Energy flux for Cauchy-Riemann beams

Abstract We present a detailed derivation of the energy flux for a Cauchy-Riemann beam propagating in free space, which is given by the product of the Gaussian beam and an entire function. In our study, we consider the waist of the Gaussian beam to be a complex number; the imaginary part of the Gaussian beam is equivalent to a collecting lens, which results in a compression-expansion of the intensity distribution. Our results show that during beam propagation, the radial component of the energy flux reverses its direction, leading to a purely azimuthal energy flux in a specific propagation plane z > 0. In addition, we validate our analytical results through experimental verification.