“excitation” for the given measure considered. Intuitively, a superposition of initial fields is optimized in a manner that the minimum/maximum measure is achieved. For instance, the transmission through a pinhole is optimized by maximizing the energy flux through the pinhole [@GarciaVidal:2005p9724].

From a theoretical perspective, the OEi optimization method is mathematically rigorous and may be distinguished from the multiple techniques currently employed ranging from genetic algorithms [@Assion:1998p9709] and random search methods [@Dennis:2010p9723] to direct search methods [@Thomson:2008p8158]. The major challenge encountered in any such approximate optimization and engineering of optical properties is the fact that electromagnetic waves interfere. As such the interference pattern not only makes the search for an optimum beam problematic but crucially renders the superposition found unreliable, as the different algorithms may converge on different local minima which are unstable with respect to the different initial parameters of the problem. In contrast, our proposed OEi method yields a unique solution to the problem and directly determines the optimum (maximal/minimal) measure possible.

In the first part of the paper, we introduce the OEi method and show its properties in a general context of optimizing the quadratic measures of interfering waves. In the second part, we apply the OEi 