Journal of Quantitative Spectroscopy & Radiative Transfer 158 (2015) 3–16 Contents lists available at ScienceDirect Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt Review Implementation of optical dielectric metamaterials: A review Shandra J. Corbitt, Mathieu Francoeur, Bart Raeymaekers n Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA article info abstract Article history: Metamaterials are a class of man-made materials with exotic electromagnetic properties. Received 18 September 2014 The ability to fabricate three-dimensional macroscale metamaterials would enable Received in revised form embedding these structures in engineering applications and devices, to take advantage 29 October 2014 of their unique properties. This paper reviews the implementation of optical Mie Accepted 8 December 2014 resonance-based dielectric (MRD) metamaterials, as opposed to the more commonly Available online 17 December 2014 used metallic-based metamaterials. Design constraints are derived based on Mie theory Keywords: and related to fabrication specifications. Techniques to fabricate optical dielectric Dielectric-based metamaterials metamaterials are reviewed, including electron-beam lithography, focused ion beam Manufacturing lithography, nanoimprint lithography, and directed self-assembly. The limitations of each Mie resonances fabrication method are critically evaluated in light of the design constraints. The Optical response challenges that must be overcome to achieve fabrication and implementation of macro- scale three-dimensional MRD metamaterials are discussed. & 2014 Elsevier Ltd. All rights reserved. Contents 1. Introduction . 3 2. Design and fabrication requirements for engineering electric and magnetic resonances with MRD metamaterials . 4 3. Fabrication techniques for MRD metamaterials . 6 3.1. Compacting randomly oriented, jagged-shaped particle distributions . 6 3.2. Directed self-assembly. 7 3.3. Electron beam lithography . 8 3.4. Focused ion beam lithography and milling . 10 3.5. Imprinting/embossing techniques. 10 4. Discussion and outlook . 11 4.1. Alternative fabrication techniques . 11 4.2. Outlook ......................................................................................... 11 Acknowledgments . 12 Appendix A Physics of electric and magnetic resonances in MRD metamaterials . 13 References............................................................................................. 14 1. Introduction Electromagnetic metamaterials refer to a class of man- n Corresponding author. Tel.: þ1 801 585 7594; fax: þ1 801 585 9826. made materials consisting of sub-wavelength unit structures E-mail address: [email protected] (B. Raeymaekers). that display exotic properties such as negative magnetic http://dx.doi.org/10.1016/j.jqsrt.2014.12.009 0022-4073/& 2014 Elsevier Ltd. All rights reserved. 4 S.J. Corbitt et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 158 (2015) 3–16 permeability, negative electric permittivity and/or negative metamaterials are expected to be smaller than for metallic index of refraction [1–3]. The size of the unit structures, also metamaterials [25]. referred to as “meta-atoms”, is significantly smaller than the The electromagnetic response of MRD metamaterials operating wavelength, but larger than the atomic and mole- can be engineered by varying the host medium and the cular structure [1]. The electromagnetic response of a meta- shape, shape distribution, material, size, size distribution, material is the result of complex interactions between spatial arrangement or concentration of the dielectric incident electromagnetic waves and the sub-wavelength unit inclusions. The spatial arrangement of the inclusions can structures, and can be predicted via a homogenization be adjusted from randomly dispersed to periodic, since the approach based on the effective electric permittivity and effective properties rely on the resonances of the dielectric magnetic permeability. The possibility of tailoring the electro- inclusions, not the periodicity of the arrangement [1].Asa magnetic properties of a material by designing the unit result, the role of fabrication imperfections in MRD meta- structure of the meta-atoms has paved the way to conceptua- materials is less important than in the case of metallic lizing many novel devices and technologies such as super- metamaterials, where alignment and periodicity of the lenses [4–8],hyperlenses[9,10], and optical cloaking [11–13]. features is critical to obtaining the desired response. Metamaterials also find application in nanoantennas [14,15], MRD metamaterials operating in the microwave spec- radiative cooling [16], thermal radiative property control tral band have been experimentally studied over the past [17–20] as well as in energy harvesting and conversion few years [28–32]. The size of the inclusions and their devices [21,22] to only name a few. separation distance can be as large as a few millimeters Most metamaterials operating in the optical frequency and, thus, fabrication is less challenging and can be band that are documented in the literature are made of accomplished with traditional, macroscale techniques. metallic meta-atoms such as split-ring resonators, thin This review focuses on MRD metamaterials operating wires, rods or fishnet structures [1,23]. They require two at optical wavelengths, which covers both the visible and types of meta-atoms to induce both electric and magnetic the infrared spectral bands. Although several optical MRD responses. For instance, split-ring resonators are employed metamaterials have been developed theoretically [33–42], for tailoring the effective permeability while wires enable few authors provide detailed information about possible control of the effective permittivity [24], thus offering fabrication methods, and even fewer published works flexibility to the metamaterial designer. However, metallic documenting successful fabrication and implementation metamaterials also present several drawbacks. Fabrication of optical MRD metamaterials [27,43–48]. In addition, the of the intricate structures that form the meta-atoms specimens fabricated in these studies are typically micro- typically requires sophisticated micromanufacturing tech- scale two-dimensional (2D) specimens, with restrictions niques, which are time consuming and not easily scalable on the orientation of incident waves. Thus, they cannot to manufacture macroscale three-dimensional (3D) speci- easily be used in macroscale engineering applications. To mens that can be integrated in engineering devices [25]. take advantage of the exotic electromagnetic properties of Additionally, large ohmic losses exist, and the effective MRD metamaterials in engineering systems and applica- electromagnetic response of the metamaterial is anisotro- tions, fabrication of 3D macroscale metamaterial speci- pic as a result of the asymmetric geometry of the metallic mens is imperative. Hence, high-precision, high- split-ring and wire inclusions. throughput, and low-cost scalable manufacturing pro- In contrast, Mie resonance-based dielectric (MRD) cesses are needed to fabricate macroscale 3D MRD struc- metamaterials consist of dielectric meta-atoms, such as tures operating at optical frequencies. Furthermore, spherical, cylindrical, or randomly shaped inclusions integration between metamaterial design and fabrication embedded in a dielectric host medium. The electric and is critical to successfully implementing macrosale MRD magnetic resonances of the inclusions are the building metamaterials. Thus, the objective of this review is two- blocks that dictate the effective electromagnetic properties fold. First, we establish the design and fabrication require- of the metamaterial. Mie theory offers an exact solution of ments needed to implement MRD metamaterials. Second, Maxwell's equations for electromagnetic wave scattering we review the manufacturing techniques that have been and absorption by a single spherical particle [26]. The term reported in the literature to successfully fabricate a proof- “Mie” is loosely used for MRD metamaterials to specify of-concept of all-dielectric optical metamaterials. Addi- that the effective electromagnetic response of the meta- tionally, we discuss fabrication techniques that have been material depends on the electric and magnetic resonances proposed, or are viable in principle, but have not yet been of the dielectric inclusions. However, these dielectric successfully implemented for MRD metamaterials. We inclusions are not restricted to spheres and may take point out that a review of fabrication techniques for various shapes. metallic-based metamaterials has been provided by Bol- MRD metamaterials present potential advantages com- tasseva and Shalaev [23]. pared to metallic metamaterials. Since the electromagnetic response of MRD metamaterials relies on the electric and 2. Design and fabrication requirements for engineering magnetic resonances of dielectric inclusions, only one type electric and magnetic resonances with MRD of inclusion can be used to induce both effective electric metamaterials and magnetic resonances. Additionally, an isotropic elec- tromagnetic response can be obtained with spherical The effective electromagnetic response of MRD meta- inclusions or by using a large amount of randomly materials depends on the interplay between the dielectric oriented, non-symmetric inclusions [27]. Losses for MRD inclusions