Abstract
Hyperbolic metamaterials have attracted considerable interest in the research community for their peculiar ability to enhance control of electromagnetic waves' propagation. Although conformal transformation optics provides a unique platform for metamaterials design, this method has not been used for hyperbolic metamaterials yet. This comes from the lack of a well-defined mathematical structure. We extend conformal transformation optics to hyperbolic metamaterials, by applying Clifford algebra to analyze light propagation. We will show that the effective line element of a trajectory of light propagation conforms to ultrahyperbolic---not Euclidean---geometry. We also, by using conformal hyperbolic mapping, obtain all conformal spaces with Minkowski space-time. Finally, we employ this theory to study the electric-field pattern of dipoles.
Highlights
Electromagnetic metamaterials, known as artificial media created from subwavelength structures, can help control light propagation and engineer electromagnetic space
hyperbolic metamaterials (HMMs) play a highly important role in laboratory-based efforts to realize curved space-time; the Klein-Gordon equation governs the dynamical propagation of monochromatic extraordinary light in HMMs; in other words, the line element of the trajectory of light propagation can correspond to a timelike coordinate, i.e., a negative signature
By using Clifford algebra, we have studied the propagation of the extraordinary light in HMMs
Summary
Electromagnetic metamaterials, known as artificial media created from subwavelength structures, can help control light propagation and engineer electromagnetic space. Since the propagation of monochromatic extraordinary light in HMMs is governed by the Klein-Gordon equation instead of the Helmholtz equation [10], a mathematical framework for a description of conformal transformation optics in the context of curved space-time is worthy of close examination. Prepares a framework for realizing conformal space-time with Minkowski space-time, and conformal mapping connects classical optics with conformal field theory By using this method, we are able to control the behavior of light propagation in HMMs expected to have an important role in applied physics. We will study the electric-field patterns of dipoles in conformal HMMs. The rest of the paper is organized as follows: in Sec. II we introduce Clifford algebra to give a fully developed description of light propagation on both levels of Maxwell’s equations and ray optics.
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