Evolution of energy flow in the focal field of azimuthally polarized Lorentz–Gauss beams under helico-conical phase modulation

This paper investigates the evolution of energy flow distribution in Lorentz-Gauss beams under helico-conical modulation. Based on the Richards-Wolf vector diffraction theory, we derived the electromagnetic field expressions for azimuthally polarized Lorentz-Gauss beams. The longitudinal and transverse energy flow distributions were obtained via the Poynting vector. Subsequently, helico-conical modulation was applied to systematically examine the influence of various parameters on the energy flow distribution. Through coordinated modulation of multiple parameters, we achieved multi-directional spreading of both longitudinal and transverse energy flow components. Such energy flow distributions may offer potential applications in multi-directional optical information transfer and related fields.