Abstract
We develop an analytical framework to derive upper bounds to light--matter interactions in the optical near field, where applications ranging from spontaneous-emission amplification to greater-than-blackbody heat transfer show transformative potential. Our framework connects the classic complex-analytic properties of causal fields with newly developed energy-conservation principles, resulting in a new class of power--bandwidth limits. These limits demonstrate the possibility of orders-of-magnitude enhancement in near-field optical response with the right combination of material and geometry. At specific frequency and bandwidth combinations, the bounds can be closely approached by canonical plasmonic geometries, with the opportunity for new designs to emerge away from those frequency ranges. Embedded in the bounds is a material "figure of merit," which determines the maximum response of any material (metal/dielectric, bulk/2D, etc.), for any frequency and bandwidth. Our bounds on local density of states (LDOS) represent maximal spontaneous-emission enhancements, our bounds on cross density of states (CDOS) limit electromagnetic-field correlations, and our bounds on radiative heat transfer (RHT) represent the first such analytical rule, revealing fundamental limits relative to the classical Stefan--Boltzmann law.
Highlights
The techniques developed for local density of states (LDOS), CDOS, and radiative heat transfer should be extensible to other near-field effects ranging from
Where sðω0 þ iΔωÞ is the near-field scattering amplitude evaluated at the single complex frequency ω0 þ iΔω, and αLDOS is the electrostatic constant appearing in the sum rule defined in Eq (4)
In the limit of zero bandwidth, Hω0;Δωð0Þ equals zero, and Eq (16) comprises only the first term, which represents single-frequency LDOS: ρ 1⁄4 Im sðωÞ; as the bandwidth goes to infinity, Im sðω0 þ iΔωÞ decays rapidly and the second term converges to the sum rule [Eq (4)]
Summary
The electromagnetic near field comprises largeamplitude evanescent fields that can be harnessed to amplify spontaneous-emission rates [1,2,3,4,5,6], Casimir forces [7,8,9,10,11], Raman scattering [12,13,14,15,16,17], and greater-thanblackbody transfer of thermal energy [18,19,20,21,22,23,24]. We derive fundamental limits for local density of states (LDOS), the prototypical near-field optical response, for any bandwidth of interest and for any material platform. Upper-half plane (UHP), and the typical contourintegral analysis of a given power quantity requires the computation of residues not at a single real frequency (as in sum rules) but at a discrete set of complex frequencies. At this juncture, we identify the energy-conservation constraints at those complex frequencies, deriving bounds on how large they can be. VI, we discuss extensions of our formulation to near-field phenomena such as Lamb shifts, Raman scattering, Casimir forces, and more
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