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.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.

Physical ReviewFeb 15, 1965257 citations

Radiation Damping and the Polarization of Fluorescence Radiation

GREGORY A. BREIT, Irving S. Lowen

If the distance between two or more energy levels is comparable to their natural breadth, the levels cease to act independently. The coupling between the levels is then describable by means of a "damping constant matrix." The usual discussions concern themselves with a diagonal damping constant. Below a systematic treatment of emission, absorption and fluorescence is given without this restriction and it is shown how in general the frequencies of emission lines are affected by this radiation coupling. The theory is applied to the calculation of the polarization of fluorescence radiation. It is shown that the coupling state of the lower group of levels of the fluorescence line does not influence the polarization. Results of detailed calculations are given for the polarization of $\mathrm{H}\ensuremath{\alpha}$ excited by absorption of the second line of the Lyman series.If the distance between two or more energy levels is comparable to their natural breadth, the levels cease to act independently. The coupling between the levels is then describable by means of a "damping constant matrix." The usual discussions concern themselves with a diagonal damping constant. Below a systematic treatment of emission, absorption and fluorescence is given without this restriction and it is shown how in general the frequencies of emission lines are affected by this radiation coupling. The theory is applied to the calculation of the polarization of fluorescence radiation. It is shown that the coupling state of the lower group of levels of the fluorescence line does not influence the polarization. Results of detailed calculations are given for the polarization of $\mathrm{H}\ensuremath{\alpha}$ excited by absorption of the second line of the Lyman series.

Physical ReviewOct 1, 193417 citations

Emission, Absorption, and Photons

Michael P. Keating

Elsevier eBooksJan 1, 19880 citations

Effects of Atomic Interactions on the Absorption and Emission of Radiation

Dwight D. Hearn, Peter R. Fontana

The processes of absorption and emission of radiation by a system of two interacting atoms is investigated. Separation between the atoms is assumed to be much larger than the atomic diameter, and interactions considered are those between the individual atoms and the radiation field and the electrostatic interaction between the atoms. Calculations include those for the time-dependent probability amplitude of the intermediate and final states as well as that of the emission line shape. The line shape of the emitted radiation consists of two peaks whose amplitude, separation, and half-width are functions of both the internuclear separation R of the atoms and the energy difference of the excited states of the two atoms. For a large energy difference, the peaks are distinct; for small energy differences, the peaks are distinct at smaller separations, but merge toward the line shape characteristic of a single, isolated atom as R increases.The processes of absorption and emission of radiation by a system of two interacting atoms is investigated. Separation between the atoms is assumed to be much larger than the atomic diameter, and interactions considered are those between the individual atoms and the radiation field and the electrostatic interaction between the atoms. Calculations include those for the time-dependent probability amplitude of the intermediate and final states as well as that of the emission line shape. The line shape of the emitted radiation consists of two peaks whose amplitude, separation, and half-width are functions of both the internuclear separation R of the atoms and the energy difference of the excited states of the two atoms. For a large energy difference, the peaks are distinct; for small energy differences, the peaks are distinct at smaller separations, but merge toward the line shape characteristic of a single, isolated atom as R increases.

The Journal of Chemical PhysicsSep 1, 196910 citations

OPTICAL ABSORPTION AND EMISSION

WORLD SCIENTIFIC eBooksApr 1, 19990 citations

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.