We present a method for the calculation of the local electric field at the surface of a nanoscopic emitting structure. The method is here applied to carbon nanotubes (NT) where symmetry makes the application of the method easier. The NT is simulated as a cylindrical array of touching spheres, each sphere representing an atom of the tube. The electrostatic potential is written as a linear combination of the potentials produced by each of the spheres. We calculate the local electric field and the corresponding enhancement factor γ for both open and closed nanotubes. For a closed NT we find for γ a simple polynomial expression in terms of the ratio of the height h of the tube to its radius R, which for h/R<40 reduces to a frequently quoted formula of γ. For an open single-wall NT we find that γ is three times greater than that of a single-wall NT of the same h/R. As the thickness of the wall increases this difference diminishes. From these results one may deduce a possible explanation as to why in some experiments a closed NT emits more current than a corresponding open one while in other experiments the opposite holds true.

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Abstract. Power series expansions for the even and odd angular Mathieu functions Sem(h, cos θ) and Som(h, cos θ), with small argument h, are derived for general integer values of m. The expansion coefficients that we evaluate are also useful for the calculation of the corresponding radial functions of any kind.

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