Theory of Elliptically Polarized Photons

Abstract

The unitary transformation from linearly to elliptically polarized states of photons is determined in a scheme of the second quantization (§1). It is given by ${\mathbf{e}}_l={\mathbf{e}}_{1}cos\varphi +i{\mathbf{e}}_{2}sin\varphi$, ${\mathbf{e}}_r=i{\mathbf{e}}_{1}sin\varphi +{\mathbf{e}}_{2}cos\varphi$ where ${\mathbf{e}}_1$ and ${\mathbf{e}}_2$ are orthogonal unit vectors corresponding to linearly polarized states of photons and ${\mathbf{e}}_l$ and ${\mathbf{e}}_r$ are those corresponding to left and right elliptically polarized states of photons. A general formula for a probability of an emission of light from an atom is deduced on the basis of the Dirac electron theory so as to include up to both a magnetic dipole and an electric quadrupole term (§2). Its general form is improved as compared with the hitherto obtained one. The general theory is applied to electric dipole and quadrupole and magnetic dipole spectral lines (§3 and §4). Polarization states of the Zeeman components corresponding to all combinations of magnetic and orbital magnetic quantum numbers of an atom are completely determined for an arbitrary given direction of an observation on the basis of quantum mechanics.