Breakdown of Maxwell Garnett theory due to evanescent fields at deep-subwavelength scale

TL;DR

This paper demonstrates that the Maxwell Garnett effective medium theory fails at deep-subwavelength scales due to evanescent fields, and proposes a corrected model that accounts for position-dependent effects and 'invisible' loss phenomena.

Contribution

The authors reveal the breakdown of Maxwell Garnett theory at deep-subwavelength scales and introduce a correction that incorporates evanescent field effects for accurate predictions.

Findings

Evanescent fields cause Maxwell Garnett theory to fail at deep-subwavelength scales.

Position-dependent absorption and transmission are observed due to local evanescent fields.

A corrected model predicts these effects by considering evanescent field distributions.

Abstract

Deep-subwavelength all-dielectric composite materials are believed to tightly obey the Maxwell Garnett effective medium theory. Here, we demonstrate that the Maxwell Garnett theory could break down due to evanescent fields in deep-subwavelength dielectric structures. By utilizing two- and three-dimensional dielectric composite materials with inhomogeneities at the scale of {\lambda}/100, we show that local evanescent fields generally occur nearby the dielectric inhomogeneities. When tiny absorptive constituents are placed there, the absorption and transmission of the whole composite will show strong dependence on the positions of the absorptive constituents. The Maxwell Garnett theory fails to predict such position-dependent characteristics, because it averages out the evanescent fields. By taking the distribution of the evanescent fields into consideration, we made a correction to the Maxwell Garnett theory, such that the position-dependent characteristics become predictable. We reveal not only the breakdown of the Maxwell Garnett theory, but also a unique phenomenon of "invisible" loss induced by the prohibition of electric fields at deep-subwavelength scales. Our work promises a route to control the macroscopic properties of composite materials without changing their composition, which is beyond the traditional Maxwell Garnett theory.