The process of localisation of a plane wave and its interaction with a point charged particle is considered in the framework of the five-dimensional extended space model (ESM). The equations for the plane-wave potentials describing the process of its localisation are presented. The exact solution of these equations is found. A scheme of interaction of a localised wave with a charged particle is proposed. It is shown that, within the framework of the ESM formalism introduced by us, when a point charged particle interacts with a plane electromagnetic wave incident on it, the point particle ‘swells’, and its spatial size is determined by the plane-wave localisation parameter.