In this talk, we present extensions and applications of a recently developed optimization framework for computing bounds on figures of merit in electromagnetic settings. We focus mainly on the suppression of bandwidth-integrated local density of states (LDOS) and cloaking, but we also briefly mention new results for Casimir torque phenomena. LDOS is arguably the most important near-field response quantity given its central role in many ideas in optics such as spontaneous emission, surface-enhanced Raman scattering, near-field radiative heat transfer, and other related phenomena. We compute bounds on the minimum bandwidth-integrated LDOS achievable by a structure composed of an isotropic electric susceptibility, where we find that the bounds scale linearly with the bandwidth and as the square root of the bandwidth in systems without and with material loss, respectively. The bounds suggest that near-perfect LDOS suppression is possible for small bandwidths even in the presence of material loss, and we confirm this finding by detailing how a mechanism based on the use of slow light modes in effective one-dimensional systems can achieve arbitrarily small absorption loss. We find that perfect cloaking over any bandwidth is impossible for isotropic susceptibilities and finite device footprints. We numerically explore the scaling behaviors and general trends of the bounds, which are confirmed to be closely trailed by inverse designs, with respect to relevant experimental parameters like device size, material loss, and bandwidth of operation. We discuss the implications for the development of cloaking devices. Lastly, we mention an extension of a prior scattering operator framework for computing fluctuational electromagnetic phenomena to include torque phenomena in the thermal equilibrium and nonequilibrium regimes. There is the interesting question of whether Casimir torques must be weak, which we address by providing semianalytic expressions for the bounds. 

Adviser: Alejandro Rodriguez