The connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order. The amplitude variations of generalized Laguerre–Gauss beams, including standard and elegant Laguerre–Gauss beams as special cases, are compared with Bessel–Gauss beams. Bessel–Gauss beams can be well-approximated by elegant Laguerre–Gauss beams. For non-integral values of the Laguerre function radial order, a generalized Laguerre–Gauss beam with integer order matches the width of the central lobe well, even for low radial orders. Previous approximations are found to be inaccurate for large azimuthal mode number (topolgical charge), and an improved approximation for this case is also introduced.
The connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order. The amplitude variations of generalized Laguerre–Gauss beams, including standard and elegant Laguerre–Gauss beams as special cases, are compared with Bessel–Gauss beams. Bessel–Gauss beams can be well-approximated by elegant Laguerre–Gauss beams. For non-integral values of the Laguerre function radial order, a generalized Laguerre–Gauss beam with integer order matches the width of the central lobe well, even for low radial orders. Previous approximations are found to be inaccurate for large azimuthal mode number (topolgical charge), and an improved approximation for this case is also introduced. Read More
