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We exploit fluctuational electrodynamics to present trace expressions for the torque experienced by arbitrary objects in a passive, non-absorbing, rotationally invariant background environment. Specializing to a single object, this formalism, together with recently developed techniques for calculating bounds via Lagrange duality, is then used to derive limits on the maximum Casimir torque that a single object with an isotropic electric susceptibility can experience when out of equilibrium with its surrounding environment. The maximum torque achievable at any wavelength is shown to scale in proportion to body volumes in both subwavelength (quasistatics) and macroscopic (ray optics) settings, and come within an order of magnitude of achievable torques on topology optimized bodies. Finally, we discuss how to extend the formalism to multiple bodies, deriving expressions for the torque experienced by two subwavelength particles in proximity to one another.

The electromagnetic local density of states (LDOS) is crucial to many aspects of photonics engineering, from enhancing emission of photon sources to radiative heat transfer and photovoltaics. We present a framework for evaluating upper bounds on LDOS in structured media that can handle arbitrary bandwidths and accounts for critical wave scattering effects with no heuristic approximations. The bounds are solely determined by the bandwidth, material susceptibility, and device footprint, with no assumptions on geometry. We derive an analytical expression for the maximum LDOS consistent with the conservation of energy across the entire design domain, which upon benchmarking with topology-optimized structures is shown to be nearly tight for large devices. Novel scaling laws for maximum LDOS enhancement are found: the bounds saturate to a finite value with increasing susceptibility and scale as the quartic root of the bandwidth for semi-infinite structures made of lossy materials, with direct implications on material selection and design applications., Comment: Corrected minor typos throughout paper; corrected mislabel of inverse designs in Figure 1; added full Supplementary Information; added acknowledgments

We show how the central equality of scattering theory, the definition of the $\mathbb{T}$ operator, can be used to generate hierarchies of mean-field constraints that act as natural complements to the standard electromagnetic design problem of optimizing some objective with respect to structural degrees of freedom. Proof-of-concept application to the problem of maximizing radiative Purcell enhancement for a dipolar current source in the vicinity of a structured medium, an effect central to many sensing and quantum technologies, yields performance bounds that are frequently more than an order of magnitude tighter than all current frameworks, highlighting the irreality of these models in the presence of differing domain and field-localization length scales. Closely related to domain decomposition and multi-grid methods, similar constructions are possible in any branch of wave physics, paving the way for systematic evaluations of fundamental limits beyond electromagnetism.

Solid-state defect qubit systems with spin-photon interfaces show great promise for quantum information and metrology applications. Photon collection efficiency, however, presents a major challenge for defect qubits in high refractive index host materials. Inverse-design optimization of photonic devices enables unprecedented flexibility in tailoring critical parameters of a spin-photon interface including spectral response, photon polarization, and collection mode. Further, the design process can incorporate additional constraints, such as fabrication tolerance and material processing limitations. Here, we design and demonstrate a compact hybrid gallium phosphide on diamond inverse-design planar dielectric structure coupled to single near-surface nitrogen-vacancy centers formed by implantation and annealing. We observe up to a 14-fold broadband enhancement in photon extraction efficiency, in close agreement with simulations. We expect that such inverse-designed devices will enable realization of scalable arrays of single-photon emitters, rapid characterization of new quantum emitters, efficient sensing, and heralded entanglement schemes.

We present a method based on the scattering $\mathbb{T}$ operator, and conservation of net real and reactive power, to provide physical bounds on any electromagnetic design objective that can be framed as a net radiative emission, scattering or absorption process. Application of this approach to planewave scattering from an arbitrarily shaped, compact body of homogeneous electric susceptibility $\chi$ is found to predictively quantify and differentiate the relative performance of dielectric and metallic materials across all optical length scales. When the size of a device is restricted to be much smaller than the wavelength (a subwavelength cavity, antenna, nanoparticle, etc.), the maximum cross section enhancement that may be achieved via material structuring is found to be much weaker than prior predictions: the response of strong metals ($\mathrm{Re}[\chi] < 0$) exhibits a diluted (homogenized) effective medium scaling $\propto |\chi| / \mathrm{Im}[\chi]$; below a threshold size inversely proportional to the index of refraction (consistent with the half-wavelength resonance condition), the maximum cross section enhancement possible with dielectrics ($\mathrm{Re}[\chi] > 0$) shows the same material dependence as Rayleigh scattering. In the limit of a bounding volume much larger than the wavelength in all dimensions, achievable scattering interactions asymptote to the geometric area, as predicted by ray optics. For representative metal and dielectric materials, geometries capable of scattering power from an incident plane wave within an order of magnitude (typically a factor of two) of the bound are discovered by inverse design. The basis of the method rests entirely on scattering theory, and can thus likely be applied to acoustics, quantum mechanics, and other wave physics.

Supplement 1

We report bounds on angle-integrated absorption, scattering and far- and nearfield radiative emission, capturing both per-volume material limits and geometric effects. We then describe potential extensions of this formalism to a variety of electromagnetic phenomena.

We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between a polarizable dipole and a uniform planar semi-infinite bulk medium always comes within 10% of the lower bound, implying that nanostructuring is of limited use for increasing attraction. In contrast, the possibility of repulsion is observed even for isotropic dipoles, and is routinely found to be several orders of magnitude larger than any known design, including recently predicted geometries involving conductors with sharp edges. Our results have ramifications for the design of surfaces to trap, suspend, or adsorb ultracold gases., 6 pages, 3 figures

This research was financially supported by the European Research Council under the European Union's Seventh Framework Programme (FP/2007- 2013)/ERC Grant Agreement No. 306298 (EN -LUMINATE) and under the European Union’s Horizon 2020 Framework Programme (FP/2014- 2020)/ERC Grant Agreement No. 640012 (ABLASE) and by the EPSRC Programme Grant EP/P030017/1. L.T. thanks EPSRC for support through the CM -DTC (EP/L015110/1). Exciton-polaritons are quasiparticles with hybrid light–matter properties that may be used in new optoelectronic devices. Here, electrically pumped ultrastrongly coupled exciton-polaritons in a high-mobility donor–acceptor copolymer are demonstrated by integrating a light-emitting field-effect transistor into a metal-clad microcavity. Near-infrared electroluminescence is emitted exclusively from the lower polariton branch, which indicates efficient relaxation. A coupling strength of 24% of the exciton transition energy implies the system is in the ultrastrong coupling regime with a narrow and almost angle-independent emission. The lower polariton energy, which can be adjusted by the cavity detuning, strongly influences the external quantum efficiency of the device. Driving the transistors at ambipolar current densities of up to 4000 A cm−2 does not decrease the coupling strength or polariton emission efficiency. Cavity-integrated light-emitting field-effect transistors thus represent a versatile platform for polariton emission and polaritonic devices. Publisher PDF