Existence Conditions of High‐k Modes in Finite Hyperbolic Metamaterials

Abstract

The capability to support optical waves with very large wave vectors (high‐k) is one of the principle features of hyperbolic metamaterials (HMMs). These waves play the key role in HMM applications such as imaging and lifetime engineering. Effective medium approximation (EMA) as widely used analytical method to predict HMMs behavior, has shortcomings in calculating high‐k modes of practical structures. EMA is applicable to a subwavelength unit cell of implicitly infinite periodic structures. Using conventional EMA, in the present paper, boundary effects and spatial dispersion are taken into consideration to properly compute the high‐k modes of finite‐thickness multilayer HMMs. Applying nonlocal homogenization to stacks of alternating metal‐dielectric layers, the corresponding effective medium is examined as a high‐k waveguide sandwiched between the substrate and an ambient superstrate. The developed theory enables us to recognize two types of bulk waves coined as short‐range and long‐range propagating modes. Number of such modes as well as their cutoff conditions are quantified for the first time. Validity of the developed theory is verified both numerically by rigorous simulations of the multilayer structures with the transfer matrix method and experimentally by optical characterization of the HMMs in infrared regime.

Optics with hyperbolic materials [Invited]

“…The first observation of BPP was realized for a Au/SiO 2 multilayer structure with a Si prism coupler in the near-IR range [34]. High-k waves are also observed by Ge prism for mid-infrared wavelengths [16]. BPPs can be tailored by controlling the geometry of the metamaterial.…”

“…In this way it is possible to modify (in some extent) effective optical properties accordingly to the requirements. Note that EMA does not always hold: there are many constrains on the thicknesses of the layers, number of periods, and range of angles of incidence [16,56,57]. Moreover, for very large values of wavevectors, dispersion starts to deviate significantly from that predicted by the effective medium approximation [58].…”

“…Au/SiO 2 multilayers were fabricated for the observation of highk BPPs excited with the help of a Si prism [34]. Apart from Au as a material for conductive films for visible to near-IR wavelengths [16,34], other materials like silver (Ag) [11,[59][60][61], titanium nitride (TiN) [62], aluminum-doped zinc oxide (AZO) [63], and doped semiconductors [10] have been reported plasmonic constituent layers of HMMs. In case of semiconductors, multilayer HMM can be made of the same semiconductor but with different doping levels: highly doped layers serve as metal and low doped layers serve as dielectric [15].…”

“…Typically, HMMs contain alternating deeply-subwavelength metal and dielectric features. Among basic HMMs configurations there are multilayer stacks with thin films of subwavelength thicknesses [10][11][12][13][14][15][16], shallow [17,18] and deep nanotrenches structures [19][20][21], and arrays of metal nanowires [22][23][24][25][26][27][28] as illustrated in Fig. 1.…”

Mode-resolved directional enhancement of spontaneous emission inside/outside finite multilayer hyperbolic metamaterials

“…Yet, in practice, the constrains imposed by thickness of the building blocks and nonlocal effects proved that the LDOS of HMMs must be finite [22,23]. Af-30 filiation of LDOS to the high-k modes and the relevance of such modes to the number of periods in multilayer structures [24], creates an urge to study the individual high-k modes in finite thickness structures. Since the number of periods in HMM structures is a very practical question, an analysis of contribution of individual modes of finite thickness HMMs in total LDOS is needed to investigate the necessary number of periods required for providing a large LDOS in application-orientated multilayer HMMs.…”