Self-focusing in a BaTiO_3 crystal without external electric fields

摘要

Self-trapping in photorefractive materials is a well-known effect and was widely investigated during the past decade. Usually, the light induced Pockels effect in photorefractive crystals compensates the natural divergence of the beam, therefore, creating a beam with constant diameter, a spatial soliton. The Pockels effect is based on the redistribution of charges in the crystal and can be forced by an external electric field. Due to the crystallographic structure of their elementary cell (tetragonal phase for temperatures below the Curie temperature) some crystals as BaTiO_3 or SBN possess a preferential direction the so called c-axis. They are spontaneously poled but in a statistical manner. Applying an external electric field with temperatures higher than the Curie-temperature and then decreasing the temperature all elementary cells will be orientated in the same direction, the crystal will be poled. This poling remains even if the external field is switched off. This means that the crystal obtains a remanent internal electric polarization. The experiment shows that this internal polarization can be understood as an effective electric field and, therefore, the self-focusing of appropriate laser beams is possible. We show the self-focusing of beams of a HeNe-laser (λ = 633 nm, P = 0.1 μW, 2w_0 = 4 μm) in BaTiO_3 without external electric fields and discuss the effect in dependence on the polarization and the intensity of the light beam at the entrance surface of the crystal. The experimental results are compared with numerical solutions of the stationary paraxial normalized wave equation.