Theoretical Foundation for Interface-Specific Hyper-Rayleigh Scattering in Uniaxial Chiral Assemblies

The role of incoherence is considered in polarization-dependent second harmonic generation (SHG) measurements of uniaxially oriented assemblies. SHG microscopy continues to find growing utility for tissue, powders, and materials analysis, all of which exhibit structural heterogeneity over length scales comparable to the optical wavelength. In these cases, the detected SHG signal will generally exhibit partial decoherence, invalidating polarization analyses that implicitly assume purely polarized signal detection. The primary goal of the present study is to develop a mathematical framework for interpreting the incoherent component of the SHG signals produced in such instances. While formulas for describing hyper-Rayleigh scattering (HRS) from isotropic systems are reasonably well established, practical systems encountered experimentally in SHG microscopy measurements are often of lower symmetry. The next lowest symmetry below isotropic, and therefore the next most common samples likely to be encountered experimentally, are uniaxial assemblies, in which one spatial axis is unique from the other two. Such systems include surface assemblies, poled films, stretched polymers, lipid bilayers, most collagenous tendons, and numerous other naturally occurring biological structures. In this work, the general theory for HRS of uniaxially oriented assemblies is developed, including both achiral and chiral uniaxial assemblies. Intriguingly, this analysis predicts the possible observation of large electric dipole-allowed chiral-specific observables within just the incoherent component of the SHG response of chiral assemblies exhibiting with polar, uniaxial ensemble symmetry. The incoherent chiral contributions exhibit distinctly different symmetry than the established chiral sensitivity of coherent SHG in uniaxial assemblies, which is independent of polar order. These predictions provide context for the prior reports of chiral-specific SHG microscopy of tissues and suggest new experimental strategies for performing surface-specific and chiral-specific nonlinear optical analysis of chiral assemblies.