Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review

The description of electromagnetic arbitrary shaped beams (e.g. laser beams) under expanded forms requires the evaluation of expansion coefficients known as beam shape coefficients. Several methods have been designed to evaluate these coefficients but the most efficient one relies on the use of localization operators, leading to localized approximations and to localized beam models, whose history and features are reviewed in this paper. Localized approximations and localized beam models have been particularly useful for speeding up numerical computations in the framework of generalized Lorenz–Mie theories (GLMTs), i.e. theories dealing with the interaction between electromagnetic arbitrary shaped beams and a regular particle, allowing one to solve the problem by using the method of separation of variables. However, they can be useful in other scattering approaches, such as the extended boundary condition method (or null-field method), or more generally, when the need of an efficient description of an electromagnetic arbitrary shaped beam is required.