Fundamental limits to near-field optical response

Near-field optics is an exciting frontier of photonics and plasmonics. The tandem of strongly localized fields and enhanced emission rates offers significant opportunities for wide-ranging applications, while also creating basic questions: How large can such enhancements be? To what extent do material losses inhibit optimal response? Over what bandwidths can these effects be sustained? This chapter surveys theoretical techniques for answering these questions. We start with physical intuition and mathematical definitions of the response functions of interest (LDOS, CDOS, SERS, NFRHT, etc.), after which we describe the general theoretical techniques for bounding such functions. Finally, we apply those techniques specifically to near-field optics, for which we describe known bounds, optimal designs, and open questions.