In systems that are two and three dimensional electronically, a large polaron and a small polaron are distinct types of quasiparticles. The type of polaron formed depends on which electron-lattice interaction is of primary importance. A large polaron forms when the electron-lattice interaction due to the long-range Coulombic interactions between an electronic carrier and a solid's ions are of paramount importance. Competing effects then determine the radius of a large polaron. By contrast, a small polaron can form when a short-range electron-lattice interaction, such as the deformation-potential interaction, is dominant. A small polaron forms as its self-trapped carrier shrinks without limit until it is confined to a single site. Fundamental differences between large and small polarons produce optical spectra with distinguishing features. The absorption due to photoionization of a large polaron depends on products of the matrix elements for exciting a carrier from its self-trapped states to a free-carrier state and the density of these free-carrier states. These matrix elements fall sharply with increasing free-carrier wave vector k when kR > 1, where R is the large polaron's radius. A large polaron's photoionization produces a temperature-independent absorption band. This band is asymmetric with the absorption intensity on the high-energy side of the peak exceeding that on the low-energy side of the peak. By contrast, the small-polaron absorption arises as the self-trapped carrier is induced to transfer from its well-localized state to a localized state at an adjacent site. Phonon broadening of these local electronic energy levels produces the widths of these absorption bands. Small-polaron absorption bands are asymmetric with the absorption intensity below the peak energy exceeding that above the peak energy. With rising temperature the phonon broadening of the local electronic energy levels progressively broadens these absorption bands. In addition, the motion of a polaron in response to an ac field can produce a (Drude-like) free-carrier absorption. A large polaron's free-carrier absorption occurs at frequencies below the characteristic phonon frequency. By contrast, if the narrow bands that characterize small polarons did not result in their localization, their coherent motion would produce a free-carrier absorption that is restricted to frequencies far below the phonon frequency. The optical spectra of large and small bipolarons are similar to those for large and small polarons, respectively. Finally, carrier-induced absorption bands observed in semiconducting and superconducting cuprates are compared with the expectations of large- and small-polaronic absorptions. The high-frequency absorption bands are consistent with the existence of large-polaronic carriers. However, taken together, the free-carrier absorptions and the dc transport in the superconductors depart from expectations of independent polaronic carriers. It is suggested that if the carriers in the cuprates are polaronic, their transport in the superconductors' normal states is collective.
