. It is likely that the temperature shift, while important, will not explain the shift which has been observed. Gires and Mayer have found the lower state population of an operating ruby maser to be approximately 75% of the unexcited population rather than approximately 50% and have suggested a Stokes shift as a possible cause of the reduction in the upper state population at threshold. This paper considers the effect of such a small Stokes shift on the operation of an otherwise ideal three-level maser.
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.