Photonic Metamaterials

Negative Refractive Index Metamaterials

A far-reaching development in modern nanophotonics and nanoengineering has been the conception and practical implementation of materials exhibiting simultaneously negative electric permittivity and magnetic permeability, known also as left-handed metamaterials (LH-MMs). Their conceivable strong economic and social impact, owing to their potential applicability in diverse realms of science, such as telecommunications, radars and defence, nanolithography with light, microelectronics, medical imaging, and so on, has lately prompted an overwhelming excitement within the scientific community [1]-[3].

The history of MMs appears to be dating back to the pioneering work of Kock [4] in the late 40’s; while working at Bell Labs with Sergei Schelkunoff, renowned for his “field equivalence principles” and for his work on antennas theory, Kock published a series of works wherein he proposed numerous ideas for constructing lightweight and small-volume “artificial dielectrics”, used as microwave lenses in antenna systems. Amongst others, he studied the response to an incident quasi-static electromagnetic radiation of isolated or regularly-arrayed metallic particles of various shapes, such as spheres, discs, ellipsoids and prolate or oblate spheroids. He concluded that such structures effectively behave as a dielectric medium, whose permittivity ε and permeability μ can be purposely tuned (but not independently of each other) to an arbitrarily large or small, even negative, value by properly arranging the particles in three dimensions, i.e. the optical properties of the medium depended solely on the particles’ geometrical set up, rather than on their own intrinsic behaviour. Kock also showed that a specially-designed structure, which lately has come to be known as “split-ring resonator” (SRR), can be used to independently increase the permeability μ such that one can reduce or altogether eliminate the diamagnetic nature of the aforementioned composite structures. His work rose considerable interest within the engineering community of the time, with a number of works extending or elaborating on his ideas. Since then, it has been the subject of detailed coverage in standard engineering textbooks [5].

More than a decade later, Rotman [6] also considered the quasi-static response of an array of thin conducting wires, and he showed that such structure closely resembles, on the macroscopic level, a plasma medium. In particular, he proved that the electric permittivity ε of this artificial dielectric medium varies with frequency following a Drude-type law. Consequently, below a certain “cutoff” frequency no incident electromagnetic radiation could penetrate it. Critically, however, neither Kock nor Rotman or, indeed, any of the early contributors investigated the properties of media exhibiting concurrently negative ε and μ. Partly, that was because the main motivation behind similar works at that time was to design plasma media at RF or microwave frequencies that would closely simulate the ionosphere, prompted by NASA’s desire to secure the safe re-entrance of space-capsules into the earth’s atmosphere.              

Veselago [7] was evidently the first to systematically consider, in the late 60’s, the possibility and some properties of “double-negative materials” (DNGMs). In particular, he showed that a negative electric permittivity ε and magnetic permeability μ would imply a reversal of almost all known electromagnetic phenomena, including the angle of refraction inside a DNGM (e.g., θt = – 20o), the Doppler effect, the sign of the refractive index n (e.g. n = – 1) and the right-handedness of the E, H and k vector-triad, from where the designation of such materials as “left-handed” origins. In spite of his noteworthy findings, and apparently unaware of Kock’s and other workers’ research in the same field, Veselago did not go on to materialise his theoretical conclusions. Even so, his work did not go unnoticed and he was invited several times to highlight his research at major international scientific conferences [8].       

At present, the realm of “artificial dielectrics” or “meta-materials” (from the Greek word “meta”, which here means “beyond”) enjoys a breadth of scientific activity and exploration, having established a sound and coherent mathematical formalism, the predictions of which have been verified by numerous experimental and numerical-simulation works. This revived interest followed from a series of works by Prof. Sir John Pendry, wherein he proposed practical means for realizing LH-MMs experimentally [9]. Moreover, building on Veselago’s work, Pendry argued that a slab constructed by the same materials could, ideally, act as a “perfect lens”, overcoming the well-known diffraction limitations (see Figs. 1 and 2). After these insights, the physical construction of a composite LH structure has been demonstrated by Shelby et al. [10], and the possibility of achieving subwavelength resolution of an object with the same structure has been demonstrated with further experiments [11].

Figure1: Double mirror image in a negative refractive index (NRI) slab heterostructure (FDTD calculation).

Figure2: Ray-model analysis of the double-focusing effect in a NRI heterostructure. Also shown is the amplification of the source’s near-field (dashed, orange line) inside the NRI slab.

Recently, researchers from the Theory and Advanced Computation (TAC) group of the Advanced Technology Institute (ATI) succeeded in conclusively distinguishing and classifying all “modes” of guided electromagnetic energy along the aforementioned, generalized, LH slab heterostructures [12, 13]. In addition to oscillatory or waveguide modes (OMs/fast waves), which are also found in ordinary dielectric slab structures, a rich family of (30 in total) surface plasmon polariton modes (SPPs/slow waves), for all choices of opto-geometric parameters, were conclusively identified (see Figs. 3-4). Amongst others, closed-form expressions for the cutoff points of the modes were ascertained, a new nomenclature for identifying the oscillatory modes was proposed, invertion of the heterostructures was shown to result, remarkably, in equivalent waveguidance (same mode and dispersion diagrams) and, crucially, it was proved that the investigated waveguides were able to decelerate or altogether stop guided light pulses. This method for producing “slow-light” turns out to be unusually simple and bears a number of serious advantages compared to previously proposed ways of decelerating optical signals.

References

1. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X.   Zhang, Science 303, 1494 (2004).
2. A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature (London) 438, 17 (2005)
3. V. M. Shalaev, Nature Photonics 1, 41 (2007).
4. W. E. Kock, Bell System Technical J., 34, 828-836 (1946).
5. R. E. Collin, Field Theory of Guided Waves (IEEE Press, 2nd ed., 1991), chapter 12.
6. W. Rotman, IRE Trans. Antennas Propagat. 10, 82 (1962).
7. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
8. V. G. Veselago, in Proceedings of the First Taormina Research Conference on the Structure of Mater, Pergamon, 1972, edited by E. Burstein and F. De Martini (Pergamon Press, New York, 1974), p. 5.
9. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000), and references cited therein.
10. R. A. Shelby, D. R. Smith, and S. Shultz, Science 292, 77 (2001).
11. A. N. Lagarkov and V. N. Kissel, Phys. Rev. Lett. 92, 077401 (2004).
12. K. L. Tsakmakidis, A. Klaedtke, C. Jamois, D. P. Aryal, and O. Hess, Appl. Phys. Lett. 89, 201103 (2006).
13. K. L. Tsakmakidis, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, Phys. Rev. B 73, 085104 (2006).