Surface defect lattice solitons in biased photovoltaic–photorefractive crystals

•Surface defect lattice solitons (SDLSs) in biased PP crystals are reported.•SDLSs exist only in the semi-infinite gap for positive defect strength.•SDLSs exist in the semi-infinite to second gaps for negative defect strength.•SDLSs are those in photovoltaic–photorefractive (PP) crystals without a bias field.•SDLSs are those in biased non-PP crystals if the photovoltaic effect is negligible.

We show that surface defect lattice solitons (SDLSs) at the interface with a defect between the photonic lattices and the uniform photovoltaic–photorefractive (PP) crystals with external applied field are possible. These SDLSs exist only in the semi-infinite gap for positive defect strength, and in the semi-infinite, first, and second gaps for negative defect strength. In the semi-infinite gap, SDLSs are stable in the low power region and unstable in the high power region. In the first and second gaps, SDLSs are stable in the all power region. We find that these SDLSs are those studied previously in biased non-PP crystals when the bulk photovoltaic effect is negligible and are those in PP crystals when the external bias field is absent.