Novel procedure for the simultaneous determination of the Debye length and electro-optic coefficient for an optically active photorefractive Bi ₁₂SiO₂₀ crystal

We present a novel procedure based on an improved physical model and a versatile numerical fitting technique, to simultaneously determinate the Debye screening length and electro-optic coefficient using a thick sample of an optically active photorefractive crystal Bi₁₂SiO₂₀ (BSO). For the computation, experimental data of gain vs. grating spacing were obtained by a two-beam coupling arrangement. Unlike former calculation models, in our work, the general expression for the diffraction efficiency in the presence of self-diffraction is considered, and the influence of the optical activity in the coupling parameters is had into account for the calculation of the gain values. The fitting of the experimental data to the predicted theoretical behavior by our model is achieved by finding the closest theoretical curve to a set of data sampled from a spline-smoothed curve of the experimental data. Both, the Debye screening length l_s and the electro-optic coefficient r₄₁ are used as fitting parameters by searching in a rather wide range for each one of the parameters, so that, the estimation of their values is obtained in a more reliable and direct way from the same experiment. The calculations are performed in diffusion regimen and the procedure leads to l_s = 0.22 μm and r₄₁ = 4.5 × 10^-12m/V. Because the optical activity can alter the maximum gain and self-diffraction effects influence the energy exchange, the procedure reveals to be physically appropriated for the simultaneous determination of these physical parameters when thick photorefractive crystals with high optical activity are considered.