  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. Our analytical results enable an
easy, fast, and exact analysis of many complicated plasmonic nanowire
configurations including nanowires on substrates. This is important both for
comparison with experimental data, for applications, and as benchmarks for
numerical methods.
