We demonstrate that the local near-field vector and polarization state on planar antenna structures and in nanoscale antenna gaps can be determined by scattering-type near-field optical microscopy (s-SNOM). The near-field vector is reconstructed from the amplitude and phase images of the in-and out-of-plane near-field components obtained by polarization-resolved interferometric detection. Experiments with a mid-infrared inverse bowtie antenna yield a vectorial near-field distribution with unprecedented resolution of about 10 nm and in excellent agreement with numerical simulations. Furthermore, we provide first direct experimental evidence that the nanoscale confined and strongly enhanced fields at the antenna gap are linearly polarized. s-SNOM vector-field mapping paves the way to a full near-field characterization of nanophotonic structures in the broad spectral range between visible and terahertz frequencies, which is essential for future development and quality control of metamaterials, optical sensors, and waveguides.KEYWORDS Vector near-field mapping, near-field polarization state, phase-resolved near-field microscopy, infrared antennas, bowtie aperture, local field enhancement P lasmonic nanostructures and metamaterials enable the engineering of optical fields on the nanometer scale, which is the basis for the development of ultrasensitive molecular spectroscopy, high-resolution microscopy, and nanoscale optical circuits at frequencies ranging from the visible to the microwave spectral regime.1-4 A direct experimental access to the optical near-field distribution is critical for testing the design performance, exploring design alternatives, and verifying novel theoretical concepts. Because of their three-dimensional, complex-valued polarization state (vector field), however, nanoscale confined optical near fields are highly complex and thus are challenging experimental imaging techniques. 5,6 Generally, the local near field at a sample surface is described by a three-dimensional vector E ) (E x , E y , E z ), where each near-field component E j is characterized by both a field amplitude |E j | and a phase j .6,7 While strong field amplitudes at specific sample locations open new avenues for example in vibrational spectroscopy of single molecules, [8][9][10] it is the phase distribution that is essential for nanoscale coherent control applications.11-13 The phase difference δ ij ) j -i between individual components is thereby a fundamental quantity as it determines the polarization state of the vector near field.6 For example, a phase difference of δ ij ) 0°or 180°(for all i,j) defines linearly polarized local fields, while δ ij ) (90°and |E i | ) |E j | yields circularly polarized near fields. Engineering of the individual phases thus can be applied to control 14 the near field polarization state for novel nanophotonic applications in, e.g., quantum optics 15 or solid state physics. 16,17 To this end, it is of utmost importance to develop tools that allow for ultrahigh resolution mapping of indiv...

The connection between parameters that can be measured by means of instrumented indentation with the real mechanical properties has been a matter of discussion for several years. In fact, even hardness is not a readily measurable magnitude since the real contact area depends on both the elastic and plastic properties of the sample. Recently, Dao et al. [ Acta Mater49, 3899 (2001)] proposed a method based on numerical fittings to calculate by a forward-reverse algorithm the elastoplastic properties of a sample from the load-penetration curve obtained with a sharp indenter. This work will show, in contrast, that it is not possible to measure uniquely these mechanical properties of a sample in that way.

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