Nonlocal response in plasmonic waveguiding with extreme light confinement

Abstract

We present a novel wave equation for linearized plasmonic response, obtained by combining the coupled real-space differential equations for the electric field and current density. Nonlocal dynamics are fully accounted for, and the formulation is very well suited for numerical implementation, allowing us to study waveguides with subnanometer cross-sections exhibiting extreme light confinement. We show that groove and wedge waveguides have a fundamental lower limit in their mode confinement, only captured by the nonlocal theory. The limitation translates into an upper limit for the corresponding Purcell factors, and thus has important implications for quantum plasmonics.

A generalized non-local optical response theory for plasmonic nanostructures

“…1c). Also, convection tends to spread the charge density and within the common hydrodynamic Drude model, convection maps directly to the form of equation (2), that is, with a Laplacian correction to the local response Drude part 24 . In the following, we treat both dynamical effects on an equal footing by considering both propagating longitudinal pressure waves (in a hydrodynamic model) and diffusion (in convection-diffusion model).…”

“…Turning to the Maxwell wave equation, the above non-local =(= Á J) corrections to Ohm's law can be rewritten as a Laplacian correction to the Drude dielectric function 24,31 , as anticipated in equation (2). The convection and diffusion components of the current are of the same mathematical form and subject to the same boundary conditions.…”

“…Consequently, boundary conditions remain unchanged in the presence of diffusion (n Á J ¼ 0 on the metal surfaces so that no electrons escape the metal volumes). Thus, existing numerical schemes and methods [22][23][24][25][26] can readily be exploited to implement the GNOR approach for various plasmonic configurations. The diffusion constant is generally interlinked with other transport parameters such as the scattering time, that is,…”

“…Quite surprisingly, while the literature is rich on discussions of the former effect within hydrodynamic models, the importance of the latter in nanoplasmonic systems remains unexplored, and, according to our knowledge, there is no unifying real-space description applicable to realistic plasmonic nanostructures. Pioneering works focused on pressure-driven convective flow of charge in ideal geometries [16][17][18][19] , while the exploration of non-local response in arbitrarily shaped metal nanostructures has only recently been initiated 20 , emphasizing real-space rigorous formulations of semiclassical hydrodynamic equations 21 and different solution strategies [22][23][24][25][26] . Thus, large blueshifts in nanoscale noble metal plasmonic structures 11,27,28 have been interpreted in the context of the quantum pressurerelated non-local response 27,28 , while quantum confinement 11 and surface-screening 29 explanations have also been proposed.…”

Visualizing hybridized quantum plasmons in coupled nanowires: From classical to tunneling regime

“…This deviation from the classical result is also observed in semiclassical hydrodynamic models for waveguiding on nanowires. 39 However, S 1 and S 2 , are seen to be redshifted with respect to the classical value in the limit q → 0, and for S 1 the redshift increases further with decreasing R. A redshift is expected for decreasing size of simple metal nanostructures due to electron spill-out; as the surface to bulk ratio increases, the spill-out will lead to a decrease in the mean electron density, which results in a lower plasmon frequency. This redshift was also observed for the plasmon eigenmodes of thin slabs of sodium, 31 and for quantum calculation on small Na clusters.…”