Nanofocusing of Surface Plasmons at the Apex of Metallic Tips and at the Sharp Metallic Wedges. Importance of Electric Field Singularity

Abstract

Nanofocusing of light is localization of electromagnetic energy in regions with dimensions that are significantly smaller than the wavelength of visible light (of the order of one nanometer). This is one of the central problems of modern near-field optical microscopy that takes the resolution of optical imaging beyond the Raleigh’s diffraction limit for common optical instruments [Zayats (2003), Pohl (1984), Novotny (1994), Bouhelier (2003), Keilmann (1999), Frey (2002), Stockman (2004), Kawata (2001), Naber (2002), Babadjanyan (2000), Nerkararyan (2006), Novotny (1995), Mehtani (2006), Anderson (2006)]. It is also important for the development of new optical sensors and delivery of strongly localized photons to tested molecules and atoms (for local spectroscopic measurements [Mehtani (2006), Anderson (2006), Kneipp (1997), Pettinger (2004), Ichimura (2004), Nie (1997), Hillenbrand (2002)]). Nanofocusing is also one of the major tools for efficient delivery of light energy into subwavelength waveguides, interconnectors, and nanooptical devices [Gramotnev (2005)]. There are two phenomena of exceptional importance which make it possible nanofocusing. The first is the phenomenon of propagation with small attenuation of electromagnetic energy of light along metal-vacuum or metal-dielectric boundaries. This propagation exists in the form of strictly localized electromagnetic wave which rapidly decreases in the directions perpendicular to the boundary. Remembering the quantum character of the surface wave they say about surface plasmons and surface plasmon polaritons (SPPs) as quasi-particles associated with the wave. The dispersion of the surface wave has the following important feature [Economou (1969), Barnes (2006)]: the wavelength tends to zero when the frequency of the SPPs tends to some critical (cut off) frequency above which the SPPs cannot propagate. For SPPs propagating along metal-vacuum plane boundary this critical frequency is equal to 2 p ω (we use Drude model without absorption in metal). For spherical boundary this critical frequency [Bohren, Huffman (1983)] is equal to 3 p ω . So, the SPP critical frequency depends on the form of the boundary. By changing the frequency of SPPs it is possible to decrease the wavelength of the SPPs to the values substantially