List of problems for future research in generalized Lorenz–Mie theories and related topics, review and prospectus [Invited]

Abstract

The expression "generalized Lorenz-Mie theories" generically denotes a class of light-scattering theories describing the interaction between an illuminating electromagnetic arbitrary-shaped beam and a particle possessing a high degree of symmetry. This allows one to use the method of separation of variables in which the illuminating beam is expressed as an expansion over a set of basis functions. Such theories have been derived and applied over the past 35 years. Although, as a whole, these theories are now well developed, there remains a list of problems to be solved, some of which are described in this paper.

On the electromagnetic scattering of arbitrary shaped beams by arbitrary shaped particles: A review

“…using two basic spectral components S E x (k x , k y ) and S E y (k x , k y ) as in Eq.13. It is very important to note that, although the original description of the Gaussian beam does not satisfy Maxwell's equations, the plane wave spectrum representation does satisfy them, as the result of a remodelling process involved in this representation [9], [17]. Each plane wave in the spectrum is processed using an iterative method developed by Shifrin and applied by Acquista.…”

“…The electric and magnetic fields of the incident field are then obtained from the vector potential by classical relations in the Lorentz gauge. The original expression E does not satisfy Maxwell's equations but, by virtue of the remodelling process involved in the PWS representation [9] akin to the one explicitly explained in [17], the electric and magnetic fields in the PWS representation do satisfy them. As for the vector potential, these fields take the form of an integral representation of individual plane waves.…”

“…In a recent paper [9], we presented a list of 35 problems for future research in generalized Lorenz-Mie theories and related topics. The present paper and the companion paper [17] contribute to the solution, or to a better definition, of some of these problems.…”

“…This description is achieved by expanding the fields in terms of a complete basis of functions with expansion coefficients being or containing sub-coefficients named beam shape coefficients (BSCs). A background on GLMTs may be gained from a recent textbook [5] and also from reviews such as [6], [7], [8], [9]. Although most of the works in EBCM are devoted to plane wave illumination, there also exist a number of works devoted to illuminating ASBs, e.g.…”

“…Section 6 provides a series of mini-reviews relevant to the issues discussed in the present paper. Section 7 discusses problems and solutions to problems, in the spirit of a recent paper proposing 35 problems in light scattering theories [9]. Section 8 is a conclusion.…”