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In this paper, we present a method for computing bounds for a variety ofefficiency metrics in photonics, such as the focusing efficiency or the modepurity. We focus on the special case where the objective function can bewritten as the ratio of two quadratic functions of the field and show thatthere exists a simple semidefinite programming relaxation for this problem. Weprovide a numerical example of bounding the maximal mode conversion purity fora device of given size. This paper is accompanied by an open source Juliapackage for basic simulations and bounds.

Bounds on Efficiency Metrics in Photonics