This paper analyzes the optimal communication involving large intelligent surfaces (LIS) starting from electromagnetic arguments. Since the numerical solution of the corresponding eigenfunctions problem is in general computationally prohibitive, simple but accurate analytical expressions for the link gain and available spatial degrees-of-freedom (DoF) are derived. It is shown that the achievable DoF and gain offered by the wireless link are determined only by geometric factors, and that the classical Friis' formula is no longer valid in this scenario where the transmitter and receiver could operate in the near-field regime. Furthermore, results indicate that, contrarily to classical MIMO systems, when using LIS-based antennas DoF larger than 1 can be exploited even in strong line-of-sight (LOS) channel conditions, which corresponds to a significant increase in spatial capacity density, especially when working at millimeter waves.