Subwavelength multilayer dielectrics: ultrasensitive transmission and breakdown of effective-medium

Abstract

We show that a structure of alternating dielectric layers with deep subwavelength thicknesses exhibits novel transmission effects that depend on the order of the layers and on nanometer scale variations of the layer widths. OCIS codes: (260.2065) Effective medium theory; (260.6970) Total internal reflection (160.3918) Metamaterials;Homogenization in optics is the process of replacing a complex structure of subwavelength sized components with an "effective medium" with uniform properties. It is a fundamentally important notion which can be traced back to the earliest days of electromagnetic theory, to the Lorentz-Lorenz and Maxwell-Garnet effective medium models [1,2]. While more sophisticated homogenization approaches are being used today to obtain better values of the effective parameters at a variety of geometries [2], the basic concept of smoothing over the subwavelength features of the underlying structure and describing it in terms of effective parameters has remained unchanged.In the context of 1D systems, multilayer structures composed from two types of layers are extremely well researched systems [3]. When both layers are dielectric, the structure exhibits form-birefringence, potentially much larger than birefringence found in nature [3]. The effective description becomes much more intricate when one of the layers is metallic and can support surface plasmons. Surface plasmons have much shorter wavelengths than their parent photons. Accordingly, surface plasmon resonances can lead to a strong and short ranged interaction of light with the structure and can be sensitive to details such as surface termination which are otherwise totally negligible in the effective medium description [4,5]. On the other hand, all-dielectric systems, which fundamentally do not support such surface waves and resonances, are believed to be insensitive to subwavelength structural features and are well described by an effective medium approach [5].Here, we examine a stratified dielectric structure, and show that its transmission can depend on nanometric structural features. We show that even when the layers are 0.02λ thin, impedance matching with the exterior medium (from which the EM waves enter the multilayer structure) is not always possible. The phase of the observed reflection depends on the identity of the last layer. As a result, the transmission of the entire structure can change significantly (in the order of unity) due to the addition of a single 10nm thin layer or by reversing the order of the layers. Both these features stand in complete contradiction to the conventional effective medium approach.Consider a structure made of alternating layers of two types of dielectrics characterized by (real) permittivities ε 1,2 and thickness d (see fig.1a). According to effective-medium theory, for infinitesimally thin layers (or very long wavelengths) the permittivity of the stack for TE-polarized illumination is a simple average ε ത=(ε ଵ +ε ଶ )/2. The effects we show here, which violate effective medium theory, appear when the st...

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

“…Specifically, and following two main results in [35], we will introduce two quantities: (8) The first one, , is essentially the difference between the reflectance of the actual multilayer and its homogenized counterpart, since the structure with can be regarded as "quasi-homogenous"; we recall that all discrepancies , as defined in Equation 4, scale quadratically with the period of the structure [cf. Figure 1(c)], so is "400 times more homogenous" than .…”

“…Nevertheless, a recent theoretical paper by H.H. Sheinfux et al [35] demonstrates that this commonly believed assumption may fail in certain regimes. Namely, when the angle of incidence is close to the critical angle of the total internal reflection, the actual multilayer and its effective-medium counterpart can have significantly different transmission spectra despite the deeply subwavelength layer thicknesses (smaller than 1/50 of the wavelength).…”

“…Additionally, if the refractive indices of the medium behind the multilayer is carefully chosen, the transmission spectra become dependent on the choice of the outermost ("opening") layer (i.e., ABAB…AB vs. BABA…BA), totally contrary to the effective medium theory results. This "anomalous" EMA breakdown reportedly happens because for a wave incident at a near-critical angle, the optical properties of the multilayer arise from the interference effects between phases of Fresnel reflection and transmission coefficients in the frustrated total internal reflection regime rather than between phases accumulated during wave propagation in subwavelength layers [35].…”

“…for sensing and switching applications. However, the breakdown of the EMA reported in [35] only becomes noticeable when the multilayer contains a large number of layers (on the order of several hundreds), which should have equal thickness, as even a very minor thickness randomness would smear the effect due to its extreme sensitivity to the layer thicknesses. Such a structure, having at least 150-200 layers with 10 nm thickness and <1 nm tolerance, would be impractical for any experimental realization.…”

Effective medium approximation for deeply subwavelength all-dielectric multilayers: when does it break down?

“…However, the possibility of using the effective medium theory with geometries as simple as a multilayer dielectric stack under the principal condition of homogenization applicability, namely that the layer thicknesses must be small compared with the wavelength of light that interacts with them, has hardly ever been questioned from the very introduction of the effective medium approximation (EMA) 12 . Hence, alldielectric subwavelength multilayers, in which no waves with extremely large wave vectors are supported, have been expected to unconditionally obey the EMA Recently, the theoretical paper by Sheinfux et al 14 showed that this commonly believed assumption may fail in certain regimes even for the deeply subwavelength layer thicknesses (smaller than 1/50 of the wavelength). Namely, when the angle of incidence is approaching the critical angle of the total internal reflection, the multilayer stack and its effectivemedium counterpart exhibit significantly different transmission.…”