Terahertz Surface Plasmon-Polariton Propagation and Focusing on Periodically Corrugated Metal Wires

In this Letter, we show how the dispersion relation of surface plasmon polaritons (SPPs) propagating along a perfectly conducting wire can be tailored by corrugating its surface with a periodic array of radial grooves. In this way, highly localized SPPs can be sustained in the terahertz region of the electromagnetic spectrum. Importantly, the propagation characteristics of these spoof SPPs can be controlled by the surface geometry, opening the way to important applications such as energy concentration on cylindrical wires and superfocusing using conical structures.

Figure 1

(a) $\omega$ versus $k$ for the corrugated, azimuthally invariant wire geometry shown in the inset for two different cases: $h=R-r=0.4d$ (dashed lines) and $h=d$ (solid lines). For each value of $h$, the dispersion relations calculated for increasing values of $R$ and $r$ ($h$ fixed) are presented. The dotted line shows the band obtained with a FDTD code for $h=d$ and $R=2d$. (b) Dispersion relation of the SPP bands obtained with the FDTD code for azimuthal modes $m=0$, $m=2$, and $m=4$. The insets show the amplitude of the $\mathbf{E}$ field in a quarter cylinder for these three bands at $k=\pi /d$.

Figure 2

(a) Dispersion relations of spoof SPPs for $a=10\mu \mathrm{m}$, $d=50\mu \mathrm{m}$, and $R=100\mu \mathrm{m}$ for five different values of the inner radii $r=85$, 60, 50, 40, and $20\mu \mathrm{m}$. (b)–(d) Spatial variation of the $\mathbf{E}$ field amplitude (logarithmic scale) calculated using the finite integration technique on a wire with $a=10\mu \mathrm{m}$, $d=50\mu \mathrm{m}$, $R=100\mu \mathrm{m}$, and $r=50\mu \mathrm{m}$ for three different frequencies $f=0.6$, 1.0, and 1.2 THz.

Figure 3

Field concentration via adiabatic reduction of $r$. Distribution of the $\mathbf{E}$ field, evaluated at $f=0.6\mathrm{THz}$, along the radial direction at different locations of the wire corresponding to $r=85$, 60, 40, and $20\mu \mathrm{m}$ calculated using the quasianalytical method for an infinite wire (dotted lines) and FIT for the real finite structure (solid lines) on a linear color scale. The inset shows the distribution of the $\mathbf{E}$ field on a logarithmic scale.

Figure 4

Superfocusing on a corrugated cone of length 2 mm, with constant $h=5\mu \mathrm{m}$ and $d=50\mu \mathrm{m}$. $R$ is reduced from $100$ to $10\mu \mathrm{m}$. The plot shows the magnitude of the $\mathbf{E}$ field on a logarithmic scale spanning 2 orders of magnitude.