Relationship between two different approaches relating electromagnetic and scalar beam shape coefficients

Abstract

Two different approaches, with many different conventions, have been recently published to express electromagnetic beam shape coefficients, encoding the structure of laser beams, in terms of scalar (more specifically acoustical) beam shape coefficients. One approach, call it VP1, expresses the electromagnetic fields using one single vector potential, while the second approach, call it VP2, expresses the electromagnetic fields in terms of two vector potentials. In this paper, we discuss the relationships between the VP1 and VP2 approaches, showing how the vector potential of the VP1 approach is related to the vector potentials of the VP2 approach, and express the relationships relating the beam shape coefficients of one approach to the beam shape coefficients of the other.