Chao Pengning, Kuate Defo Rodrick, Molesky Sean, Rodriguez Alejandro
Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA.
Department of Engineering Physics, Polytechnique Montréal, Montréal, Québec H3T 1J4, Canada.
Nanophotonics. 2022 Nov 14;12(3):549-557. doi: 10.1515/nanoph-2022-0600. eCollection 2023 Feb.
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 the LDOS in structured media that can handle arbitrary bandwidths and accounts for critical wave scattering effects. 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.
电磁局域态密度（LDOS）在光子学工程的许多方面都至关重要，从增强光子源的发射到辐射热传递和光伏领域。我们提出了一个用于评估结构化介质中LDOS上限的框架，该框架可以处理任意带宽并考虑关键的波散射效应。这些界限仅由带宽、材料磁化率和器件尺寸决定，无需对几何形状做任何假设。我们推导了一个与整个设计域内能量守恒相一致的最大LDOS的解析表达式，经与拓扑优化结构进行基准测试表明，对于大型器件而言，该表达式几乎是精确的。我们发现了最大LDOS增强的新标度律：对于由有损材料制成的半无限结构，随着磁化率增加，界限会饱和到一个有限值，并且与带宽的四次方根成比例，这对材料选择和设计应用有直接影响。
