## Abstract

This special issue presents a cross-section of recent progress in the rapidly developing area of optics of hyperbolic metamaterials

©2013 Optical Society of America

The beginning of the 21st century coincided with the invention of an entirely new materials platform – *metamaterials* – engineered multi-phase composite materials containing inclusions that often have tailored shapes, sizes, mutual arrangements and orientations. Such materials exhibit unparalleled responses to many types of wave excitations, including electromagnetic, acoustic and thermal.

Metamaterials promise to alleviate the common limitations of optics, increasing the resolution of imaging systems and providing new avenues for manipulating refraction, reflection, and guidance of light. Materials with negative indices of refraction, “perfect” lenses and hyperlenses that focus and image with resolution beyond the diffraction limit, invisibility cloaks, and nanoscopic lasers — are just some of the emerging concepts that have resulted from the evolving view of what constitutes a material.

Hyperbolic (highly anisotropic) homogeneous- and meta-materials, in which dielectric permittivities in orthogonal directions have different signs, have recently generated a lot of interest because of their unique physical properties and unmatched potential applications. In striking contrast to all commonly known media, in which iso-frequency dispersion surfaces are spheroids or ellipsoids, iso-frequency dispersion surfaces in said anisotropic materials are hyperboloids, determining the name *hyperbolic (meta)material* (also known as indefinite media). Although few natural materials have hyperbolic dispersion in the far-infrared range, known hyperbolic media in the *visible* and *near-infrared* parts of the spectrum are engineered metamaterials: ordered arrays of metallic nanowires and lamellar metal/dielectric or semiconductor multi-layered thin film structures. Because of their unique dispersion characteristics, hyperbolic metamaterials can propagate waves with nominally infinitely large wavevectors (and infinitely short wavelengths) and have a broad-band singularity of the (nominally infinite) density of photonic states. The former property is used in a “hyperlens” providing for a deep sub-wavelength resolution, while the latter phenomenon leads to a wide range of fundamental quantum and classical effects.

This focus issue presents a snapshot of recent developments in optics of hyperbolic systems, covering the areas as diverse as new fabrication techniques to theoretical predictions of new phenomena unique to hyperbolic systems, and even cosmological problems that might be modeled in metamaterials.

In [1] A. Kildishev et.al present a review of progress and challenges in the area of hyperbolic materials and systems.

In [2], S.M. Pokes et.al. present the a comprehensive study of optical properties of new class of optical metamaterials, based on Si/Ag nanowire arrays. The manuscript describes the fabrication of this new material system, presents the spectroscopic study of these composites, and analyzes the dynamics of light emission in these systems. Analytical model describing the linear response of this structure is also presented.

Hyperbolicity of optical modes in composite systems remains an active research area. In [3], S. Zhukovsky et.al. study the origin of the bulk plasmon – a unique collective mode that can propagate in the bulk of hyperbolic systems.

G. Milton et.al [4]. present a theoretical analysis of a two-dimensional hyperbolic medium, and reveal curious dissipation patterns as well as a “search-light” effect with the remote dipoles strongly interacting when placed to the appropriate positions.

Hyperbolic systems are known to offer strong enhancement of density of states. Inspired by this phenomenon, strong enhancement of Casimir torque inside hyperbolic structures is discussed by T. Morgado with colleagues [5], who design the required dispersion by combining metal nanorods with dielectric fluids, and show an efficient channeling of quantum fluctuations.

With regards to practical applications of hyperbolic media, the perspectives of transfer of thermal energy by hyperbolic structures are studied in [6] and [7]. C. Simovski et al. [6] study the viability of a huge enhancement of the radiative heat transfer in thermophotovoltaic systems, and discuss the optimal design strategy, while Y. Guo et al [7] investigate the role of specific electromagnetic states enabled by myltilayered stack of metamaterials with hyperbolic dispersion, in achieving an efficient thermal emission. It has been demonstrated that the heat transfer across a nano-gap in the metamaterial systems can be very strong, and its spectral selectivity can be optimized on demand.

Strongly anisotropic structures often drastically modify optics of closely positioned quasi-static systems, like dipoles. Anomalous behavior of field distribution in quasi-static systems in proximity to hyperbolic structures is discussed in [4].

In the absence of diffraction limit, the limitations to performance of hyperbolic metamaterials come from optical absorption and from nonlocal optical response. The former class of limitations can be somewhat compensated by optical gain. The perspectives of such compensation, and the possibilities for nonlinear interaction in hyperbolic structures are discussed in [8]. The “ultimate limits” of hyperbolicity, dictated by optical nonlocalities are analyzed in [9]. In particular, it is shown that focusing characteristics of a hyperbolic metamaterial lens in the local response approximation and and in the non-local hydrodynamic Drude model can differ significantly.

Hyperbolic metamaterials continue to inspire and enable numerous science-fiction-like applications. In this issue, sub-wavelength imaging with lenses based on strongly anisotropic metamaterials are discussed in [10].

Strong suppression of reflection from roughened hyperbolic metamaterials is reported in [11]. This phenomenon, demonstrated experimentally in arrays of silver nanowires grown in alumina membranes, is consistent with a broad-band singularity in the density of photonic states. It paves the road to a variety of applications ranging from the stealth technology to high-efficiency solar cells and photodetectors.

Novel possibilities for controlling light polarization with thin anisotropic metamaterials are discussed in [12]. In particular, it is shown that l/20 thick slab of a highly anisotropic metamaterial may provide nearly linear-to-circular polarization conversion or 90° linear polarization rotation. In a related class of applications, metamaterials offer new opportunities for manipulating optical pulses. On this track, J.Sun et.al [13]. discusses a design of biaxial metamaterial based on silver nanowires, which provides and inter-conversion between Gaussian beams and vortices.

The work of Z. Huang et.al [14]. presents a new class of transmission resonances that can be observed in hyperbolic structures. The work demonstrates that hyperbolic structures can be combined with conventional material to build ultra-thin Fabri-Perot-type resonators.

Hyperbolic systems find their applications far beyond photonics and plasmonics. In their work [15] I. Smolyaninov et.al. use thermal fluctuation of nanoparticle concentration in a cobalt based nanofluid, which lead to transient formation of hyperbolic regions, to study the evolution of individual Minkowski space-times the cosmological multi-universe.

We hope that the collection of the papers, presented in this issue, will not only familiarize the reader with the current cutting-edge research on optics of hyperbolic systems, but will motivate new research directions in this exciting and rapidly developing research field.

## Acknowledgments

We are grateful to all the authors for their valuable contributions, to the Optics Express Editors, Martijn de Sterke and Andy Weiner, for their support, and are especially thankful to OSA staff, and to Carmelita Washington in particular, for making this issue a reality.

## References and links

**1. **V. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic Metamaterials: new physics behind a classical problem,” Opt. Express **21**(12), 15048–15064 (2013).

**2. **S. Prokes, O. J. Glembocki, J. E. Livenere, T. U. Tumkur, J. K. Kitur, G. Zhu, B. Wells, V. A. Podolskiy, and M. A. Noginov, “Hyperbolic and plasmonic properties of Silicon/Ag aligned nanowire arrays,” Opt. Express **21**(12), 14962–149714 (2013).

**3. **S. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express **21**(12), 14982–14987 (2013).

**4. **G. Milton, R. C. McPhedran, and A. Sihvola, “The searchlight effect in hyperbolic materials,” Opt. Express **21**(12), 14926–14942 (2013).

**5. **T. Morgado, S. I. Maslovski, and M. G. Silveirinha, “Ultrahigh Casimir interaction torque in nanowire systems,” Opt. Express **21**(12), 14943–14955 (2013).

**6. **C. Simovski, S. Maslovski, I. Nefedov, and S. Tretyakov, “Optimization of radiative heat transfer in hyperbolic metamaterials for thermophotovoltaic applications,” Opt. Express **21**(12), 14988–15013 (2013).

**7. **Y. Guo and Z. Jacob, “Thermal hyperbolic metamaterials,” Opt. Express **21**(12), 15014–15019 (2013).

**8. **C. Argyropoulos, N. M. Estakhri, F. Monticone, and A. Alù, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express **21**(12), 15037–15047(2013).

**9. **W. Yan, A. Mortensen, and M. Wubs, “Hyperbolic metamaterial lens with hydrodynamic nonlocal response,” Opt. Express **21**(12), 15026–15036 (2013).

**10. **B. H. Cheng, Y. C. Lan, and D. P. Tsai, “Breaking optical diffraction limitation using optical hybrid-super-hyperlens with radially polarized light,” Opt. Express **21**(12), 14898–14906 (2013).

**11. **E. E. Narimanov, H. Li, Y. A. Barnakov, T. U. Tumkur, and M. A. Noginov, “Reduced reflection from roughened hyperbolic metamaterial,” Opt. Express **21**(12), 14956–14961 (2013).

**12. **P. Ginzburg, F. J. Rodriguez Fortuno, G. A. Wirtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Y. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, “Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials,” Opt. Express **21**(12), 14907–14917 (2013).

**13. **J. Sun, J. Zeng, and N. M. Litchinitser, “Twisting light with hyperbolic metamaterials,” Opt. Express **21**(12), 14975–14981 (2013).

**14. **Z. Huang and E. E. Narimanov, “Zeroth-order transmission resonance in hyperbolic metamaterials,” Opt. Express **21**(12), 15020–15025 (2013).

**15. **I. I. Smolyaninov, B. Yost, E. Bates, and V. N. Smolyaninova, “Experimental demonstration of metamaterial “multiverse” in a ferrofluid,” Opt. Express **21**(12), 14918–14925 (2013).