Optical nonlinearities of small polarons in lithium niobate

Abstract

An overview of optical nonlinearities of small bound polarons is given, which can occur in the congruently melting composition of LiNbO3. Such polarons decisively influence the linear and nonlinear optical performance of this material that is important for the field of optics and photonics. On the basis of an elementary phenomenological approach, the localization of carriers in a periodic lattice with intrinsic defects is introduced. It is applied to describe the binding energies of four electron and hole small polarons in LiNbO3: small free Nb4+Nb polarons, small bound Nb4+Li polarons, small bound Nb4+Li:Nb4+Nb bipolarons, and small bound O− hole polarons. For the understanding of their linear interaction with light, an optically induced transfer between nearest-neighboring polaronic sites is assumed. It reveals spectrally well separated optical absorption features in the visible and near- infrared spectral range, their small polaron peak energies and lineshapes. Nonlinear interaction of light is assigned to the optical formation of short- lived small polarons as a result of carrier excitation by means of band-to- band transitions. It is accompanied by the appearance of a transient absorption being spectrally constituted by the individual fingerprints of the small polarons involved. The relaxation dynamics of the transients is thermally activated and characterized phenomenologically by a stretched exponential behavior, according to incoherent 3D small polaron hopping between regular and defect sites of the crystal lattice. It is shown that the analysis of the dynamics is a useful tool for revealing the recombination processes between small polarons of different charge. Nonlinear interaction of small polarons with light furthermore results in changes of the index of refraction. Besides its causal relation to the transients via Kramers-Kronig relation, pronounced index changes may occur due to optically generated electric fields modulating the index of refraction via the linear electro-optic effect, also. Based on a microscopic picture and by considering the local structural environment of bound polarons, the appearance of photovoltaic currents is explained straightforwardly as a result of the optically induced carrier transfer. Both transient absorption and index changes are spatially confined to the intensity profile of the interacting light allowing for the recording of efficient mixed absorption and phase volume holograms. By means of holographic spectroscopy, these small-polaron based optical nonlinearities are verified either without or with the action of the linear electro-optic effect; their prominent features are highlighted by appropriate experimental studies wherin the ultrafast response on the picosecond time scale is the most recognized one. Based on these findings, the consequences for applications of LiNbO3 in the field of nonlinear optics and photonics are presented. Besides visionary examples like real-time, 3D holographic displays, the impact of optical nonlinearities of small polarons for present applications are discussed with frequency conversion and respective limiting effects, such as green-induced infrared absorption and optical damage, as important example.