Semi-Experimental Determination of the Linear Clamped Electro-Optical Coefficients of Polar Crystals from Vibrational Spectroscopic Data

Eric Bouhari ,B Mohamadou ,P Bourson

doi:10.3390/cryst12010052

Abstract

The present work highlights a new general method devoted to computations of the clamped linear electro-optical coefficients from the measured fundamental vibrational frequencies and the nonlinear dielectric susceptibility constants. The calculations are based on the formula analog to that of the Lyddane–Sachs–Teller relation, which is systematically used for the calculations of the clamped linear electro-optical coefficient of oxide ferroelectric crystals such as LiNbO3, LiTaO3, BaTiO3, PbTiO3, and KNbO3. The computed electro-optical coefficients are in good agreement with those obtained from direct measurements and the first-principles calculations or other semi-empirical models. In addition, the famous r51 or r42 coefficients of the tetragonal BaTiO3, PbTiO3, and KNbO3 crystals are finally calculated with high accuracy and discussed in connection with the soft mode behavior.

Highlights

The linear electro-optic (Pockels) effect is the change of the refractive indices under the applied electric field of low frequency through its coupling with an exciting electric field
By taking advantage of the product form of this complex nonlinear dielectric response function (CNLDF), we derived another version of the Lyddane–Sachs– Teller (LST) relation, which is systematically used for the computations of EO coefficients, and we show that the relative errors of the indirectly measured EO coefficients could only depend on the measured Raman peak linewidth and its associated wavenumber
We are only interested in the calculations of the linear clamped EO coefficients through (16), which requires the following data: the transverse optic (TO) and longitudinal optic (LO) fundamental wavenumbers associated with the selected Raman tensor element, the third-order nonlinear dielectric susceptibility components, and the diagonal element of the high-frequency linear dielectric tensor ( 0n2ll; l = 1, 2, 3; and 0 is the vacuum permittivity)

Summary

Introduction

The linear electro-optic (Pockels) effect is the change of the refractive indices under the applied electric field of low frequency through its coupling with an exciting electric field. The NLO coefficients can be semi-empirically calculated using the bond charge model (BCM) [12] Based on this model, Shu and Yariv [13] derived some improvements which are currently used for the electro-optical calculation of a large band of NLO crystalline materials [14,15]. Kaminow [20] first pointed out a relationship that conveys the calculations of the EO coefficients from the measured nonlinear dielectric susceptibility coefficients (d-NLO), the Raman polarizabilities, and the effective charge parameter. This relation provides EO coefficients that are very close to those obtained from direct measurements, there is one important difficulty: the correct algebraic value of the Raman polarizability. No report publishes the correct value of the r51 coefficient of barium titanate BaTiO3 and lead titanate PbTiO3 perovskite crystals

Methods

Results

Discussion

Conclusion