The orbital angular momentum of light: Genesis and evolution of the concept and of the associated photonic technology

We present an overview of the main issues concerning the orbital angular momentum of light, starting form the framework of its definition, passing through the developments of the toolbox of recent devices and methods introduced for its generation, manipulation and detection, touching on some of the linear and nonlinear radiation-matter interaction phenomena that depend on this quantity, and finally mentioning its most relevant applications to quantum optics and quantum information. This review is meant as a fairly comprehensive survey, although unavoidably incomplete, of a long-standing subject whose relevance has been recognized and established only relatively recently. Of course, the debate on the mechanical degrees of freedom of light, especially those related to the deep nature of the angular momentum, has followed the entire history of the theory of electromagnetic radiation, from its initial formulation in terms of classical waves till the establishment of the quantum field theory. We shall attempt to discuss the reasons of such a tardy acknowledgment, especially compared with the case of the spin angular momentum. Although touching on many different aspects of the subject, our treatment will be somewhat biased towards covering in more detail those aspects of the field which intersected our own research, including the angular momentum exchange with soft materials such as liquid crystals, the spin-orbit optical interaction effects occurring in anisotropic inhomogeneous materials, and the quantum applications of these processes. More generally, we shall try to highlight some of the many problems faced within this research field during the last two decades, as well as the future challenges and potential applications.