Analytical recurrence formula for the zeroth-order metal wire plasmon of terahertz waves

An analytical recurrence formula for the zeroth-order metal wire plasmon of terahertz waves is presented. In the derivation, the property that the relative permittivity of a metal in the spectral region of terahertz wave is huge, the property that the effective index is about 1, some properties of modified Bessel functions, and a suitable Taylor expansion are employed. The recurrence formula is numerically tested for 11 nonmagnetic metals for the whole spectral region of terahertz waves and for the wide radius range from 10 mum to infinity. We find that the relative deviation for the effective index always becomes smaller than 2.1x10(-6) after only four recurrences if a suitable initial input is used. Some related problems, such as the connection to the Newton method and the dependence of the accuracy on frequency, are also discussed.