How To Maximize Birefringence and Nonlinearity of π-Conjugated Cyanurates

Materials with large birefringence (Delta n) are highly needed by fiber-optic isolators, whereas crystals showing strong second-order harmonic generation (SHG) are the key component for all-solid-state laser devices. Cyanurate constructed by the planar pi-conjugated ring (C3N3O3, CY) is a class of fascinating materials exhibiting not only very large Delta n (larger than that of calcite) but also strong SHG (2 times that of beta-BaB2O4, BBO). Here, we report five new cyanurates (I-V) and their single-crystal structures; among them, II realizes a Delta n = 0.4, the maximum in the cyanurate family, and IV realizes a d(33) = 6.69 pm/V, one of the highest values in the cyanurate family. We discover a dependence between An and the coplanarity of the CY rings that is explicitly described by a Boltzmann function, in which the coplanarity is defined by the dihedral angle (gamma) between the CY plane and the principal optical axes XY plane. II realizes the maximum An due to its zero y that indicates perfect coplanarity. Such a Delta n-gamma dependence also allows the Delta n prediction of cyanurates. Furthermore, we uncover that the SHG intensity of cyanurates increases monotonically as the angle (gamma) between the maximum hyperpolarizability (beta(max)) vector and the crystal 2(1) polar axis decreases. We predict the d(ij) to extend well beyond such a value and to maximize at theta = 0 degrees. Our results have significant implications for the future rational design and discovery of high-performance materials of pi-conjugated and other related systems.