There is an unsettled problem in choosing the correct expressions for the local momentum density and angular momentum density of electromagnetic fields (or indeed, of any non-scalar field). If one only examines plane waves, the problem is moot, as the known possible expressions all give the same result. The momentum and angular momentum density expressions are generally obtained from the energy-momentum tensor, in turn obtained from a Lagrangian. The electrodynamic expressions obtained by the canonical procedure are not the same as the symmetric Belinfante reworking. For the interaction of matter with structured light, for example, twisted photons, this is important; there are drastically different predictions for forces and angular momenta induced on small test objects. We show situations where the two predictions can be checked, with numerical estimates of the size of the effects.
We calculate transition amplitudes and cross sections for excitation of hydrogen-like atoms by the twisted photon states, or photon states with more than one unit of angular momentum projection along the direction of propagation.
If the target atom is located at distances of the order of atomic size near the vortex center, the transitions rates into $l_f>1$ states become comparable with the rates for standard electric dipole transitions. It is shown that when the transition rates are normalized to the local photon flux, the resulting cross sections for $l_f>1$ are singular near the optical vortex center, i.e., high-multipole excitations take place in the region of zero field intensity near phase singularity. Relation to the "quantum core" concept introduced by Berry and Dennis is discussed.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.