How To Maximize Birefringence and Nonlinearity of π-Conjugated Cyanurates

Abstract

Materials with large birefringence (Δ<i>n</i>) 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 π-conjugated ring (C₃N₃O₃, CY) is a class of fascinating materials exhibiting not only very large Δ<i>n</i> (larger than that of calcite) but also strong SHG (2 times that of β-BaB₂O₄, BBO). Here, we report five new cyanurates (<b>I</b>-<b>V</b>) and their single-crystal structures; among them, <b>II</b> realizes a Δ<i>n</i> = 0.4, the maximum in the cyanurate family, and <b>IV</b> realizes a <i>d</i>₃₃ = 6.69 pm/V, one of the highest values in the cyanurate family. We discover a dependence between Δ<i>n</i> 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 (γ) between the CY plane and the principal optical axes <i>XY</i> plane. <b>II</b> realizes the maximum Δ<i>n</i> due to its zero γ that indicates perfect coplanarity. Such a Δ<i>n</i>-γ dependence also allows the Δ<i>n</i> prediction of cyanurates. Furthermore, we uncover that the SHG intensity of cyanurates increases monotonically as the angle (θ) between the maximum hyperpolarizability (β_max) vector and the crystal 2₁ polar axis decreases. We predict the <i>d</i>_<i>ij</i> to extend well beyond such a value and to maximize at θ = 0°. Our results have significant implications for the future rational design and discovery of high-performance materials of π-conjugated and other related systems.