In this talk, we present an extension of a prior scattering operator framework for computing fluctuational electromagnetic phenomena to include torque phenomena in the thermal equilibrium and nonequilibrium regimes. The challenge in theoretical proposals to detect a Casimir torque in real experimental systems stems from the weakness of the effect and the requirement of ultra-sensitive measurements; a larger effect requires the ability to place objects at a small separation. There is the interesting question of whether Casimir torques must be weak. In the equilibrium case, we present semianalytic structure-agnostic bounds on the Casimir torque between an anisotropic (reciprocal or nonreciprocal) dipolar particle and a macroscopic body composed of a local isotropic electric susceptibility, separated by vacuum. In the nonequilibrium case, we derive limits on the maximum Casimir torque that a single object can experience when out of equilibrium with its surrounding environment. We find that the maximum torque achievable at any wavelength scales in proportion to the volume of the body in both subwavelength (quasistatics) and macroscopic (ray optics) settings, and comes within an order of magnitude of achievable torques on topology optimized bodies.

Switching attention from fluctuational electromagnetic phenomena, we focus on the suppression of bandwidth-integrated local density of states (LDOS) and cloaking. 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 a material 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 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 trailed closely by inverse designs, and discuss the implications to the development of cloaking devices.

Adviser: Alejandro Rodriguez