Approaching the upper limits of the local density of states via optimized metallic cavities

Abstract

By computational optimization of air-void cavities in metallic substrates, we show that the local density of states (LDOS) can reach within a factor of ≈10 of recent theoretical upper limits and within a factor ≈4 for the single-polarization LDOS, demonstrating that the theoretical limits are nearly attainable. Optimizing the total LDOS results in a spontaneous symmetry breaking where it is preferable to couple to a specific polarization. Moreover, simple shapes such as optimized cylinders attain nearly the performance of complicated many-parameter optima, suggesting that only one or two key parameters matter in order to approach the theoretical LDOS bounds for metallic resonators.

Trace formulation for photonic inverse design with incoherent sources

“…for topology optimization (Liang and Johnson 2013;Wang et al 2018;Yao et al 2020). More generally, this situation corresponds to the correlation matrix being low-rank: if is rank K, we can compute the trace in K solves.…”

“…In this particular case, after examining a large number of local optima (not shown), we found that the best local optimum is simply a circular disk with a particular radius. The existence of many local optima with performance varying by factors of 2-5 is not unusual in wave problems (Yao et al 2020;Diaz and Sigmund 2010;Bermel et al 2010), and while various heuristic strategies have been proposed to avoid poor local minima (Mutapcic et al 2009; Aage and Egede Johansen 2017; Bermel et al 2010;Schneider et al 2019) beyond simply probing multiple random starting points, the only way to obtain rigorous guarantees is to derive theoretical upper bounds (Miller et al 2016;Yao et al 2020) as discussed further in Sect. 5 (purely numerical global search can generally provide practical guarantees only for very low-dimensional Maxwell optimization Azunre et al 2019).…”

“…In the cases of fluorescence (Polimeridis et al 2015), near-field thermal radiation (Rodriguez et al 2013), and Casimir forces (Gong et al 2021), for example, tractable methods for arbitrary geometries were only obtained recently. This challenge is compounded when one wishes to perform inverse design (Molesky et al 2018)large-scale optimization of emission over many geometric parameters, perhaps even over "every pixel" of a design region via topology optimization (TopOpt) (Jensen and Sigmund 2011)-because one must then repeat the computation 10-1000 s of times as the design evolves, e.g., to maximize spontaneous emission (Rogobete et al 2003;Liang and Johnson 2013;Wang et al 2018;Yao et al 2020) or Raman emission (Christiansen et al 2020) from a single molecule, much less a distribution of sources.…”

Optimal Materials for Maximum Large-Area Near-Field Radiative Heat Transfer

“…Thus, for wavelength-scale patterning, the open questions are two-fold: will the larger size scale of the patterning relieve the stringent feature-size constraints imposed by effective-medium theory and, in tandem, will it enable substantially larger HTCs and RHT rates beyond the values predicted here? Given the significant recent work in both large-scale, computational “inverse design”, − as well as analytical and computational bounds to optical response, ,,,− conclusively answering such questions should be feasible in the near future.…”

Trace formulation for photonic inverse design with incoherent sources

“…One trivial special case in which the trace computation drastically simplifies is that of only a few sources or a few input channels, most famously in the case of the local density of states (LDOS): emission by a molecule at a single location in space but with a random polarization [1,24]. In the case of LDOS, this reduces the trace computation to three Maxwell solves, one per principal polarization direction, making the problem directly tractable for topology optimization [47][48][49]. More generally, this situation corresponds to the correlation matrix B being low-rank: if B is rank K, we can compute the trace in K solves.…”