Nonlinear optical processes provide completely new contrast mechanisms for microscopy. The polarization vector of a focused field is three-dimensional (3D) and spatially inhomogeneous, thereby opening up new opportunities for the characterization of complex nano-objects. The 3D control of focal fields further benefits from the use of unconventional states of polarization, e.g., radially (RP) and azimuthally polarized (AP) incident beams. Of particular importance is the fact that focused RP beam gives rise to a strong longitudinal electric-field component at the focus. In contrast, focused AP beam maintains a strictly transverse electric-field distribution in the focal volume, mimicking the structure of the incident beam before focusing. In this Paper, we summarize several new capabilities and additional benefits made possible by vector beams in nonlinear microscopy of various types of nano-objects. As one of the first demonstrations, we have shown that second-harmonic generation microscopy with vector beams has superior sensitivity to the morphology of individual metal nanoparticles. We have also shown that efficient coupling of incident light to metal nano-objects requires tailored focal fields matching the modes of individual particles and even their assemblies (or so-called oligomers). We also used vector beams to characterize the crystal structure of semiconductor nanodisks and to couple light to vertically-aligned semiconductor nanowires. In addition, nanowires have been used to probe the longitudinal fields of advanced polarization states in three dimensions.
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