Pure Appl. Opt. 5 (1996) 89–93. Printed in the UK Calculation of third-order non-linear optical susceptibility of metal–oxide crystals K Koynov, P Mitev, I Buchvarov and S Saltiel Department of Physics, University of Sofia, 1164 Sofia, Bulgaria Received 26 June 1995, in final form 12 September 1995 Abstract. Third-order susceptibility tensor components of metal–oxide crystals are calculated using an approach based on the bond charge model used previously for the calculation of χ (2) and χ (3) of simple crystal structures. Calculated values of χ (3) of PbMoO 4 , CaWO 4 , CaCO 3 and KDP are compared with the experimental data. 1. Introduction The study of cubic susceptibility χ (3) is very important because it is responsible for such non- linear effects as self-focusing, self-phase modulation, four-wave-mixing processes, Raman scattering and others. Third-order processes are expected to be a base for the construction of all optical switching devices [1]. The development of models to calculate χ (3) gives rise to the possibility of predicting the values of the tensor components of non-linear susceptibilities in crystals not investigated experimentally. Moreover, the comparison of the theoretical and experimental results for χ (3) helps to evaluate the correct models to describe susceptibilities in crystals. There are several approaches for the calculation of non-linear optical susceptibilities. The most accurate model is the quantum mechanical approach [2]. It is only applied for the simplest crystals [3] because of the need for a lot of computer resources to calculate the accurate wavefunctions and energies for a large number of excited states. The other models are based on approximations. The theory of bond orbitals [4] gives a simple method to approximately calculate the eigenstates of the crystals. Using the bond orbital model, Phillips [5] and Van Vechten [6] developed a dielectric description of ionicity that has been successfully employed in many areas connected with crystal structures. In particular they obtained the expression of χ (1) for tetrahedral crystal structures. Levine [7, 8] extended this theory for other types of crystal structures and developed, on its basis, an electrodynamical model for χ (2) that gives excellent agreement with experiments. Chemla [9] developed further the χ (2) theory of Levine and adapted it for the calculation of χ (3) in semiconductor crystals with simple structure. The application of this model for other metal–oxide crystals does not give acceptable agreement with experiment. In particular this theory does not give the correct sign of χ (3) in PbMoO 4 . To our knowledge, a model for calculation of χ (3) in metal–oxide crystals with mixed ionic and covalent bonds has not been published. In this paper we present a model for calculation of the magnitude and sign of χ (3) tensor components of metal–oxide crystals. The model is a modification of the Bond Charge Model (BCM) used previously by Levine [8] for calculation of χ (2) and by Chemla [9] for calculation of χ (3) . The calculations are compared with the experimental data. 0963-9659/96/010089+05$19.50 c  1996 IOP Publishing Ltd 89