Polarizability of nanowires at surfaces: exact solution for general geometry.

The polarizability of a nanostructure is an important parameter that determines the optical properties. An exact semi-analytical solution of the electrostatic polarizability of a general geometry consisting of two segments forming a cylinder that can be arbitrarily buried in a substrate is derived using bipolar coordinates, cosine-, and sine-transformations. Based on the presented expressions, we analyze the polarizability of several metal nanowire geometries that are important within plasmonics.

Exact polarizability and plasmon resonances of partly buried nanowires.

The electrostatic polarizability for both vertical and horizontal polarization of two conjoined half-cylinders partly buried in a substrate is derived in an analytical closed-form expression. Using the derived analytical polarizabilities we analyze the localized surface plasmon resonances of three important metal nanowire configurations: (1) a half-cylinder, (2) a half-cylinder on a substrate, and (3) a cylinder partly buried in a substrate. Among other results we show that the substrate plays an important role for spectral location of the plasmon resonances.

Nanoparticle plasmon resonances in the near-static limit.

Localized surface plasmon resonances of metal nanoparticles of arbitrary shape are analyzed in the near-static limit with retardation included to the second order. Starting from the electrostatic approximation, the second-order correction to the resonant dielectric constant is expressed by means of a triple surface integral. For arbitrary nanoparticles with cylindrical symmetry we show how the triple surface integral can be significantly simplified, resulting in a computationally efficient scheme for evaluation of nanoparticle plasmon eigenresonances in the near-static limit.

Scaling for gap plasmon based waveguides.

Using the effective-index approach and an explicit expression for the propagation constant of gap surface plasmon polaritons (G-SPPs) obtained for moderate gap widths, we introduce a normalized waveguide parameter characterizing the mode field confinement and obtain the corresponding expressions for various (gap, trench and V-groove) G-SPP based waveguides. Usage of the obtained relations is investigated with a finite-element method, demonstrating that waveguides with different dimensions and operating at different wavelengths, but having the same normalized parameter, exhibit very similar field confinement. These relations allow one to design G-SPP waveguides for single-mode operation supporting a well-confined fundamental mode.