Photon Emission from Micro- and Mesoscopic Sources: Near-Field Aspects

Abstract

Until now we have discussed photon wave mechanics in free space only. From an observational point of view it is absolutely necessary however that we extend the fundamental theory so as to take into account the photon–matter interaction. In this interaction, photons are either generated or destroyed. A photon is generated in an emission process from a source and destroyed in an absorption process in a detector. When the source and detector are in each others far-field zones the emission and absorption processes can be studied separately at least in the framework of first quantization, but if the source and detector are in near-field contact the two processes interfere in an extremely complicated manner. In the presence of field–matter interactions, photon wave mechanics is a very broad field of study, and in the present chapter we shall discuss the emission processes only, paying particular attention to the electrodynamics in the rim zone of the source. Even the photon emission process is quite complicated to tackle theoretically, because the photon during the emission process acts back on the source particles and change their dynamics. In the quite limited framework of linear electrodynamics we discussed this back-action on the basis of the coupled-antenna theory in Chap. 13. Although we did not relate the coupled-antenna theory to photon wave mechanics as such this can be done if one wishes so. In this chapter, we shall not address the back-action problem. One may address the photon emission theme starting from the complex field theory (Chap. 15), the energy wave function formalism (Chap. 16), or the four-potential theory (Chap. 16). Rigorous descriptions will result in the same observational predictions in all three schemes of photon wave mechanics. Different approximations made during intermediate calculations in the various formulations may of course lead to unphysical differences in the final prediction. In what follows we shall base our analysis mainly on the photon energy wave function theory, and certain modifications of this theory’s near-field aspects. The close resemblance of the energy wave function formalism to the complex field theory makes it easy to “translate” the treatment below to the CF-theory. From a conceptual point of view the near-field aspects of the photon emission process appear formally in a quite different disguise in the four-potential theory, and in the final section of this chapter we shall briefly discuss this formal change in our point of view.