Accurate hybrid asymptotic modeling of higher-order Bessel beams with radial phase-gradient reversal

Abstract Accurate theoretical modeling is essential for advancing applications of Bessel beams, yet describing their fine phase structure and local phase-gradient characteristics remains analytically and computationally challenging. Traditional methods, such as the stationary phase method (SPM), capture the overall intensity distribution but fail to resolve high-frequency phase oscillations at large radial distances. By contrast, the standard Debye asymptotic method improves the outer-field description through a two-saddle-point approximation, but its accuracy deteriorates near the axis, where its asymptotic assumption is invalid. Here, we propose a three-zone hybrid-Debye framework that connects the near-axis small-argument approximation with the outerfield Debye asymptotic solution. Relative to the conventional SPM, the proposed model reduces the reported radial relative error by one to two orders of magnitude over the tested propagation range. Analysis of the exact field further reveals alternating signs in the reduced radial phase-gradient quantity pᵣ, whereas the normalized total radial flux Sᵣ remains positive. The hybrid model accurately reproduces the radial intensity-ring structure associated with the underlying two-saddle-point interference. This approach provides an accurate and computationally tractable semi-analytical tool for studying higher-order Bessel-beam propagation.