Vector Bessel beams: General classification and scattering simulations
Glukhova S.A. and Yurkin M.A. Vector Bessel beams: General classification and scattering simulations, Phys. Rev. A 106, 033508 (2022). (PDF)
I guess, everybody heard about interesting features of the Bessel beams, such as the ability to propagate over a long distance without diffraction. So we had a natural idea to implement these beams in the ADDA code to make corresponding scattering simulations easily accessible. And we did it - you can go and try it, the paper even contains link to sample Python scripts. But this simple task quickly got out of our hands, once we started writing formulae.
A couple of years along this road, we devised arguably the most straightforward classification, which highlights the algebraic relations between all existing beam types and polarizations. These relations cover not only the fields, but also their quadratic combinations such as the time-averaged Poynting vector and the energy density. In particular, this allowed us to describe all beams, for which the latter quantities are circularly symmetric. Surprisingly, one of the types was previously unknown - there is always room for a discovery.
Overall, this paper contains answers to everything you have been afraid to ask, at least, with respect to mathematical details of various vector Bessel beams (some are depicted below). Combined with many figures with beam profiles, it should be a convenient general reference for such beams. With respect to scattering simulations, we also proposed a generalization of Mueller calculus for any vortex beam. The obvious drawback is the length of the manuscript (24 two-column pages with 143 equations), which caused immediate concerns from the editor upon submission. But the reviewer's verdict was more optimistic - each part is potentially useful for some readers.
Finally, I congratulate Stefania Glukhova with her first paper. She has recently obtained M.Sc. degree, but many of the results in this paper already appeared in her B.Sc. thesis. It seems unfortunate that the first paper was so exhausting (not to mention four rounds of proofs to correct all the tiny details in equations), although this became kind of a tradition for my students. However, "what does not kill me makes me stronger", so I am sure that Stefania is now ready to succeed in the PhD studies and future research career.
