Analytical theory of real-argument Laguerre-Gaussian beams beyond the paraxial approximation

We study the propagation of real-argument Laguerre-Gaussian beams beyond the paraxial approximation using the perturbation corrections to the complex-argument Laguerre-Gaussian beams derived earlier by Takenaka et al. [J. Opt. Soc. Am. A2, 826 (1985)JOAOD60740-323210.1364/JOSAA.2.000826]. Each higher-order correction to the amplitude of the real-argument beam (l, m) is represented as a superposition of the same-order corrections to the amplitudes of the complex-argument beams (l, q) with q=0,1,2,…,m. We derive explicit expressions for the electric and magnetic fields of transversely and longitudinally polarized real-argument beams and calculate the chirality densities of these beams up to the fourth order of the smallness parameter. For the first time to the best of our knowledge, we show that essentially achiral Gaussian beams (corresponding to l=m=0) possess nonzero chirality density due to the wavefront curvature. The obtained corrections to the paraxial beams may prove useful for precise laser beam shaping and in studies of optomechanical forces.