Quantum-mechanical properties of Bessel beams

Abstract

Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. As we show explicitly, the operators that are usually associated with linear momentum, orbital angular momentum, and spin do not satisfy the algebra of the translation and rotation group. Nevertheless, we identify some components of these operators that represent observable quantities in an appropriate basis, thus characterizing the quantum numbers of Bessel photons. Some physical consequences of these results are discussed.