Effects of deterministic disorder at deeply subwavelength scales in multilayered dielectric metamaterials

Abstract

It is common understanding that multilayered dielectric metamaterials, in the regime of deeply subwavelength layers, are accurately described by simple effective-medium models based on mixing formulas that do not depend on the spatial arrangement. In the wake of recent studies that have shown counterintuitive examples of periodic and aperiodic (orderly or random) scenarios in which this premise breaks down, we study here the effects of deterministic disorder. With specific reference to a model based on Golay-Rudin-Shapiro sequences, we illustrate certain peculiar boundary effects that can occur in finite-size dielectric multilayers, leading to anomalous light-transport properties that are in stark contrast with the predictions from conventional effective-medium theory. Via parametric and comparative studies, we elucidate the underlying physical mechanisms, also highlighting similarities and differences with respect to previously studied geometries. Our outcomes may inspire potential applications to optical sensing, switching and lasing.

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

“…It is noteworthy that the physical mechanism of the breakdown of EMT in 1D dielectric multilayers [16][17][18][19][20][21][22][23][24][25][26][27] and 2D/3D dielectric composite structures studied here is fundamentally different. In 1D dielectric multilayers, the EMT breaks down close to the total internal reflection angle originates from tunneling effects of evanescent waves.…”

“…On the other hand, deep-subwavelength all-dielectric composite materials, where surface wave resonances are not supported, are generally believed to tightly obey the Maxwell Garnett EMT. Interestingly, very recently, Sheinfux et al [16] show the breakdown of EMT in deep-subwavelength all-dielectric multilayers, which has been numerically and experimentally demonstrated [17][18][19][20][21][22][23][24][25][26][27]. They found that the transmission through the multilayer structure depends strongly on nanoscale variations at the vicinity of the effective medium's critical angle for total internal reflection.…”

Anomalous Light Transport Induced by Deeply Subwavelength Quasiperiodicity in Multilayered Dielectric Metamaterials

“…To gain a comprehensive view of the phenomenology and identify the critical parameters, we carry out a parametric study of the transmission response of the multilayered metamaterial by varying the incidence direction, electrical thickness and number the layers, and scale ratio. In what follows we assume the same constitutive parameters for the layers (ε L = 1, ε H = 5) and exterior medium (ε e = 4) utilized in previous studies on periodic and aperiodic (either orderly or random) geometries [4,10,13,14,20,21], so as to facilitate direct comparison of the results. Recalling the approximation in (12), this corresponds to an effective medium with ε ≈ 3; we stress that this value is essentially independent of the scale ratio, and therefore holds for all examples considered in our study.…”

“…Recalling the approximation in (12), this corresponds to an effective medium with ε ≈ 3; we stress that this value is essentially independent of the scale ratio, and therefore holds for all examples considered in our study. In the same spirit, although we are not bound with specific sequence lengths, we assume power-of-two values for the number of layers N , similar to our previous studies on Thue-Morse [20] and Golay-Rudin-Shapiro [21] geometries. Moreover, to ensure meaningful comparisons among different geometries, we parameterize the electrical thickness in terms of the average thickness d in (6), so that structures with same number of layers have same electrical size.…”

“…These geometries have been extensively studied in the diffractive regime of photonic "quasicrystals" [17][18][19], but their interplay with mixed evanescent/propagating light transport at deeply subwavelength scales remains largely unexplored. In particular, we have studied the Thue-Morse [20] and Golay-Rudin-Shapiro [21] geometries, characterized by singular-continuous and absolutely continuous spatial spectra, respectively [22]; from a measure-theoretic viewpoint (Lebesgue decomposition theorem), these represent two of the three distinctive spectral traits of aperiodic order [22]. For these geometries, we have explored the critical parameter regimes leading to the occurrence of the EMT-breakdown phenomenon, highlighting some similarities and fundamental differences from what observed in the periodic and random scenarios.…”