Liaw J.-WMao S.-YLuo J.-YKu Y.-CKuo M.-K.MAO-KUEN KUO2021-08-052021-08-05202110944087https://www.scopus.com/inward/record.uri?eid=2-s2.0-85107288396&doi=10.1364%2fOE.425958&partnerID=40&md5=0a458187719e8aced0ac4a0a19e049cbhttps://scholars.lib.ntu.edu.tw/handle/123456789/577074The surface plasmon polaritons (SPPs) of higher-order mode propagating along a plasmonic nanowire (NW) or an elongated nanorod (NR) are studied theoretically. The dispersion relations of SPPs in NWs of different radii, obtained from a transcendental equation, show that the propagation lengths of SPPs of mode 1 and 2 at a specific frequency are longer than that of mode 0. For the higher-order mode, the spatial phase of the longitudinal component of electric field at a cross section of a NW exhibits the topological singularity, which indicates the optical vortex. Of importance, the streamlines of Poynting vector of these SPPs exhibit a helical winding along NW, and the azimuthal component of orbital momentum density exists in the nearfield of NW to produce a longitudinal orbital angular momentum (OAM). Two types of standing wave of counter-propagating SPPs of mode 1 and 2 are also studied; they perform as a string of beads or twisted donut depending on whether the handedness of two opposite-direction propagating SPPs is same or opposite. In addition, a SPP of mode 1 propagating along an elongated NR can be generated by means of an end-fire excitation of crossed electric bi-dipole with 90° phase difference. If the criterion of a resonator for a mode-1 standing wave (string of beads) is met, the configuration of a plasmonic NR associated with a pair of bi-dipoles with a phase delay (0° or 180°) at the two ends can be applied as a high-efficiency nanoantenna of transmission. Our results may pave a way to the further study of SPPs of higher-order mode carrying OAM along plasmonic waveguides. ? 2021 Optical Society of America.Elastic waves; Electric excitation; Electric fields; Electric windings; Electromagnetic wave polarization; Electromagnetic waves; Nanorods; Nanowires; Phonons; Photons; Surface plasmons; Azimuthal components; Dispersion relations; Longitudinal components; Orbital angular momentum; Plasmonic waveguides; Specific frequencies; Surface plasmon polaritons; Transcendental equations; Surface plasmon resonance[SDGs]SDG3journal article10.1364/OE.4259582-s2.0-85107288396