Photovoltaic self-focusing in lithium niobate

Photorefractive media are known to support spatial solitons, i.e. beams that do not spread during propagation because self-focusing may balance natural diffraction [1]. For visible wavelengths this also occurs in lithium-niobate (LN), one of the most important crystals in modern optical technology. Previous studies have shown that when LN is not biased, beams undergo strong self-defocusing. The effect is attributed to the nature of the photovoltaic effect that drives photorefractive charge separation, and in particular to the sign of the relevant Glass coefficient. The result is that in these conditions only one class of solitons can be observed, the so-called dark solitons, consisting in dark notches in an otherwise illuminated wavefront that maintain unaltered their shape [2]. In turn, in unbiased barium-titanate an appropriate geometry can be found for which the photovoltaic nonlinearity is “opposite“ to that of LN and can lead to bright solitons, that is beams that have a bell-like transverse intensity profile centred on the beam axis [3]. Whereas LN is known to support self-focusing and bright solitons through the χ2 nonlinearity [4], or through the screening-photovoltaic nonlinearity, that is when it is biased by an external field [5,6], to date no self-focusing and bright self-trapping is known to occur through the photorefractive effect in an unbiased sample.