Table 1.

Antenna circuit parameters

Gap capacitance		Current induced in antenna
Blunt tips (39)	${\mathit{C}}_{\mathit{gap}}=\frac{{\mathit{\epsilon }}_{\mathit{g}}\mathit{A}}{\mathit{d}}$	Parallel plate current induced by ac dipole (40)	${\mathit{I}}_0\mathrm{=}\frac{\mathit{q}\omega {\mathit{x}}_0}{\mathit{d}}$
Round tips (41)	${\mathit{C}}_{\mathit{gap}}=\frac{\mathrm{\pi }{\mathit{\epsilon }}_{\mathit{g}}\mathit{r}}{2}\left[\mathit{ln}\left(\frac{\mathit{r}}{\mathit{d}}\right)+2\gamma \right]$
Lumped reactance terms		Resistance terms
Faraday (38) inductance	${\mathit{L}}_{\mathit{f}}=\frac{{\mu }_{\mathit{o}}}{{\pi }^2}\mathit{l}\times \ln \left(\frac{\mathit{l}}{\mathit{r}}\right)$	Radiation (38) resistance	${\mathit{R}}_{\mathit{rad}}=\frac{2\pi }{3}{\mathit{Z}}_{\mathit{o}}{\left(\frac{{\mathit{l}}_{\mathit{eff}}}{\lambda }\right)}^2{\mathit{n}}_{\mathit{A}}$
Kinetic (42) inductance	${\mathit{L}}_{\mathit{k}}=\frac{{\mathit{l}}_{\mathit{eff}}}{\mathit{A}}\mathit{Re}\left\{\frac{1}{{\omega }^2{\mathit{\epsilon }}_{\mathit{o}}\left(1-{\mathit{\epsilon }}_{\mathit{m}}\right)}\right\}$	Ohmic (42) resistance	${\mathit{R}}_{\mathit{ohmic}}=\frac{{\mathit{l}}_{\mathit{eff}}}{\mathit{A}}\mathit{Im}\left\{\frac{1}{\omega {\mathit{\epsilon }}_{\mathit{o}}\left(1-{\mathit{\epsilon }}_{\mathit{m}}\right)}\right\}$
Antenna (38) capacitance	${\mathit{C}}_{\mathit{A}}=\frac{{\mathit{\epsilon }}_{\mathit{A}}\mathit{l}}{\ln (\frac{\mathit{l}}{\mathit{r}})}$	Spreading (35, 42) resistance	${\mathit{R}}_{\mathit{spread}}=\frac{1}{\beta \mathit{d}}\mathit{Im}\left\{\frac{1}{\omega {\mathit{\epsilon }}_{\mathit{o}}\left(1-{\mathit{\epsilon }}_{\mathit{m}}\right)}\right\}$

Shown are circuit parameters of wire antennas, where r = wire radius, l = antenna length, l_eff = effective antenna length accounting for current → 0 at ends; for a half-wave antenna l_eff = 0.64l; A = antenna wire cross-sectional area, Z_o ≡ √(μ_o/ε_o), the impedance of free space; x_o = optical ac peak dipole moment length centered in a gap-spacing d; βd is the diameter on the adjacent electrodes over which the dipole currents spread (β = 1.6 for flat electrodes); n_A and ${\mathit{\epsilon }}_{\text{A}}$ are the refractive index and dielectric constant of the medium surrounding the antenna; ε_m = metal relative dielectric constant; and ε_g = dielectric constant in the gap.