Excitonic absorption edge in alkali halides and the Urbach-Martienssen rule studied by three-photon difference-frequency generation

Abstract

Three-photon diA'erence-frequency generation (TP-DFG) is used to excite resonances on the lower exciton-polariton branch in alkali halides. The line shape of the resonances is investigated in KI and Rbl for temperatures between 1.5 and 800 K. A drastic variation of the linewidth ranging from 0.2 to about 50 meV is observed as a function of temperature and polariton energy. The experimental results are interpreted in the framework of polariton response theory, which links the shape of the TP-DFG resonance to the complex dielectric function. From the measured positions and widths of the resonance peaks, accurate data on dispersion and absorption are obtained for the region of the exponential tail of the excitonic absorption edge. The method allows us to determine the parameters of the Urbach-Martienssen rule by measurements on large single crystals.

Local polariton states in polar crystals with impurities

“…Numerical estimates show that for excitons with high frequencies and small damping it is possible to have for γ cr ∼ 10 −2 , where we have used parameters for exciton polaritons in KI from Ref. [17]. We conlcude, therefore, that one could observe local exciton-polariton states with frequencies within the polariton gap, induced by impurities with trap depth much smaller than for ordinary local excitons.…”

Rubidium Iodide (RbI)

“…In the region 0.260/zm -> A -> 0.230 ~m, we calculated the values of the refractive index n and extinction coefficient k by means of the values of parameters characterizing resonances on the lower exciton-polariton branch in RbI single crystals evaluated with three-photon difference-frequency generation (TP-DFG) by Fr6hlich et al [3]. Namely, as a modem method of nonlinear optical spectroscopy, the TP-DFG method opens up new possibilities to study elementary excitations in solids and, moreover, in the corresponding spectral region this method allows the determination of the spectral dependences of the optical constants of thick bulk samples of the single crystals in a reliable way.…”

“…Namely, as a modem method of nonlinear optical spectroscopy, the TP-DFG method opens up new possibilities to study elementary excitations in solids and, moreover, in the corresponding spectral region this method allows the determination of the spectral dependences of the optical constants of thick bulk samples of the single crystals in a reliable way. Equations enabling us to carry out these calculations are introduced in the paper mentioned [3]. Equations enabling us to carry out these calculations are introduced in the paper mentioned [3].…”

“…Namely, Baldini and Rigaldi's data [2] and the data derived from the TP-DFG measurements [3] correspond to 298 K. Li's values of n [4], Sprockhoff's values of n [5], and the data of Pai et al [6] correspond to 293, 298, and 300 K, respectively. However, strictly speaking there are small differences at temperatures corresponding to the data summarized.…”