We introduce a powerful but simple methodology for numerical modeling of the far field of a hollow searchlight laser beam that is produced by passing a laser beam through a reflaxicon. Such a beam can be used in remote sensing as a space beacon. The far field is described by a Fourier–Bessel transform over an aperture function that includes a conical phase term introduced by the reflaxicon. Computations of the far field of the reflaxicon are difficult. The conventional approach for calculating the far field of such ideal aperture distributions as a plane wave or a Gaussian beam is to find exact solutions in the form of hypergeometric series and determine their asymptotic approximations for large values of some parameter. This approach does not extend to more complicated aperture distributions. We modify the transform by using the asymptotic form for the Bessel function as well as by limiting this form to include only the low-frequency (difference frequency) term. This approach is easily related to a one-dimensional Fourier transform of the aperture distribution, and thus numerical evaluations that make use of this approach can use the fast Fourier transform.
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