Manipulation and Verification of Longitudinal Electric Fields for Nonlinear Optical Microscopy

Polarization, which is a fundamental property of light, describes the direction of oscillation of the electric component of the optical field. It is often assumed to be transverse to the direction of propagation of the optical wave. This is, for instance, the case for paraxial, i.e., collimated or weakly focused, laser beams. For nonparaxial, i.e., tightly focused, laser beams, however, the polarization of such beams shows a three-dimensional behavior as manifested by the generation of non-vanishing fields directed along the longitudinal direction, within the focal volume. These longitudinal fields have tremendous effects in the context of optical microscopy, and especially nonlinear microscopy because of the tensorial and symmetry dependence of the nonlinear response. So far, techniques able to precisely tailor the longitudinal field components at focus have relied on cumbersome setups and have seen their capabilities hindered by the lack of appropriate probes that can be used to unambiguously and directly detect such longitudinal fields.

This Thesis aims to meet this challenge and to provide new ways to control and probe longitudinal electric fields at the focus of a high numerical aperture objective. Relying on state-of-the-art spatial phase-shaping techniques of an incident optical field, we manage to control various parameters of the longitudinal electric field within the focal volume, including its transverse spatial distribution and depth of field, demonstrated by collection of second-harmonic generation from vertically aligned GaAs nanowires. The results presented in this Thesis suggest that the strength and spatial distribution of longitudinal fields can be generally controlled but also probed using our techniques. This work also opens up new opportunities for better understanding optical responses at the nanoscale and is expected to provide alternative imaging techniques for different types of nanostructures and possibly later for biological samples. Finally, our phase-shaping techniques provide alternative tools towards more advanced control of polarization in three-dimensions at focus.