Temperature dependent photon echo (PE) and nonphotochemical hole burning (NPHB) measurements are reported on resorufin in three organic glasses: ethanol (1.5–11 K), glycerol (1.1–25 K), and d-ethanol (1.5–11 K). In all cases, the NPHB results are broadened considerably from the PE results at low temperatures, but the two measurements coalesce at high temperatures. The temperature dependences are found to deviate from the power law dependence expected for two-level system dephasing, and the deviation is attributed to dephasing by a pseudolocal mode. The appropriate correlation functions for PE and hole burning experiments are shown to be different from each other. They also differ from the correlation function for the optical absorption (OA) experiment, which has been the basis for most calculations of optical dephasing in glasses. The broadening of hole widths beyond the PE result is shown to be a measure of the slow spectral diffusion processes in the glass. Other types of dephasing measurement are also analyzed and each measurement is shown to be sensitive to spectral diffusion to a different degree. By making standard assumptions about glass dynamics, the main experimental results can be accounted for. A long range chromophore–glass interaction and a 1/R distribution of relaxation rates R at short times are indicated.
An exact algorithm is formulated to calculate the expected walk length (n) for a walker (atom, molecule) undergoing random displacements on a finite or infinite (periodic) d-dimensional lattice with traps (reactive sites). The method is illustrated for the case of a single deep trap surrounded by shallow traps and the calculated value of (n) agrees to within 0.3% of the Monte Carlo result for all lattices considered. The theoryintroduced is capable of generalization to many new classes of problems in lattice statistics.PACS numbers: 05.40.+iTo investigate the interplay between spatial extent and dimensionality in influencing reactiondiffusion processes, we have undertaken recently a program of Monte Carlo calculation of random walks on lattices with traps. 1 " 3 In the course of analyzing recent data generated in these studies, we have found that a quite general algorithm can be written down to predict the number (n) of steps required before trapping (i.e., the expected walk length) on finite and infinite (i.e., periodic) lattices subject to a variety of boundary conditions. Moreover, the method developed seems capable of much further generalization so that although we consider specifically the case of a deep trap (trapping probability, T = 1) surrounded by iV-1 sites which may be partially absorbing (trapping probability, 0^ s < 1), a great variety of other situations seems accessible to analysis. The method is based on a classification of the symmetry of the sites surrounding the deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry. We illustrate the method using two simple examples and cite a number of additional, representative results to show the generality of the method.Consider a 5x5 periodic lattice with a deep trap (T = 1) at the center and JV-1 = 24 surrounding sites, each characterized by a trapping probability s. From the symmetry of the unit cell, it is seen that there are five "types" of lattice sites, 1 = i«n> r + l) + i«w> 2 + l)+i«w> 2 + l)+i«n) 3 + D.Since the expected walk length from a deep trap (T = 1), (n) T , is zero this expression simplifies to {n) 1 = $[l+2((n) 2 + l) + {(n) 3 + l)].
Theory of photon echoes and hole burning in low temperature glasses: How good are the standard approximations?The first two-pulse photon echo experiments on a chromophore in an organic glass are reported. The homogeneous electronic dephasing of resorufin in ethanol glass is measured from 1.5-11.4 K. The temperature dependence ofthe dephasing time does not fit the power law frequently predicted by theory for the dephasing characteristic of glasses. However, the temperature dependence can be accounted for by including dephasing from librations or acoustic phonons, mechanisms known to be important in crystals. The dephasing decay is found to be a single exponential for over six factors of e. The dephasing is also shown to be uncorrelated with the extent of non photochemical hole burning (NPHB). However, the homogeneous linewidth deduced from the photon echo is four times narrower than the linewidth obtained from NPHB, demonstrating that the hole is broadened by additional processes.
The homogeneous optical dephasing time T2 for the organic glass system resorufin in ethanol is measured by picosecond twopulse photon echoes from 1.5 to I 1.4 K. A non-power law temperature dependence of T2 is measured. Non-photochemical hole burning (NPHB) linewidths are four times broader than the homogeneous linewidth, demonstrating that additional factors contribute to NPHB.
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