The boron–oxygen compound LiB₃O₅ is recognized as a new nonlinear-optical crystal. This follows theoretical calculations of the second-harmonic generation (SHG) coefficients using the anionic group theory and the complete neglect of differential overlap approximation to obtain the localized wave functions of component groups. An optically perfect single crystal with space group P_na2₁, grown at the Fujian Institute of Research on the Structure of Matter by the high-temperature flux method, is found to be transparent from 160 nm to 2.6 μm. It has a SHG coefficient comparable with that of β-BaB₂O₄ as well as two other outstanding advantages: a high damage threshold of 25 GW/cm² (at 1.064 μm, 0.1 nsec) and a wide acceptance angle of 25 mrad for θ ≠ 90° and 95 mrad for θ = 90° with a 6-mm-long crystal.

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.

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