Quantum polarization properties of radiation

Abstract

New bosonic operators, describing the polarization properties of photons at any point with respect to a source, are introduced. It is shown that, unlike the classical picture, the local quantum description of polarization needs nine independent local Stokes operators, forming a representation of the SU(3) subalgebra in the Weyl-Heisenberg algebra of photons. The Cartan algebra of this SU(3) determines the cosine and sine of radiation phase operators. It is shown that the use of plane wave photons can lead to wrong results for quantum fluctuation of polarization even in the far zone. Dual representation of multipole photons is proposed. The exponential operator is diagonal in this representation, hence dual number states describe radiation phase states.. The discrete spectrum of exponential operator is found for dipole and quadrupole photons and a natural behaviour in the classical limit. Application of the results to the near-field optics is discussed.