Dispersion of Surface Plasmon Polaritons on Metal Wires in the Terahertz Frequency Range

We report the experimental and theoretical study of the dispersive behavior of surface plasmon polaritons (SPPs) on cylindrical metal surfaces in the terahertz frequency range. Time-domain measurements of terahertz SPPs propagating on metal wires reveal a unique structure that is inconsistent with a simple extrapolation of the high frequency portion of the dispersion diagram for SPPs on a planar metal surface, and also distinct from that of SPPs on metal nanowires observed at visible and near-infrared frequencies. The results are consistent with a numerical solution of Maxwell’s equations, showing that the dispersive behavior of SPPs on a cylindrical metal surface at terahertz frequencies is quite different from that of SPPs on a flat surface. These findings indicate the increasing importance of skin effects for SPPs in the terahertz range, as well as the enhancement of such effects on curved surfaces.

Figure 1

(a) Time-domain waveforms of THz SPP pulses after propagating 20 cm on aluminum wires with diameters of $2388\mu \mathrm{m}$, $813\mu \mathrm{m}$, $51\mu \mathrm{m}$, and $18\mu \mathrm{m}$ (from top to bottom). The inset shows the time delay of the peak of the detected THz waveforms relative to that of waveform measured on the largest wire, for both aluminum and stainless steel wires.

Figure 2

The dots (●), triangles (△), and crosses (×) show the experimentally determined phase velocity of SPP’s propagating on Al wires of diameters $813\mu \mathrm{m}$, $51\mu \mathrm{m}$, and $18\mu \mathrm{m}$, respectively (with the $2388\mu \mathrm{m}$ wire used as a reference). The calculated phase velocities of these three wires (also referenced to the largest wire) are shown by the thick solid line, the thin solid line, and the dashed line, respectively. The weak oscillatory features in the data are not reproducible, and are due to noise in the measurements. The amplitude of these features is a rough indication of the error bars for these data points, as defined by the variation between successive measurements taken under identical conditions. The inset shows the calculated phase velocities over a broader spectral range, for four wire diameters as indicated. The turnover and rapid decrease of $v_p$ at low frequencies is a unique feature of the curved surface; SPPs propagating on a flat surface do not exhibit this feature. As expected from the discussion given in the text, the turnover point moves to increasing frequency as the wire diameter decreases.

Figure 3

Calculated dispersion relations for SPPs on a planar Al surface and on an Al wire of $25\mu \mathrm{m}$ diameter, together with the plane wave dispersion relation in air. ${\omega }_{\mathrm{sp}}$ is the theoretical value of the surface plasmon frequency [35]. The inset shows a zoomed-in view of the low-frequency portion of the dispersion diagram. In this inset, we plot $\omega$ against $k-k_0$, where $k_0$ denotes the propagation constant of plane waves in air.