Generalized Lorenz-Mie Theories: From Problems Solved in the Past to Problems to be Solved in the Future

Generalized Lorenz-Mie Theories (GLMTs) form a set of analytical scattering theories describing the scattering interaction between arbitrary electromagnetic shaped beams and a set of particles possessing enough symmetries to allow one to deal with Maxwell's equations using the method of separation of variables. Although under development since more than 4 decades, there remain many problems to investigate and solve. This paper briefly recalls some problems solved in the past and, more important, will propose new problems to be solved in the future.