TEMPERATURE CYCLING OF PERSISTENT HOLE SPECTRA - A METHOD FOR INVESTIGATING THE TLS DENSITY IN AMORPHOUS MATERIALS

Spectral-diffusion kernels of hole-burning spectra can be modeled with a stochastic theory of dye-matrix interaction which, in its; original form, was devised by Markoff in the beginning of this century to describe shapes of inhomogeneous absorption lines. When the theory is extended to take the tunneling modes (two-level systems; TLSs) of the amorphous solid state into account, it can be readily applied to the inhomogeneous Iine-broadening phenomenon of spectral diffusion. In the case of dipolar interaction between TLSs and probe molecules, the shape of the kernel is Lorentzian or Gaussian in the limits that the average distance between the active tunneling modes is large or small, respectively, as compared to the size of the probe molecules. In the intermediate regime, the specific shape of the kernel is uniquely related to the TLS density. Starting from this finding, it is shown how temperature cycling of spectral holes can be used to determine the density of those TLSs which can perform flips at the ''excursion'' temperature, as well as their coupling parameter with the dye molecules. For convenient evaluation of experimental data, an empirical analytical fit function for the diffusion kernel is presented and compared with exact numerical calculations.