Chapter 6 Negative-Index Metamaterials

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6 Negative-Index Metamaterials
consequences were discussed in works by Sir Arthur Schuster and Lamb as early as 1904 [1, 2]; later the optical properties of NIMs were studied by Russian physicists Mandel’stam [3] and Sivukhin [4]. The first systematic study of the general properties of a hypothetical medium with a negative refractive index is attributed to Veselago, then with the Lebedev Physical Institute in Moscow, who analyzed the consequences for electromagnetic waves interacting with such a medium and reported on his initial effort in searching for such materials [5]. He pointed out that when both " and are simultaneously negative, the negative square root must be chosen in the refractive index equation. Veselago coined the term “left-handed materials (LHMs)” for such media, because the field vectors E, H and the wave vector k form a left-handed system. He also noted that many remarkable properties would be associated with a negative index medium. The recent boom in NIMs was indeed inspired by Sir John Pendry, who not only provided a practical recipe on the building blocks for NIMs [6, 7], but also made critical predictions on the possible applications of metamaterials including perfect lenses and superlenses with subwavelength resolution [8], and an electromagnetic cloak of invisibility [9]. Left-handed materials are probably the most prominent class of metamaterials among all branches in the present metamaterial research. In fact, during the first few years of the metamaterial boom, the idea of a negative index of refraction was emphasized so much that the term metamaterial was often taken to be synonymous with negative index materials or left-handed materials. Although the term “left-handed materials” introduced by Veselago was initially assumed to be applicable for materials with "; and n being simultaneously negative (and real), this term now has been used in a much broader context and includes other optical systems that possess antiparallel phase velocity and Poynting vector. Such a “left-handedness” property can occur in a variety of systems, including photonic crystals, highly-anisotropic materials, metal-insulator-metal waveguides, and more. Some of these systems will be discussed in the last section of this chapter. Also it is worth noting that the term “left-handed materials” may introduce unnecessary confusion because this term also arises in the study of chiral materials. Therefore nowadays the term “negative-index (meta)materials” prevails among researchers in related fields. Another term used by metamaterial researchers for the same substance is “double-negative materials,” which emphasizes the fact that both " and have negative values in such a material. There are also other terms for NIMs, such as “backward wave media,” “negative phase-velocity media,” etc. These names, however, appear relatively sparsely in the literature. Because the index of refraction is a fundamental material parameter that enters into almost all basic formulae for optics, bringing the refractive index into a new domain of negative values has truly excited the imagination of researchers worldwide. These NIMs bring the concept of refractive index into a new domain of exploration and thus promise to create entirely new prospects for manipulating light, with revolutionary impacts on present-day optical technologies.
W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and ApplБайду номын сангаасcations, DOI 10.1007/978-1-4419-1151-3 6, c Springer Science+Business Media, LLC 2010
Chapter 6
Negative-Index Metamaterials
6.1 A Brief Historical Review
The refractive index is one of the most important parameters for an optical medium. Defined as n D c=v, it measures the comparative velocity of light in different media. When a light beam travels across the boundary between two different materials, it bends owing to the change in refractive index at the interface. This phenomenon, refraction, gives the reason why a water pool appears shallower than it actually is, why a straw placed partially in water at a slant seems to bend towards the surface, and why people can use eyeglasses to adjust the path of light in front of their eyes and alleviate the effects of conditions such as myopia. The refractive index is a complex number n D n0 C i n00 , where the imaginary part 00 n characterizes the losses in the material. Using the electromagnetic description of light given by Maxwell’s equations, the refractive index n is related to basic material parameters, namely the permittivity " and the permeability , via n2 D " . Therefore there is ambiguity in choosing the sign of n because mathematically there p are two solutions for the refractive index: n D ˙ " . For all known naturally occurring transparent materials like water or glass, both " and are positive and p thus the refractive index can be written as n D " . For anisotropic media like crystals or absorbing materials such as metals, the situation is more complicated and a tensor or complex value of the refractive index is required for describing the optical behavior of such materials. However, for any naturally existing material it is always true that the positive square root should be chosen. But what about a negative sign in front of the square root? Is there any fundamental law of physics that prevents such a thing from happening? If not, what would happen to electromagnetic fields in a medium with a negative index of refraction? And finally, how could we create such a material in reality? All these questions are to be addressed in this chapter. Although the research field of negative-index materials (NIMs) is a fairly new topic that has blossomed in the literature for fewer than 10 years, it is probably not that surprising to learn that a few scientific giants actually considered phenomena related to NIMs quite some time ago. These studies were perhaps so early that they could not be fully appreciated by contemporaries. Negative phase velocity and its