States, Modes, Fields, and Photons in Quantum Optics

The quantum nature of light enables potentially revolutionary communication technologies. Key to advancing this area of research is a clear understanding of the concepts of states, modes, fields, and photons. The concept of field modes carries over from classical optics, while the concept of state has to be considered carefully when treating light quantum mechanically. The term 'photon' is an overloaded identifier in the sense that it is often used to refer to either a quantum particle or the state of a field. This overloading, often used without placing in context, has the potential to obfuscate the physical processes that describe the reality we measure. We review the uses and relationships between these concepts using modern quantum optics theory, including the concept of a photon wave function, the modern history of which was moved forward in a groundbreaking paper in this journal by Iwo Bia{\l}ynicki-Birula, to whom this article is dedicated.
Comment: This article belongs to the special issue of Acta Physica Polonica A printed in honor of Professor Iwo Bialynicki-Birula on the occasion of his 90th birthday (Ed. Tomasz Sowinski, DOI:10.12693/APhysPolA.143.S0)