Theory of hyperbolic stratified nanostructures for surface-enhanced Raman scattering

Abstract

We theoretically investigate the enhancement of surface enhanced Raman spectroscopy (SERS) using hyperbolic stratified nanostructures and compare to metal nanoresonators. The photon Green function of each nanostructure within its environment is first obtained from a semi-analytical modal theory, which is used in a quantum optics formalism of the molecule-nanostructure interaction to model the SERS spectrum. An intuitive methodology is presented for calculating the single molecule enhancement factor (SMEF), which is also able to predict known experimental SERS enhancement factors of an example gold nano-dimer. We elucidate the important figures-of-merit of the enhancement and explore these for different designs. We find that the use of hyperbolic stratified materials can enhance the photonic local density of states (LDOS) by close to 2 times in comparison to pure metal nanostructures, when both designed to work at the same operating wavelengths. However, the increased LDOS is accompanied by higher electric field concentration within the lossy hyperbolic material, which leads to increased quenching that serves to reduce the overall detected SERS enhancement in the far field. For nanoresonators with resonant localized surface plasmon wavelengths in the near-infrared, the SMEF for the hyperbolic stratified nanostructure is approximately an order of magnitude lower than the pure metal counterpart. Conversely, we show that by detecting the Raman signal using a near-field probe, hyperbolic materials can provide an improvement in SERS enhancement compared to using pure metal nanostructures when the probe is sufficiently close (<50 nm) to the Raman active molecule at the plasmonic hotspot.

Nanoscale plasmonic slot waveguides for enhanced Raman spectroscopy

“…For Raman spectroscopy of a bulk-like sample (with an ensemble of molecules), an alternative spatially averaged Raman enhancement factor (AEF) is defined to also capture the effects of increased light-matter interaction volume using an ensemble of molecules, which allows us to compute the volume enhancement factor (VEF) for a specific device length, and compare it to a reference Gaussian beam. Below, we adapt a recently developed quantum optics approach to model the Raman spectrum of a molecule within a general medium, which was previously applied to describe SERS using plasmonic nanoresonators 27,28 . Here, we extend this approach to WGs, by utilizing the photon Green function, conveniently computed using a semi-analytical normal mode theory 25,26 .…”

“…The detection area A D and the integration geometry for Eq. ( 2) are dependent on whether the Raman scattered power of a molecule in the vicinity of a WG (P SM ) or in free space (P SM 0 ) is being calculated; further details are given in Appendix D. Using a quantum optomechanical theory of SERS and its detection 27,28 , the Raman spectrum is expressed in terms of the E-field operator Ê by S(r D , r m , ω) = Ê † (r D , r m ; ω) • Ê(r D , r m ; ω) and can be calculated as…”

“…Such enhancement benefits a number of applications including nonlinear optics 46 , chemical sensing 47,48 , high-resolution imaging 49 , energy harvesting 50,51 , and single photon sources 52 . For many of these applications, such as single photon sources 39 and SERS 28 , the efficiency of the total emission into radiative channels (also sometimes termed the single-photon β-factor) is also very important.…”

“…Moreover, the slot WG structure can be precisely controlled during fabrication, which means the guided plasmonic mode can be excited repeatably. To model these complex geometries and interactions, we combine a first-principles electromagnetics and quantum optics approach, starting with the E-field Green function of the WG in terms of normal modes 25,26 , and then generalizing a recently developed quantum optomechanical theory to obtain the Raman enhancement 27,28 . This serves to rigorously determine the advantages and application niche of our proposed plasmonic slot WGs in comparison to previous techniques for Raman enhancement, and allows one to quickly assess the important figures-of-merit in a semi-analytical and intuitive way.…”

Model of a Dipole With Atomic Structure

“…В модели Герца нет реальных внутридипольных векторов E, H и S [1], что не позволяет рассмотреть физические механизмы формирования реактивных и активных потоков энергии, соответственно ближнего и дальнего полей. В последнее время все больше и больше исследований: как теоретических [5,6], так и экспериментальных [7,8], показывают принципиальное отличие физических процессов, происходящих в ближнем и дальнем полях. В диполе Герца нет понятия межзарядовой силы F, а следовательно и механизма установления равновесия амплитуды колебаний l 0 дипольных зарядов под действием внешнего индуцирующего поля Е 0 .…”