Quantum mechanics

Magnetic field

Poynting vector

Metallurgy

Materials science

Computational physics

Energy (signal processing)

Atomic physics

Radial polarization

Inverse

Physical chemistry

Polarization (electrochemistry)

Linear polarization

Laser

Physics

Laser beams

Mathematics

Optics

Quantum electrodynamics

Geometry

Energy flux

Laser beam quality

Chemistry

Flux (metallurgy)

Elliptical polarization

Physical review. A/Physical review, A

We report the formation of a negative energy flux in the case of tight focusing of an arbitrary-order radially polarized annular beam. We consider not only the longitudinal component of the Poynting vector (energy flux density) and the region of its negative values, but also the local inverse energy flux as an integral characteristic over the region of negative values. Theoretically, the Richards-Wolf formulas in the Debye approximation are used to maximize the negative value of the energy flux density on the optical axis in the focal region for the second-order radial polarization ($m=2$). In this case, the local inverse energy flux, an integral characteristic in the bulk region of negative values, increases with increasing radial polarization order, i.e., for $m&gt;2$. Jones matrices are employed to show that the result obtained will be valid for azimuthal polarization, as well as for a circularly polarized vortex beam. The results of numerical simulation are in good agreement with theoretical calculations. In addition, taking into account the approximate nature of the Richards-Wolf formulas, we also additionally model the tight focusing of a circular beam based on the solution of Maxwell's equation using the finite element method. It is shown that the local inverse energy flux in the case of the second-order radial polarization will be 1.5 times less than that in the case of the third-order radial polarization. In turn, the use of the fourth-order radial polarization makes it possible to increase the local inverse energy flux by a factor of 2.

Inverse energy flux of focused radially polarized optical beams