2005/11/30 by Iwo Bialynicki-Birula, Iwo Białynicki‐Birula, Zofia Bialynicka-Birula +1 · 1 citation
Engineering · Physics and Astronomy · #Angular momentum #Beam (structure) #Bessel function #Electromagnetic field #Electromagnetic radiation #Momentum (technical analysis) #Near-Field Optical Microscopy #Optics #Orbital Angular Momentum in Optics #Photon #Physics #Quantum #Quantum electrodynamics #Quantum mechanics #Quantum optics and atomic interactions #quant-ph
paper · pdf · doi:10.1016/j.optcom.2005.11.071
To be published in the special issue of Optics Communications honoring Bruce Shore
arxiv created 2006/01/12 · openalex publication_date 2006/06/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector -- a complex combination of the electric and magnetic field vectors -- that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre-Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.