Three-wave mixing in chiral liquids

TLDR: A single-center chiral model of the three-wave mixing (sum-frequency generation) nonlinearity and its magnitude is developed, showing that the second-order susceptibility in chiral liquids is much smaller than previously thought.

Abstract: Second-order nonlinear optical frequency conversion in isotropic systems is only dipole allowed for sum- and difference-frequency generation in chiral media We develop a single-center chiral model of the three-wave mixing (sum-frequency generation) nonlinearity and estimate its magnitude We also report results from ab initio calculations and from three- and four-wave mixing experiments in support of the theoretical estimates We show that the second-order susceptibility in chiral liquids is much smaller than previously thought Coherent three-wave mixing in second-order nonlinear optical processes is, in the electric dipole approximation, only symmetry allowed in noncentrosymmetric media, such as crystals, poled polymers, and interfaces However, the intrinsic symmetry breaking due to molecular chirality allows sum- and difference-frequency generation even for isotropic systems, such as liquids, gases, and optically isotropic polycrystalline materials [1,2] Apart from their importance in chemistry and biology, chiral liquids offer attractions as nonlinear optical media, as they are self-healing, lend themselves to “wet” synthetic methods, and do not require the growth of crystals A high second-order nonlinearity due to chirality was reported over thirty years ago for sum-frequency generation (SFG) from chiral sugar solutions where the sumfrequency susceptibility was found to be comparable to that of low refractive index piezoelectric crystals, such as quartz (17% of d SiO 2 111 ) [3,4] In this Letter we present a model of the second-order nonlinear optical properties of simple chiral liquids The estimates from the model, and the results from high-level ab initio computations, suggest that three-wave mixing in chiral liquids is much smaller than previously thought [1,3–5] We report three- and four-wave mixing experiments in chiral liquids, providing a limit on the magnitude of the sum-frequency nonlinearity in support of our theoretical estimates First we consider the theoretical basis for three-wave mixing in chiral liquids The observables for natural optical rotation and for electric-dipolar sum-frequency generation in a chiral liquid are both time-even pseudoscalars; however, the two phenomena are distinct The rotational strength R which determines optical rotation and circular dichroism (CD) near a transition k √ g is defined by R Imgj ˆ mjk ? kj ˆ mjg and requires a magnetic-dipole transition moment kj ˆ mjg, whereas the sum-frequency generator is purely electric dipolar It follows that the three-wave mixing susceptibility is a polar tensor of rank three Its isotropic component is completely antisymmetric