Superresolution with dynamic nanogratings and acoustic phonon scatteringWe show how to overcome the diffraction limit with ultrahighfrequency 

Radiative decay engineering in hyperbolic metamaterialsOne obvious application of the infinite photonic density of state that is the hallmark of hyperbolic materials is in controlling emission properties of dipoles coupled to the medium. In the Tutorials in Metamaterials chapter (info below) and in my thesis I provide the exciting details! 

Slow light in hyperbolic metamaterialsHMMs exhibit negative group velocities in waveguides, making it possible to slow down or even stop light. This paper was the first to give a detailed description of slow light in planar waveguides, a full year before this topic became officially cool. 

Reflection and transmission properties of hyperbolic structuresI provided models and calculations for the two groups doing proofofprinciple experiments in planar hyperbolic materials. The result of our work can be seen here and here. 

Negative refraction and planar lenses in HMMsNot olny does hyperbolic media support negative refraction, but, by some metrics, it performs better than the traditional plasmonic μ< 0 superlens. Details can be found in this paper and in Chapter 4 of my thesis. 

The HyperlensAfter developing the basic computations for planar hyperbolic metamaterials, I helped adapt this formalism for the case of cylindrical structures. This turned out to be an intensely interesting problem in its own right, and it is currently being studied by Zubin Jacob. Here is the preprint of the original paper. It was one of the more intense paperwriting experiences of my career, but it did result in hundreds of citations! 

Naturallyoccuring hyperbolic materialsA littleappreciated fact about the hyperbolic dispersion relation is that under certain circumstances, it can occur in nature. When it does, it can be found typically in the midtofar IR (or even THz) in a narrow frequency band. Examples include bismuth at 50 micron wavelengths and sapphire around 20 microns. Here's a preprint that describes three known natural hyperbolic materials. 
Book chapters:
 L. V. Alekseyev and E. Narimanov, Radiative Decay Engineering in Metamaterials, in Tutorials in Metamaterials, M. A. Noginov and V. A. Podolskiy (Eds.), pp. 209223. New York: CRC Press, 2012
 L. V. Alekseyev, Z. Jacob, E. Narimanov, Optical Hyperspace: Negative Refractive Index and Subwavelength Imaging, in Tutorials in Complex and Photonic Media, M. A. Noginov et al. (Eds.), pp. 3355. Bellingham: SPIE Press, 2009
Publications:
 Alekseyev LV, Narimanov EE, Khurgin J. Superresolution spatial frequency differentiation of nanoscale particles with a vibrating nanograting. Applied Physics Letters 100, 011101 (2012)
 Alekseyev LV, Narimanov EE, Khurgin J. Superresolution imaging via spatiotemporal frequency shifting and coherent detection. Optics Express 19, 2235022357 (2011)
 Alekseyev LV, Narimanov EE, Tumkur T, et al. Uniaxial epsilonnearzero metamaterial for angular filtering and polarization control. Applied Physics Letters 97(13):131107 (2010)
 Jacob Z, Alekseyev LV, Narimanov E. Semiclassical theory of the hyperlens. Journal of the Optical Society of America. A, Optics, image science, and vision 24(10):A529 (2007)
 Hoffman AJ, Alekseyev L, Howard SS, et al. Negative refraction in semiconductor metamaterials. Nature Materials 6(12):94650 (2007)
 Alekseyev LV, Narimanov E. Slow light and 3D imaging with nonmagnetic negative index systems. Optics Express 14(23):11184 (2006)
 Jacob Z, Alekseyev LV, Narimanov E. Optical Hyperlens: Farfield imaging beyond the diffraction limit. Optics Express 14(18):824756 (2006)
 Alekseyev LV, Podolskiy VA, Narimanov EE. Nonmagnetic negativerefraction systems for terahertz and farinfrared frequencies. arXiv:1201.4514v1 [physics.optics] (2006)
 Podolskiy VA, Alekseyev LV, Narimanov EE. Composite materials with giant anisotropy and negative index of refraction. Proc. SPIE 5928, 59280C (2005)
 Podolskiy VA, Alekseyev LV, Narimanov EE. Strongly anisotropic media: the THz perspectives of lefthanded materials. Journal of Modern Optics 52(16):23432349 (2005)
Ph.D. thesis:
Nonmagnetic Optical Metamaterials: Fundamentals and Applications
(Department of Electrical Engineering, Princeton University, 2011)