Near field and far field of elegant Hermite-Gaussian and Laguerre-Gaussian modes

An alternative set of eigensolutions of the paraxial wave equation to that of the ordinary Hermite-Gaussian modes is that of the so-called ‘elegant’ Hermite-Gaussian modes. The analogous elegant Laguerre-Gaussian modes are derived. The near- and far-field behaviours of the elegant Hermite-Gaussian and Laguerre-Gaussian modes are investigated. The similarity between the elegant Laguerre-Gaussian beams and the Bessel-Gaussian beams is discussed.