We calculate transition amplitudes and cross sections for excitation of hydrogen like atoms by the twisted photon states, or photon states with large angular momentum projection on the direction of propagation. It is shown that when the transition rates are normalized to the local photon flux,the resulting cross sections for are singular near the optical vortex center , in close relation to the 'quantum core' concept introduced by Berry and Dennis. We also show that the photon state develops polarization singularity in the beam center due to circular dichroism of the photon absorption by atoms via higher multipoles.
. A. Afanasev, C.E. Carlson, and A. Mukherjee, High-multipole excitations of hydrogen-like atoms by twisted photons near a phase singularity, Journal of Optics 18, 074013 (2016)
Andrei Afanasev, "Cross section and polarization singularities in the twisted-photon absorption by atoms (Conference Presentation)," Proc. SPIE 10120, Complex Light and Optical Forces XI, 101200T (Presented at SPIE OPTO: February 01, 2017; Published: 28 April 2017); https://doi.org/10.1117/12.2255751.5397967369001.
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