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Nonlinear optical microscopy is a biocompatible avenue for probing ordered molecular assemblies in biological tissues. As in linear optics, the nonlinear optical response from ordered systems is polarization-sensitive. This dependence can be used to identify and characterize local molecular ordering with micrometer-scale 3D resolution in a nonlinear microscope. In particular, third-harmonic generation (THG) microscopy is a nonlinear optical modality sensitive to the electronic nonlinear susceptibility χ(3) of a material. THG microscopy can be used to map χ(3) spatial variations (i.e. material interfaces), and to probe birefringence. In principle, polarization-resolved THG (P-THG) can therefore be used to probe ordered molecular arrays. However, the orientation, distribution, and nonlinear optical properties of the molecules near the beam focus all affect the detected signal. It is therefore necessary to develop a theoretical method which decouples these effects and permits the extraction of orientational information from P-THG images. In this report, we first present P-THG images of model systems (lipid droplets, multilamellar lipid vesicles) and biological tissues (human skin biopsy) which establish that P-THG is sensitive to lipid ordering and that it is maximized when excitation polarization is parallel to the ordered lipid molecules, giving impetus for the development of a thorough theoretical analysis. We then outline a multiscale model spanning the molecular (nm) and ensemble (μm) scales predicting the PTHG signal, consisting of three main steps: (i) calculation of the molecular electronic hyperpolarizability; (ii) determination of the anisotropic χ(3) for various molecular distribution parameters; and (iii) numerical calculations of the P-THG signal from lipid-water interfaces. This analysis links the measured P-THG response to lipid molecular structure and ordering.
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