Covariant photon wave mechanics of evanescent fields

A photon wave mechanical theory describing evanescent electromagnetic fields, as these appear in p-polarized total internal reflection from a flat dielectric-to-vacuum interface, is presented. In this first-quantized field theory, the Lorenz gauge four-potential relates to the wave functions of the transverse (T), longitudinal (L), and scalar (S) photons. For a homogeneous medium, the source domain (rim zone) of the L photons is shown to coincide with the longitudinal vector-field parts of an electron sheet current density located at the interface. The identical rim zones of the T and L photons exhibit one-dimensional (1D) exponential confinement with a spatial decay constant equal to the magnitude of the incident field's wave vector along the interface plane. The S-photon 1D localization is complete (has δ-function character). Dynamical equations are established for the L- and S-photon variables in the wave-vector-time domain. These Hamiltonian-like equations are easily upgraded to the second-quantized level. The link to the wave mechanics of near-field photons is made. When extended to the quantum electrodynamic level, the present theory is an alternative to the pioneering Carniglia-Mandel (CM) triplet-photon description. It is argued that our theory provides one with an improved physical understanding of the basic role of T photons in evanescent fields. Wave mechanics of evanescent fields give additional insight in the T-photon localizability problem. The particular difficulties arising for s-polarized external fields are addressed referring to the rim zone of quantum wells.