The anionic group theory of the non-linear optical effect and its applications in the development of new high-quality NLO crystals in the borate series

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Abstract
Starting from a general quantum-mechanical perturbation theory on the nonlinear optical (NLO) effect in crystals, this review gives a systematic presentation of the basic concepts and calculation methods of the ‘anionic group theory for the NLO effect of crystals’ and a brief discussion of the approximations involved. Calculations have been made for the second harmonic generation (SHG) coefficients of a few typical NLO crystals. Comparisions between these theoretical values and the experimental values made both on powdered crystals and on single crystals suffice to show the feasibility of the theoretical treatment and calculation methods. On this basis, borate ions of various structure types are classified and systematic calculations are carried out for the NLO susceptibilities of some typical borate crystals with good prospects of applications in opto-electronics. Through these calculations, a series of structural criteria serving as useful guidelines for searching and developing new NLO crystals in borate series are presented. These structural criteria have good prospects of wider applications in searching and developing for other new types of NLO crystal materials. The criteria are as follows. (1) The planar six-membered ring (B3O6)3- and the planar trigonal (BO3)3 group, each possessing a conjugated 7t-orbital system, are far more favourable for producing larger SHG coefficients than the non-planar tetrahedral (BO4)5- group. Moveover, in the planar group, the larger the electronic population in the conjugated 7c-orbital system, the greater the SHG effects will be. As a result, the SHG effects will decrease in the order (2) The SHG coefficients can be adjusted to a certain extent by suitable arrangement of the three-and four-coordinated B atoms, such as (BO3)3- and (BO4)5-, (B3O6)3- as opposed to(B3O7)5- and (B3O8)7-. On the basis of these structural criteria, we have been successful in developing some new high-quality NLO materials, including the LiB3O5 crystal as an excellent NLO material. Suggestions are put forward for searching for and developing other promising new NLO materials in the borate series. The recent development of two new-type NLO borate crystals, β-BaB2O4 and LiB3O5, is described.