[@Kogelnik:1966p9295], and the optical forces on Mie-sized particles [@Barton:1989p1732]. In the case of waveguides and photonic crystals, for example, eigenmodes describe electromagnetic fields that are invariant in their intensity profile as they propagate along the fibre or crystal. Additionally, these modes are orthogonal and as such light coupled to one of these modes remains, in theory, in this mode forever. This optical mode decomposition can be expanded to include additional properties such as orbital and spin angular momentum [@Mazilu:2009p9267]. All-together, the eigenmode expansion method is a well-established method for the representation of the propagation of optical fields.

In this paper, we report a novel method which we term “Optical Eigenmodes (OEi)” which represents a generalization of the powerful concept of eigenmode decomposition going beyond the propagation properties of light. Crucially, we show that eigenmode decomposition is applicable to the case of any quadratic measure which is defined as a function of the electromagnetic field. Prominent examples of optical quadratic measures include the energy density and the energy flux of electromagnetic fields. The OEi method makes it possible to describe an optical system and its response to incident electromagnetic fields as a simple mode coupling problem and to determine the optimal 