Amplitude and phase gratings based on spatially modulated densities of optically generated polarons in thermally reduced LiNbO$_3$

In thermally reduced, nominally pure LiNbO$_3$ a variety of small polarons can be observed, being responsible for the distinct photochromic properties of this material. In this contribution we use a spatially modulated excitation of polarons for the recording of holographic gratings. These gratings inherit some of the pronounced features of the polarons like a stretched-exponential relaxation behavior with a lifetime in the ms-range. Beside amplitude gratings we also find phase gratings leading to a high diffraction efficiency in some recording and readout geometries. The origin of these phase gratings can't be explained by the classic photorefractive effect due to Fe$_{\mathrm{Li}}$ or other photorefractive dopants. In contrast, our findings are discussed in the frame of a model taking into account a local change of the refractive index by the polaronic distortion of the crystal lattice. Measurements of activation energies also indicate that these gratings can be attributed to the small bound ($\mathrm{Nb}^{4+}_{\mathrm{Li}}$)-polaron.