Abstract
The validity of Kirchhoff’s laws in plasmonic nanocircuitry is investigated by studying a junction of plasmonic two-wire transmission lines. We find that Kirchhoff’s laws are valid for sufficiently small values of a phenomenological parameter κ relating the geometrical parameters of the transmission line with the effective wavelength of the guided mode. Beyond such regime, for large values of the phenomenological parameter, increasing deviations occur and the equivalent impedance description (Kirchhoff’s laws) can only provide rough, but nevertheless useful, guidelines for the design of more complex plasmonic circuitry. As an example we investigate a system composed of a two-wire transmission line and a nanoantenna as the load. By addition of a parallel stub designed according to Kirchhoff’s laws we achieve maximum signal transfer to the nanoantenna.
Highlights
The strong subwavelength light confinement of guided plasmonic modes supported by noble-metal nanowires[1,2,3] is a prerequisite for the realization of optical nanocircuits bridging the size mismatch between nanoelectronics and micrometer-scaled optical devices
At variance with the purely transverse guided modes sustained by perfect conductors, plasmonic modes possess a significant longitudinal component that is not taken into account in the standard impedance description
As the parallel junction is formed by introducing the upward two-wire transmission lines (TWTLs) (u) (Fig. 2b) the intensity transmitted through the junction region into the horizontal output TWTL (t) is significantly reduced, in favor of both mode intensity propagating in the upward direction and mode intensity being reflected due to the impedance mismatch at the junction
Summary
The strong subwavelength light confinement of guided plasmonic modes supported by noble-metal nanowires[1,2,3] is a prerequisite for the realization of optical nanocircuits bridging the size mismatch between nanoelectronics and micrometer-scaled optical devices. At optical frequencies noble metals do not behave as perfect conductors but, due to the small negative real part of their permittivity, as plasmonic materials This holds several implications, for example the non-negligible skin depth compared to the wire cross section, which in turn creates volume currents with no counterparts in RF27. The lumped element model of electronic circuits and Kirchhoff ’s laws can be understood as an approximation of Maxwell’s equations in the low-frequency domain (quasistatic limit), equivalent to assuming the involved wires, when compared to the circuit’s operation wavelength, as quasi one-dimensional in cross section and their junctions as point-like objects. We investigate the validity of the Kirchhoff ’s circuit laws in the optical regime by considering a fundamental, yet simple system, i.e. a junction of two-wire transmission lines (TWTLs) supporting an antisymmetric guided plasmonic mode. By addition of a parallel stub designed according to Kirchhoff ’s laws we realize maximum transfer of signal between circuit elements, a necessary prerequisite for the design of efficient devices, and use this example to further test the validity of the lumped-element impedance approach
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