Anomalous effective medium approximation breakdown in deeply subwavelength all-dielectric photonic multilayers

Abstract

We present a comprehensive analysis of the applicability of the effective medium approximation to deeply subwavelength (period ≤λ/50 all-dielectric multilayer structures. We demonstrate that even though the dispersion relations for such multilayers differ from the effective medium prediction only slightly, there can be regimes when an actual multilayer stack exhibits significantly different properties compared to its homogenized model. In particular, reflection near the critical angle is shown to strongly depend on even very small period variations, as well as on the choice of the multilayer termination. We identify the geometries for which the influence of the subwavelength features is maximized and demonstrate that the difference between the reflectance from the actual multilayer and the effective medium prediction can be as great as 0.98. The results of this analysis can be useful for high-precision multilayer ellipsometry and in sensing applications.

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

“…It is apparent the general agreement between the EMT and periodic cases, both displaying a rather marked transition from a highly transmissive (with mild Fabry-Pérot-type oscillations) to an essentially opaque regime for incidence angles approaching the critical valueθ c = 60 o . In fact, as previously mentioned, the EMT and periodic responses may differ substantially in the transition region aroundθ c[8,[10][11][12][13][14][15], although this is hardly visible on the scale of the graphs here. Conversely, the responses of the GRS-type configurations are visibly different, with low-transmission regions extending for mostd/λ=0.01 d/λ=0.02 d/λ=0.025 Inverse localization length, λ/ξ (a) Inverse localization length (scaled by the wavelength) for a GRS-type configuration with N = 2048 layers and different electrical thicknesses (blue-solid: d/λ = 0.01; red-dashed: d/λ = 0.02; magenta-dotted: d/λ = 0.025), as a function of the incidence angle.…”

Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation

“…The homogenization in this case is given by the Maxwell Garnett (quasistatic) approach, which is called the effective medium approximation (EMA). Recently, the homogenization of the subwavelength dielectric layered structures has attracted close attention in connection with the discovered EMA breakdown [35][36][37]. The EMA breakdown typically is quite pronounced near the critical angle of total internal reflection defined for the effective medium.…”

Polymer multimode waveguide bend based on a multilayered Eaton lens

“…On the other hand, when the thickness of the layers is much smaller than the wavelength of the light, the interference effects are negligible. Therefore, in the long-wavelength limit, the multilayer structure can be regarded as a homogenous medium [25]. Multilayer structures as homogenous media have been utilized in various devices and applications such as hyperlenses, invisibility cloaks, couplers, and waveguide crossings [26][27][28][29][30].…”