Probing of Optical Near-Fields by Electron Rescattering on the 1 nm Scale

Abstract

We present a new method of measuring optical near-fields within ∼1 nm of a metal surface, based on rescattering of photoemitted electrons. With this method, we precisely measure the field enhancement factor for tungsten and gold nanotips as a function of tip radius. The agreement with Maxwell simulations is very good. Further simulations yield a field enhancement map for all materials, which shows that optical near-fields at nanotips are governed by a geometric effect under most conditions, while plasmon resonances play only a minor role. Last, we consider the implications of our results on quantum mechanical effects near the surface of nanostructures and discuss features of quantum plasmonics.The excitation of enhanced optical near-fields at nanostructures allows the localization of electromagnetic energy on the nanoscale [1,2]. At nanotips, this effect has enabled a variety of applications, most prominent amongst them are scanning near-field optical microscopy (SNOM) [3][4][5][6][7], which has reached a resolving power of 8 nm [8], and tip-enhanced Raman spectroscopy (TERS) [3,9]. Because of the intrinsic nanometric length scale, measuring and simulating the tips' near-field has proven hard and led to considerably diverging results (see Refs. [1,7] for overviews). Here we demonstrate a nanometric field sensor based on electron rescattering, a phenomenon well known from attosecond science [10]. It allows measurement of optical near-fields, integrating over only 1 nm right at the structure surface, close to the length scale where quantum mechanical effects become relevant [11][12][13][14][15]. Hence, this method measures near-fields on a scale that is currently inaccessible to other techniques (such as SNOM or plasmonic methods in electron microscopy [16][17][18]), and reaches down to the minimum length scale where one can meaningfully speak about a classical field enhancement factor. In the future, the method will allow tomographic reconstruction of the optical near-field and potentially the sensing of fields in more complex geometries such as bow-tie or split-ring antennas.In general, three effects contribute to the enhancement of optical electric fields at structures that are smaller than the driving wavelength [7,[20][21][22]. The first effect is geometric in nature, similar to the electrostatic lightning rod effect: the discontinuity of the electric field at the material boundary and the corresponding accumulation of surface charges lead to an enhanced near-field at any sharp protrusion or edge. This effect causes singularities in the electric field at ideal edges of perfect conductors. For real materials at optical frequencies, the electric field is not as strongly enhanced and remains finite [23]. The second effect occurs at structures whose size is an odd multiple of half the driving wavelength: optical antenna resonances can be observed there. The third effect concerns only plasmonic materials like gold and silver, where an enhanced electric field can arise due to a localized surface plasmon resonance. ...

Attosecond-controlled photoemission from metal nanowire tips in the few-electron regime

“…Furthermore, there is a spread of CEP phases, which increases from 0.2 π at a rotation angle of 0 • to 0.6 π at an angle of 80 • . This means that compared to strong-field photoemission experiments in gases and also from edged nanotips, 11,34,35 the strong-field emitted electrons will experience a considerable range of different local field strengths as well as CEPs. We also checked different radii of the transition of the individual facets of 5 and 15 nm for parallel (perpendicular) orientation, which resulted in maximum field enhancements of ∼8.5 (∼5) and ∼14 (∼8.5), respectively.…”

“…11,34 In inhomogeneous fields at nanostructures, electrons might experience the decay of the near-field during their sub-cycle propagation, [43][44][45] which leads to the suppression of rescattering and a decrease of the cutoff energy compared to Eq. (2).…”

“…9,10 Strong external fields may even induce a nonlinear behavior and transitions in electronic properties of nanomaterials on ultrafast time scales. [11][12][13][14][15] The many applications arising within the field of nanophotonics motivate a more detailed understanding of collective electron dynamics. While spectroscopic methods give only limited information about dynamical processes, time-resolved measurements performed on the time scale of the fastest dynamics are extremely powerful in order to gain much deeper insight into the underlying fundamental processes and have the potential to disentangle the complex multi-electron physics.…”

From Attosecond Control of Electrons at Nano‐Objects to Laser‐Driven Electron Accelerators

“…Because the semi-classical excursion length of the field-sensing electron is <1 nm, this method allows measuring the optical near-field on extremely small, (sub-) nanometer length scales [32,41], see Figure 6.6a. With an angle-resolved spectrometer, the fields can even be reconstructed in a vectorial fashion [24], as discussed in detail in Chapter 9.…”

An Ultrafast Switch for Electron Emission

“…Typical peak near-field intensities at the tip's apex are on the order of I ω ¼ 3 × 10 11 W=cm 2 for the fundamental and I 2ω ¼ 7 × 10 9 W=cm 2 for the second harmonic, including field enhancement [39,40] (see SM for details [31]). The near fields of both colors result in electron emission in the multiphoton regime with minimum Keldysh parameters, γ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi W 0 =2U p p of γ ω;min ¼ 2.7 and γ 2ω;min ¼ 47, where U p is the ponderomotive energy.…”