Surface-enhanced Raman spectroscopy: nonlocal limitations

Abstract

Giant field enhancement and field singularities are a natural consequence of the commonly employed local-response framework. We show that a more general nonlocal treatment of the plasmonic response leads to new and possibly fundamental limitations on field enhancement with important consequences for our understanding of SERS. The intrinsic length scale of the electron gas serves to smear out assumed field singularities, leaving the SERS enhancement factor finite even for geometries with infinitely sharp features. For silver nano-groove structures, mimicked by periodic arrays of half-cylinders (up to 120 nm in radius), we find no enhancement factors exceeding ten orders of magnitude (10 10 ).

Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics

“…In nanoplasmonics only the Thomas-Fermi functional was used until now [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] , while to our knowledge the second-order gradient correction has thus far been neglected. Below we will give an example where the calculations of optical properties based on only the Thomas-Fermi functional disagree with experiment, while agreement is found when including the von Weizsäcker functional, in combination with the XC functionals as discussed below.…”

“…In the SC-HDM we fix (rather than fit) the distance parameter at d ¼ 1 Å, which is of the order of the aforementioned distances between the first plane of nuclei and the edge of the jellium background 58 . By contrast, for the HW-HDM we take d to vanish, because the free electrons do not spill into the free space in this case 13 . Figure 3a shows the absorption cross-sections for the Ag nanowire, computed for the same three models as for the Na nanowire in Fig.…”

Robust Subnanometric Plasmon Ruler by Rescaling of the Nonlocal Optical Response

“…A variety of theoretical approaches that incorporate different levels of sophistication have been adopted to address the optical response, but certain lack of unification still persists. In particular, the community of surface physics has elaborated accurate nonlocal treatments to address the surface response of conduction electrons of metal surfaces and small metallic objects [1,[4][5][6][7][8][9], whereas the community of nano-optics has focused on developing practical local and nonlocal treatments where the emphasis is placed on the geometrical aspects of the metal boundaries rather than on the actual response of the electrons [2,3,[10][11][12][13][14][15][16]. This Letter bridges both fields, providing a unified and practical picture of the optical response in coupled metallic nanoparticles located at subnanometric proximity.…”

“…89 eV is the bulk plasma frequency of Na and accounts for the damping, (ii) the nonlocal hydrodynamic model (NLHD) [10,[13][14][15][16] description of the metal permittivity tensor as implemented by Toscano and co-workers in the COMSOL MULTIPHYSICS package [15,28], and (iii) the quantumcorrected model (QCM) [29] allowing us to perform classical calculations that take into account electron tunneling through the junction separating nanowires. The particular application of QCM for a sodium dimer is described in detail in Ref.…”

Hydrodynamic theory for quantum plasmonics: Linear-response dynamics of the inhomogeneous electron gas

“…Comparing with the DFT and TDDFT, the TFHT gains its advantage of numerical efficiency [38][39][40], however, suffers from the blame of the inaccuracy especially for the simple metals due to the neglect of the electron spill-out [28,29]. Combined with advanced numerical techniques, such as the finite-element method [38,39,41] or the Green function surface-integral method [42][43][44][45], the HT can be applied to relatively large and complex plasmonic structures that are beyond practical reach for the DFT and TDDFT.…”