Energy flow control of focused vector Bessel-Gaussian beams based on polarization-phase mixed modulation

Based on vector diffraction theory, the energy flow control of focused vector Bessel-Gaussian beams with polarization-phase mixed modulation is studied. The energy distribution characteristics of the transverse, longitudinal, and total energy flow fields under different parameters are discussed in detail. The results demonstrate that, at the focal plane, by adjusting the beam parameter β, the proportion of transverse and longitudinal components in the energy flow field can be finely adjusted, and a purely longitudinal energy flow field is obtained. By varying the value of the azimuthal polarization parameter m, the energy flow distribution is freely controlled. Adjusting the radial polarization parameter n allows for the modification of the number and strength of the annular vortices. Modulation of the parameter γ introduces nonlinear wavefront distortion, causing the energy flow distribution in the focal region to evolve from a symmetric structure to an asymmetric vortex structure.