Abstract
The rigorous theory of normal electromagnetic modes of a cylindrical nanowire of finite length is developed. The exact integral equation which determines the solution of Maxwell's equations obeying the boundary conditions at the whole nanowire surface is derived. The nanowire normal (Fabry-P\'erot) modes are defined as nontrivial solutions of the source-free equation. The approach is considered in more detail for elongated nanowires whose length is much larger than their diameter. The resonance condition obtained for a single-mode nanowire resembles the formula for the Fabry-P\'erot resonator if one introduces an effective wavelength-dependent phase shift which can be determined from the calculation of the nanowire response function.
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