  We report a mathematically rigorous technique which facilitates the
optimization of various optical properties of electromagnetic fields. The
technique exploits the linearity of electromagnetic fields along with the
quadratic nature of their interaction with matter. In this manner we may
decompose the respective fields into optical quadratic measure eigenmodes
(QME). Key applications include the optimization of the size of a focused spot,
the transmission through photonic devices, and the structured illumination of
photonic and plasmonic structures. We verify the validity of the QME approach
through a particular experimental realization where the size of a focused
optical field is minimized using a superposition of Bessel beams.
