Physical limits in electromagnetism

Photonic devices play an increasingly important role in advancing physics and engineering. Although improvements in nanofabrication and computational methods have driven progress in expanding the range of achievable optical characteristics, they have also greatly increased design complexity. These developments motivate the study of fundamental limits on optical response. Here we review recent progress in our understanding of these limits with special focus on an emerging theoretical framework that combines computational optimization with conservation laws to yield physical limits capturing all relevant wave effects. Results pertaining to canonical electromagnetic problems such as thermal emission, scattering cross-sections, Purcell enhancement and power routing are presented. Finally, we identify areas where further research is needed, including conceptual extensions and efficient numerical schemes for handling large-scale problems.