Modeling of Infrared-Visible Sum Frequency Generation Microscopy Images of a Giant Liposome

The article explores the theory of infrared-visible sum frequency generation microscopy of phospholipid envelopes with dimensions larger than the wavelength of the nonlinear emission. The main part of the study concerns derivation and accounting for the contributions of effective nonlinear responses specific to sites on the surfaces of a bilayer envelope and their dependence on polarization condition and experimental geometry. The nonlinear responses of sites are mapped onto the image plane according to their emission directions and the numerical aperture of a sampling microscope objective. According to the simulation results, we discuss possible approaches to characterize the shape of the envelope, to extract molecular hyperpolarizabilities, and to anticipate possible heterogeneity in envelope composition and anisotropy of the environment proximal to the envelope. The modeling approach offers a promising analytic facility to assist connecting microscopy observations in engineered liposomes, cellular envelopes, and subcellular organelles of relatively large dimensions to molecular properties, and hence to chemistry and structure down to available spatial resolution.