Focusing of Radially Polarized Electromagnetic Waves by a Parabolic Mirror

Abstract

It is well-known that a strong longitudinal electric field and a small spot size are observed when radially polarized beams are tightly focused using a high numerical aperture parabolic mirror. The longitudinal electric field component can accelerate electrons along the propagation axis at high intensities in the focal region, which opens an application in particle acceleration. In this paper, we present a rigorous derivation of the electric field obtained when a radially polarized, monochromatic, flat-top beam is focused by a parabolic mirror. The formulae were deduced from the Stratton–Chu integral known from vector diffraction theory. We examined the influence of the focusing parameters on the distribution of both the longitudinal and radial electric field components. In the small numerical aperture and short wavelength regimes, excellent agreement was found with the results obtained from the Rayleigh–Sommerfeld formula. The calculation method can be adapted for various beam types and for electromagnetic pulses as well.