First-order hyperpolarizability of organic molecules: hyper-Rayleigh scattering and applications

Abstract Hyper-Rayleigh scattering (HRS) is a parametric optical effect in which two incident photons of frequency ω are annihilated to create a scattered photon of frequency 2ω. Unlike second harmonic generation (SHG), the HRS signal is isotropic, incoherent, and dephased with the excitation photon. HRS has been widely used to investigate novel materials with potential for the development of technologies, such as more efficient frequency doubling, high-resolution microscopy, fast electro-optic modulation, ultrafast lasers, and even to identify the interaction and affinity between biological molecules. In this chapter, we describe the potential of the HRS technique to investigate the first-order hyperpolarizability of organic molecules. For that, we initially present fundamentals of the first-order hyperpolarizability in materials. Theoretical approaches applied to estimate the first-order hyperpolarizability are also presented. These approaches employ different quantum chemical methods combined with a numerical or analytical scheme. Three of the most commonly used schemes, namely the finite field (FF) scheme, the sum-over-states (SOS) scheme, and the coupled-perturbed scheme, are briefly described. These approaches are used to aid in the understanding of the fundamental aspects that can be exploited, at the molecular level, to reach remarkable first-order hyperpolarizability (>10−27 cm5/esu). Moreover, we present in detail different experimental setups used to quantify in HRS experiments. Finally, recent results about the first-order hyperpolarizability are described and discussed for organic molecules with distinct molecular structures, as well as the use of the HRS effect as a technique to quantify specific interactions of biological materials.