Theory of the forces exerted by Laguerre-Gaussian light beams on dielectrics

The classical theory of the electromagnetic field associated with paraxial Laguerre-Gaussian light is generalized to apply to propagation in a bulk dielectric, and the theory is quantized to obtain expressions for the electric and magnetic field operators. The forms of the Poynting vector and angular momentum density operators are derived and their expectation values for a single-photon wave packet are obtained. The Lorentz force operator in the dielectric is resolved into longitudinal, radial, and azimuthal components. The theory is extended to apply to an interface between two semi-infinite dielectric media, one of which is transparent with an incident single-photon pulse, and the other of which is weakly attenuating. For a pulse that is much shorter than the attenuation length, the theory can separately identify the surface and bulk contributions to the Lorentz force on the attenuating dielectric. Particular attention is given to the transfer of longitudinal and angular momentum to the dielectric from light incident from free space. The resulting expressions for the shift and rotation of a transparent dielectric slab are shown to agree with those obtained from Einstein box theories.