Three-Dimensional Electromagnetic Metamaterials with Non-Maxwellian Effective Fields
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1014-AA10-01
Three-Dimensional Electromagnetic Metamaterials with Non-Maxwellian Effective Fields Jonghwa Shin, Jung-Tsung Shen, and Shanhui Fan Ginzton Lab, Stanford University, Stanford University, CA, 94305 ABSTRACT It is commonly assumed that the long-wavelength limit of a metamaterial can always be described in terms of effective permeability and permittivity tensors. Here we report that this assumption is not necessary—there exists a new class of metamaterial consisting of several interlocking disconnected metal networks, for which the effective long-wavelength theory is local, but the effective field is non-Maxwellian, and possesses much more internal degrees of freedom than effective Maxwellian fields in a local homogeneous medium. INTRODUCTION Metamaterial systems have become of interest lately because they are the foundation of a variety of unusual electromagnetic effects 1. Such systems consist of a periodic array of metallic or dielectric elements, and operate in a long-wavelength regime where the wavelengths of electromagnetic radiations are far larger than the periodicity. The properties of metamaterial systems can be described by solving Maxwell’s equations in highly inhomogeneous microscopic structures. As an alternative approach that generates deeper physical insights, however, one also seeks to illustrate their long-wavelength properties by constructing an effective field theory in an equivalent homogenous medium [1,2]. (The process for constructing such equivalent medium is sometimes referred to as homogenization [3].) If the effective, macroscopic fields satisfy Maxwell’s equations, we refer to them as Maxwellian. While many metamaterial systems can be described by equivalent uniform Maxwellian media with interesting effective ε and µ tensors [4–10], there is no general proof that it is always possible. Instead, various difficulties of homogenization for certain metallic systems have been noted, for example, in Refs. [11,12]. Here we study three-dimensional structures consisting of several interlocking, disconnected metal networks. Each network by itself is connected in full three dimensions. We formulate theory based on non-Maxwellian effective fields. The effective field features large numbers of internal degrees of freedom, which are completely determined by the geometry. The complexity of the effective field here suggests that the physics of metamaterial can be easily designed to be far richer than what has been typically assumed. We include three examples (Fig. 1) of such systems with a cubic unit cell having either cubic (Oh) or pyritohedral (Th) point group symmetry (13), and report a set of remarkable electromagnetic phenomena in the longwavelength limit. In particular, there is no constraint on the number of modes that can be supported by this class of systems, and their modes’ degeneracy and spatial dispersion are simply related to the geometry.
Figure 1. Interlocking metallic-network structures. (a)-(c) Structures in a single cubic unit cell are depicted. Each color represents a sep
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