Physical interpretation of the paraxial estimator

Abstract

The paraxial estimator (PE) is a parameter quantifying the paraxiality of a light beam. Even if some of its features were previously tackled, key details on its behavior were not fully presented. This paper robustly presents the physical meaning of the PE in a global way, enlarging its interpretation out of the paraxial region what permits to get a first view of the beam propagation dynamics from the value of this parameter. The physical interpretation is given in the spatial domain and in the spectral domain as well. In the first one, the value of PE is related to the competition between the fast oscillations and the remaining oscillations of a propagating field. Looking at spectral domain, the PE deals with the spectral dispersion (or width) of the plane waves forming the field. In this context, a negative value of PE concerns the effective contribution of the evanescent waves what only happens in a strong nonparaxial regime. The PE also accounts the geometric and physical features on the concept of the paraxial approximation in a natural way. An analysis performed for beams propagating through a spherical thin lens reveals that the loss of paraxiality is due to the geometric effect of ray bending by the lens and by another physical effect, concerning the nonideal collimation of the beam.