Abstract— The applicability of the light absorption method for measuring particle concentrations during fast recording of absorption spectra in different ranges of frequency tuning rates and in different measurement schemes has been considered. If the molecular resonance time is shorter than the decay times of induced particle polarization in the open space of the medium, scanning of the transmission radiation frequency is accompanied by well-known transient coherent effects, the stationary spectrum is distorted, and oscillations arise. In this case the conventional total absorption methods can hardly be applied directly. A method based on reconstructing the stationary spectrum from the wing of the experimentally observed absorption line is proposed. When carrying out highly sensitive measurements of absorption in the medium inside of a high-Q external optical cavity, absorption line distortions arise as well, but at much lower frequency tuning rates. The observed spectra exhibit asymmetry, oscillations are not observed, and the violation mechanism is related in this case to the limitation of the probe-light coherence length (in comparison with the effective optical path length) and finite photon lifetime in the cavity. It is shown that direct application of the classical relations linking the total absorption with the particle concentration yields adequate results in this situation. The role of instrumental distortions in integral measurements is discussed.
Abstract The possibility of performing quantitative absorption measurements of particle concentrations using frequency-tunable lasers is investigated. At fast frequency scanning, when the recording time of spectrum is shorter or comparable with its formation time, well-known time-dependent interference interactions between the radiation incident on an absorbing medium and the radiation induced in it are observed. Under these conditions steady-state absorption spectra are distorted, and the classical relations lying in the basis of absorption measurements are violated. The character of the distortions depends on the type and density of particles, their absorption state, the mechanisms of spectra formation, and the laser beam power and geometry. In this paper, we report the results of studying the manifestations of Doppler profile narrowing caused by the Dicke effect in time-dependent spectra and their influence on the results of measuring the concentrations of absorbing particles. It is shown that the static spectrum can be reconstructed and quantitative measurements by integrated absorption spectroscopy can be performed under these conditions.
Effects caused by fast laser frequency sweeping across absorption lines are investigated. Oscillations in the time dependence of intensity of radiation generated by the medium, which are caused by beats between oscillations at variable excitation frequency and constant eigenfrequencies, are discovered. The time intervals between local maxima of the oscillations are inversely proportional to the difference between the eigenfrequency of the atomic oscillator and the instant frequency of the external radiation. The method of using fast frequency sweeping for determining indices of absorption at high optical densities (k 0 z ~ 100) is proposed.
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.
The nonstationary pump-probe interaction between short laser pulses propagating in a resonant optically dense coherent medium is considered. Special attention is paid to the case where the density of two-level particles is high enough that a considerable part of the energy of relatively weak external laser fields can be coherently absorbed and reemitted by the medium. Thus, the field of the medium reaction plays a key role in the interaction processes, which leads to collective behavior of an atomic ensemble in the strongly coupled light-matter system. Such behavior results in fast excitation interchanges between the field and a medium in the form of optical ringing, which is analogous to polariton beating in solid-state optics. This collective oscillating response, which can be treated as successive beats between light wave packets of different group velocities, is shown to significantly affect the propagation and amplification of the probe field under its nonlinear interaction with a nearly copropagating pump pulse. Depending on the probe-pump time delay, the probe transmission spectra show the appearance of either a specific doublet or coherent dip. The widths of these features are determined by the density-dependent field-matter coupling coefficient and increase during the propagation. Besides that, the widths of the coherent features, which appear close to resonance in the broadband probe spectrum, exceed the absorption-line width, since under the strong-coupling regime, the frequency of optical ringing exceeds the rate of incoherent relaxation. Contrary to stationary strong-field effects, the density- and coordinate-dependent transmission spectra of the probe manifest the importance of collective oscillations and cannot be obtained in the framework of a single-atom model.
We have calculated the line profiles to be expected when a Fabry–Perot interferometer is used to measure absorption lines. We have shown that large errors may be introduced in the measurement of the integrated absorption, even when an interferometer of high finesse is used. Curves and tables are given for finding the true absorption width and the true peak absorption from the apparent values observed under different operating conditions of the emission light source and the interferometer. We show qualitatively that the distortions are partially due to the presence of nonzero wings in the instrument-bandpass function. Finally, we show a Fourier series expansion of the integral giving the transmittance of the Fabry-Perot interferometer when absorbing atoms are in the light path.
Sodium vapor, in the density range
1013 to 5 \ifmmode\times\else\texttimes\fi{}
1014 ${\mathrm{cm}}^{\ensuremath{-}3}$, was excited by a cw dye laser, tuned 20-150 GHz from either the
D1 or
D2 resonance line. We observed a three-peak scattered spectrum, consisting of the Rayleigh component at the laser frequency, and the two fluorescence components (direct and sensitized) at the atomic resonance-line frequencies. Corrections to the Rayleigh signals for anisotropy and polarization effects, and to the fluorescence signals for radiation trapping, were made in order to obtain the ratio of the sum of the total intensities of the two fluorescence components to that of the Rayleigh component. This ratio combined with a measurement of the line-wing absorption coefficient yields the sodium density and the
D-line self-broadening rate coefficients [${k}_{\mathrm{br}}=4.67\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$
cm3${\mathrm{s}}^{\ensuremath{-}1}$ (\ifmmode\pm\else\textpm\fi{}15%) for the
D2 line and ${k}_{\mathrm{br}}=3.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$
cm3${\mathrm{s}}^{\ensuremath{-}1}$ (\ifmmode\pm\else\textpm\fi{}15%) for the
D1 line]. Asymmetry in the self-broadened line wings due to fine-structure recoupling was observed. The measured intensity ratio of the
D lines, combined with pulsed measurements of the effective radiative decay rates in the presence of radiation trapping, yields the fine-structure collisional-mixing cross section [$\ensuremath{\sigma}(3{P}_{\frac{3}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}})=172$
A˚2(\ifmmode\pm\else\textpm\fi{}18%)] at $T\ensuremath{\cong}300\ifmmode^\circ\else\textdegree\fi{}$ C. Our results are compared to other experiments and to theory.