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Physical review. B, Condensed matter

Optical linewidths and photon-echo decays of impurities in glasses

W. O. Putikka, David L. Huber

Published Aug 15, 1987• 52 citations
Publisher

Abstract

Using a stochastic model, we calculate the temperature dependence of the homogeneous linewidth and the two-pulse photon-echo decay rate of optically active impurities in glasses. The theory applies to the low-temperature regime T\ensuremath{\lesssim}10 K, where it is assumed that the dephasing arises from an elastic dipole interaction of the impurity with an array of thermally excited tunneling systems. Averaging over the tunneling parameters and using relaxation rates appropriate to vitreous silica, we find that the photon-echo decay rate varies as ${T}^{1.1}$ and the homogeneous linewidth as ${T}^{1.2}$ for 0.1\ensuremath{\le}T\ensuremath{\le}1 K, assuming a constant density of states for the tunneling systems. Both the photon-echo amplitude and the optical dipole-moment correlation function decay exponentially in time. The rates, however, are different, with a ratio of photon-echo dephasing time to optical-absorption dephasing time of 6.9 at T=1 K, assuming a constant density of states. The relation of our results to various experimental studies is discussed.

DOI
10.1103/physrevb.36.3436

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A detailed description is presented of photon echo experiments in Nd3+{\mathrm{Nd}}^{3+}Nd3+-doped silica optical fibers at temperatures below 1 K. Dephasing rates ${T}_{2}^{\mathrm{\ensuremath{-}}1}$ have been obtained from two-pulse echo sequences at 0.89 \ensuremath{\mu}m and are found to follow a T1.3{T}^{1.3}T1.3 temperature dependence. An interpretation of this result is presented which invokes the interaction of tunneling systems with the optical ions via a dipole-dipole elastic interaction. The dynamics of the interaction originates in a spectral diffusion process and three pulse stimulated echo experiments confirm this interpretation.
A theoretical description of the temperature-dependent dephasing rate of rare-earth ions in glass is given for temperatures T<1T<1T<1 K. The model invokes elastic dipole-dipole interactions between the rare-earth ions and atomic tunneling systems. The calculation explains features of a recent photon-echo experiment on SiO2{\mathrm{O}}_{2}O2​:Nd3+{\mathrm{Nd}}^{3+}Nd3+, namely, the magnitude and T1.3{T}^{1.3}T1.3 dependence of the dephasing rate.
A modified theoretical model of photon echoes (PE) in low-temperature doped glasses based on the tunneling two-level system (TLS) and stochastic sudden jump models has been developed. The distinguishing feature of the model is its adaptation for Monte Carlo technique. The developed approach is more general than usual PE theories and allows us to take into account the different microscopic parameters of spectral dynamics in doped amorphous solids: in particular, the minimal radius of interaction between TLS and chromophore molecules, the dispersion of this coupling constant, and the changes of matrix properties nearby chromophore (shell-effect). The developed theory was applied for calculations of two-pulse PE decays for an organic amorphous system with typical parameters. It was found that the slope of temperature dependence of the homogeneous line width is decreased with an increase in the above-mentioned minimal radius. This effect could be one of the main reasons for the discrepancy between some PE experimental results versus calculation using standard PE theory.
We calculate the photon echo decay for a strongly coupled electron–phonon system, without making unrealistic assumptions about excitation pulse durations. We find that asymptotically, the photon echo decay is exponential, and we provide a formal expression for the decay rate 1/T2 which is independent of pulse duration. In contrast to the usual results, our expression for 1/T2 is nonperturbative in the electron–phonon interaction. We calculate the dependences of the echo amplitude on pulse power and duration, finding that the strong electron–phonon coupling modifies the simple two level system result. We also focus on the relationship between the zero phonon line shape in the homogeneous optical absorption spectrum, and the photon echo decay rate. We find that the zero phonon line shape is Lorentzian, with width 1/πT2. We show that the usual optical Bloch equation approach to analyzing time-domain experiments, which normally is only applicable if the electron–phonon coupling is weak, can be extended to the case of strong coupling. These strong coupling Bloch equations are adequate for analyzing the time dependence, but not the pulse power and duration dependences, of time-domain experiments. Our results indicate that within the Condon approximation, electron–phonon coupling cannot explain the very low temperature anomaly of recent photon echo experiments on impurities in molecular crystals.
The theory of optical photon echo and hole burning spectroscopies in low temperature glasses is discussed within the framework of the tunneling two-level system and stochastic sudden jump models. Exact results for the relevant theoretical quantities involve certain averages over the distributions of the two-level system energies and relaxation rates. The standard approximations for these averages are critically examined, for experimentally realistic parameters, via comparison to numerically exact calculations. The general conclusion is that the standard approximations are often used under conditions where they are not expected to be quantitatively accurate.