Exciton dynamics in molecular solids from line shape analysis: an assessment of the extent of line shape distortion resulting from use of real crystals

For crystal absorption systems, the line profile of the frequency dependence of the dielectric permittivity ε(ω) contains information about the exciton dynamics that may be studied by the autocorrelation function generated by the Fourier transformation of ε(ω) into the time domain. However, ε(ω) obtained through transforming normal incidence reflectance data R (ω) of a real crystal when the photon-crystal eigenmodes are strongly coupled may be considerably distorted from ε(ω) of a perfect infinite crystal. In this paper, we consider the ways by which such distortions may arise and, by using a model for ε(ω) that might reasonably correspond to the 4000 Å b -polarized 0-0 absorption system at low temperatures of crystalline anthracene probed on the (001) face, we illustrate the dependence of the extent of distortions on the line profile of ε(ω) upon the following number of factors, viz., (i) spatial dispersion of the exciton bands; (ii) use of an oblique angle of incidence as an approximation to normal incidence in determining R (ω); (iii) thickness of the crystal slab used to determine R (ω); (iv) extent of roughness on the crystal surface; (v) mole fraction of defects in the crystal; and (vi) mole fraction of impurities in the crystal. The treatment allows definition of the condition [real ε(ω) < 0] under which various quasiparticles (longitudinal excitons, surface excitons, excitons bound to impurities) may be excited in a particular crystal system. The methods employed in this paper are of general applicability to strongly absorbing crystal systems and will be of use in understanding exciton dynamics in such systems. The data provide a firm foundation for interpreting reflectance data of a strongly absorbing crystal system, and thus we are able to discuss existing spectral data for anthracene crystals, especially narrow structure observed in low temperature reflection spectra, as well as suggest areas for both theoretical and experimental work