Surface plasmon polaritons of higher-order mode and standing waves in metallic nanowires

Abstract

The 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.

Conversion of a Helical Surface Plasmon Polariton into a Spiral Surface Plasmon Polariton at the Outlet of a Metallic Nanohole

“…Here, ε 2r is the relative permittivity of metal. Using eqs and satisfying E 1 z ( a , θ, z ) = E 2 z ( a , θ, z ) and the other components of EM field matching the boundary conditions at the wall of nanohole, we can obtain a transcendental equation where β m is a complex wavenumber of the mode- m SPP. , We can calculate the dispersion relation of mode- m SPP in a nanohole by solving eq numerically to find the complex root of β m . In particular, the behavior of the mode-1 SPP will be concerned due to its long propagation length in the following.…”

“…The OAM carried by the transmission light will be identified by the phase singularity. 19 − 21 , 33 Moreover, the interferences of two spiral SPPs from a pair of nanoholes and multi-spiral SPPs from a 2D array of nanoholes will be studied.…”

“…We propose that the major cause is due to the conversion of a helical SPP of mode 1 creeping from the outlet of a nanohole into a Hankel-type SPP of order 1 at the film’s surface. First, we theoretically characterize the SPPs of various modes propagating along an infinitely long metallic nanohole by solving a transcendental equation. − Comparing these modes, we think that a helical SPP of mode 1 is the dominant mode propagating along a metallic nanohole based on a consideration of the propagation length. Alternatively, we use a finite element method (FEM) to numerically investigate how a helical SPP converts into a spiral SPP at the outlet of a nanohole in a thick metal film; a schematic is plotted in Figure .…”

“…In addition, the radiation of the energy flux of a helical SPP from the outlet of nanohole will be studied. The OAM carried by the transmission light will be identified by the phase singularity. − , Moreover, the interferences of two spiral SPPs from a pair of nanoholes and multi-spiral SPPs from a 2D array of nanoholes will be studied.…”

Sodium-Based Cylindrical Plasmonic Waveguides in the Near-Infrared

“…Surface plasmons (SPs) [1] have been considered as prospective candidates for the integration and miniaturization of photonic components and circuits, owing to their remarkable capabilities of squeezing light into regions far smaller than the diffraction limit [2,3]. Various noble metal-based designs have been suggested and investigated to support wellconfined SP modes, including nanowires [4][5][6][7][8], slot waveguide [9][10][11], dielectric-loaded waveguide [12], long-range waveguide [13], and wedge waveguide [14], to mention a few. Due to the presence of metal (usually gold and silver), SP waveguides inevitably suffer from high propagation loss, and there exist trade-offs between losses and confinements for plasmonic waveguides stated above.…”