Effect of absorption on terahertz surface plasmon polaritons propagating along periodically corrugated metal wires

In this paper, a rigorous method for analyzing surface plasmon polaritons (SPPs) on a periodically corrugated metal wire has been formulated, based on a modal expansion of electromagnetic fields. Compared with the previous method, our method takes into account the finite conductivity of the wire as well as higher-order modes within the wire grooves in the expansion, thus is able to accurately calculate the loss of these spoof SPPs propagating along the wire. In the terahertz frequency range, the properties of the loss of spoof SPPs on corrugated Al wires are analyzed. The loss of the spoof SPPs grows significantly with the increase of field confinement, and it is often considerably large when the frequency is close to the asymptotic frequency. The effect of absorption on the energy concentration and superfocusing of terahertz radiation is also analyzed, and found to be tolerably small, except very close to the asymptotic frequency.

Figure 1

(Color online) Convergence of the (a) real and (b) imaginary parts of the propagation constant $\beta$ calculated from Eq. (17) for $d=50\mu \mathrm{m}$, $R=100\mu \mathrm{m}$, and $f=0.8\mathrm{THz}$. The corresponding results obtained within the PEC approximation are included as squares for comparison. The wire geometry is shown in the inset. Solid marks correspond to the groove case of $a=0.2d$ and $h=d$, and open marks correspond to the case of $a=0.6d$ and $h=0.9d$.

Figure 2

(Color online) (a) Attenuation coefficients and (b) dispersion relations of spoof SPPs for various groove cases. The lattice constant $d=50\mu \mathrm{m}$, and $R=100\mu \mathrm{m}$.

Figure 3

(Color online) Spatial variation of the amplitude of the $\mathbf{H}$ field in a unit cell of the wire structure for various frequencies. The wire has the following parameters: $d=50\mu \mathrm{m}$, $a=0.2d$, $h=d$, and $R=100\mu \mathrm{m}$.

Figure 4

(Color online) (a) Attenuation coefficients and (b) dispersion relations of spoof SPPs for different outer radii $R=100$, 200, and $500\mu \mathrm{m}$. The solid lines correspond to the groove case of $a=0.2d$ and $h=d$, and the dot-dashed lines correspond to the case of $a=0.6d$ and $h=0.9d$. The lattice constant is $d=50\mu \mathrm{m}$.

Figure 5

(Color online) (a) Attenuation coefficient of spoof SPPs versus the inner radius $r$. The outer radius $R=100\mu \mathrm{m}$ and $d=50\mu \mathrm{m}$ are fixed. The inset shows the dispersion relations for $r=85$, 60, 50, 40, and $20\mu \mathrm{m}$. [(b) and (c)] Field concentration via adiabatic reduction of $r$ in the Al wire for the frequencies $f=0.6$ and $0.55\mathrm{THz}$.

Figure 6

(Color online) (a) Attenuation coefficient of spoof SPPs versus the outer radius $R$ for three different frequencies $f=0.6$, $2$, and $2.75\mathrm{THz}$. The groove depth $h=5\mu \mathrm{m}$ and $d=50\mu \mathrm{m}$ are fixed. The inset shows the dispersion relation for $R=10\mu \mathrm{m}$, where the three frequencies are indicated. (b) Distribution of the amplitude of the $\mathbf{H}$ field in the radial direction for $R=10\mu \mathrm{m}$ at the frequencies $f=0.6$, 2, and $2.75\mathrm{THz}$. The corresponding results for the smooth Al wire with radius $R=10\mu \mathrm{m}$ are plotted as dot-dashed lines for comparison.