Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines

Abstract

Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines AbstractHere we discuss the theory and analyze in detail the guidance properties of linear arrays of metamaterial/ plasmonic small particles as nanoscale optical nanotransmission lines, including the effect of material loss. Under the assumption of dipolar approximation for each particle, which is shown to be accurate in the geometry of interest here, we develop closed-form analytical expressions for the eigenmodal dispersion in such arrays. With the material loss included, the conditions for minimal absorption and maximum bandwidth are derived analytically by studying the properties of such dispersion relations. Numerical examples with realistic materials, including their ohmic absorption and frequency dispersion, are presented. The analytical properties discussed here also provide some further physical insights into the mechanisms underlying the subdiffraction guidance in such arrays and their fundamental physical limits. The possibility of guiding beams with subwavelength lateral confinement and reasonably low decay is discussed, offering the possible use of this technique at microwave, infrared, and optical frequencies. Interpretation of these results in terms of nanocircuit concepts is presented, and possible extension to two-and three-dimensional nanotransmission line optical metamaterials is also foreseen. Here we discuss the theory and analyze in detail the guidance properties of linear arrays of metamaterial/ plasmonic small particles as nanoscale optical nanotransmission lines, including the effect of material loss. Under the assumption of dipolar approximation for each particle, which is shown to be accurate in the geometry of interest here, we develop closed-form analytical expressions for the eigenmodal dispersion in such arrays. With the material loss included, the conditions for minimal absorption and maximum bandwidth are derived analytically by studying the properties of such dispersion relations. Numerical examples with realistic materials, including their ohmic absorption and frequency dispersion, are presented. The analytical properties discussed here also provide some further physical insights into the mechanisms underlying the subdiffraction guidance in such arrays and their fundamental physical limits. The possibility of guiding beams with subwavelength lateral confinement and reasonably low decay is discussed, offering the possible use of this technique at microwave, infrared, and optical frequencies. Interpretation of these results in terms of nanocircuit concepts is presented, and possible extension to two-and three-dimensional nanotransmission line optical metamaterials is also foreseen.

Parallel-chain optical transmission line for a low-loss ultraconfined light beam

“…The curves are obtained using full-wave analysis, consistent with the solutions in Refs. [4][5][6][7][8][9][10][11][12][13][14][15][16], which for the case of linear chains take into account all the dynamic coupling among the infinite number of particles in the array. Figure 1 reports the propagation length ͑defined as the length after which the guided field is e −1 of the original value͒ and Re͓␤͔ / k 0 for these two geometries, as depicted in the inset.…”

“…3,4,16 Consider, for instance, the geometries in the inset of Fig. 1͑a͒, i.e., a chain of silver nanoparticles and a cylindrical waveguide made of silver, both of radius a = 10 nm, embedded in a glass substrate.…”

“…The coupling between two such identical chains of nanoparticles may be analyzed by considering both longitudinal and transverse ͑dominant in this regime of interest here͒ coupling induced between the two chains. For a single isolated chain, 16 for e i␤x propagation, the corresponding guided wave number ␤ satisfies the following closed-form adimensional dispersion relations:…”

“…Specifically, as described in Ref. 16, at sufficient distance from the dipoles, each chain may be described as an averaged current line with amplitude −i pe i␤z / d, with p being the eigenvector corresponding to the solution of Eq. ͑1͒.…”

“…1,2 If one wants to squeeze the beam so that its total transverse cross-section is subwavelength, plasmonic waveguides may be realized in the form of cylindrical waveguides ͑nanorods͒ 3,4 or linear chains of closely spaced nanoparticles. [5][6][7][8][9][10][11][12][13][14][15][16][17] Due to their design flexibility, the propagation properties of linear chains may be tailored at will, effectively realizing laterally confined optical connectors. Experimental realization of such devices in the nanoscale, however, has shown severe losses, mainly caused by material absorption and disorder.…”