Energy and momentum flux in a high-numerical-aperture beam using the extended Nijboer-Zernike diffraction formalism

We describe the energy and momentum flux in the case of an aberrated optical imaging system with a high numerical aperture (NA). The approach is based on the extended Nijboer-Zernike diffraction theory, that, in its high-NA version, yields an accurate analytic representation of the electromagnetic field vectors in the focal region of imaging systems that suffer from aberrations and/or transmission defects[1]. In an earlier publication, we have derived the electromagnetic energy density from the field vectors. In this paper, we expand our analysis to the energy flow (Poynting vector) and to the quantities related to the linear and angular momentum of the radiation. Several examples of the energy and momentum flow are presented. In particular, we show how the linear and angular momentum distribution in the focal region depend on the initial polarisation state and on the parameters describing the wavefront shape of the converging beam. For the angular momentum flow, we show how the separation between spin and orbital momentum is modified when going from the paraxial case to a high-NA focused beam.