Oblique section of a paraxial light beam: criteria for azimuthal energy flow and orbital angular momentum

Abstract

Comparison of the intensity distributions in a transverse cross section, orthogonal to the beam propagation axis, and in an oblique section, inclined to the axis by some acute angle, provides information about the transverse energy flows in the beam, in particular, the transverse energy circulation. The beam intensity pattern in an oblique section differs from the 'geometric-optics' expectations, which can be quantitatively described by the corresponding shift of the beam 'centre of gravity'. Measurements of this shift can be used for the study and characterization of the transverse energy flows and for evaluation of the beam orbital angular momentum. Situations in which the intensity distribution in oblique sections plays an important role occur in the beam transformation at a diffraction grating (in non-zero diffraction orders) and even at the beam propagation through a reflecting boundary. An optical vortex generation with the help of a hologram possessing a 'fork' structure supplies a special case of such a situation.