The optical activity of an artificial non-magnetic uniaxial chiral crystal at microwave frequencies

Theron, I.P.; Cloete, J.H.

doi:10.1163/156939396x01125

Cited by 32 publications

(15 citation statements)

References 20 publications

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“…The choice of the solutions presented in (1) and (2) guarantees the satisfaction of the boundary conditions at the perfectly conducting plates at and . To satisfy the boundary conditions at the interface between the two slabs we should have (3) which leads to (4) In order to have a nontrivial solution, i.e., to have and , the determinant in (4) must vanish. That is (5) which can be simplified to (6) In the above dispersion relation, the quantities , , , , and are all generally frequency dependent.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability

Engheta

2002

Antennas Wirel. Propag. Lett.

570

329

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In this letter, we present and analyze theoretically some ideas for thin one-dimensional (1-D) cavity resonators in which a combination of a conventional dielectric material and a metamaterial possessing negative permittivity and permeability has been inserted. In this analysis, it is shown that a slab of metamaterial with negative permittivity and permeability can act as a phase compensator/conjugator and, thus, by combining such a slab with another slab made of a conventional dielectric material one can, in principle, have a 1-D cavity resonator whose dispersion relation may not depend on the sum of thicknesses of the interior materials filling this cavity, but instead it depends on the ratio of these thicknesses. In other words, one can, in principle, conceptualize a 1-D cavity resonator with the total thickness far less than the conventional λ/2. Mathematical steps and physical intuitions relevant to this problem are presented. KeywordsCavity resonator, metamaterials, negative index of refraction, negative permeability, negative permittivity, phase compensator, phase conjugation. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. -dimensional (1-D) cavity resonators in which a combination of a conventional dielectric material and a metamaterial possessing negative permittivity and permeability has been inserted. In this analysis, it is shown that a slab of metamaterial with negative permittivity and permeability can act as a phase compensator/conjugator and, thus, by combining such a slab with another slab made of a conventional dielectric material one can, in principle, have a 1-D cavity resonator whose dispersion relation may not depend on the sum of thicknesses of the interior materials filling this cavity, but instead it depends on the ratio of these thicknesses. In other words, one can, in principle, conceptualize a 1-D cavity resonator with the total thickness far less than the conventional /2. Mathematical steps and physical intuitions relevant to this problem are presented. Disciplines Electrical and Computer EngineeringIndex Terms-Cavity resonator, metamaterials, negative index of refraction, negative permeability, negative permittivity, phase compensator, phase conjugation.

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Section: Formulation Of the Problemmentioning

confidence: 99%

An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability

Engheta

2002

Antennas Wirel. Propag. Lett.

570

329

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“…42 To derive the linear relations (38) we first make the substitutions ∇ k → ik k and ∂/∂t → − iω in (1)-(3), and then perform macroscopic averages such as (15) in the manner described above. Then (20) and (21) yield…”

Section: Response Fieldsmentioning

confidence: 99%

On the transition from microscopic to macroscopic electrodynamics

Lange

Raab

Welter

2012

Journal of Mathematical Physics

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Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model J. Chem. Phys. 122, 034103 (2005); 10.1063/1.1831271Density-functional theory calculations of optical rotatory dispersion in the nonresonant and resonant frequency regions Implicit in the change from microscopic electrodynamics to a macroscopic, multipole theory is a set of molecule-fixed coordinate systems -and hence an arbitrary set of molecular origins {O n } -relative to which the positions of molecular constituents are specified. We examine the extent to which this theory satisfies a Van Vleck-Buckingham-type translational invariance with respect to the choice of {O n } in a linear, homogeneous, anisotropic medium. For contributions above electric dipole order, the theory is only partially invariant, and therefore incomplete: the corresponding macroscopic Maxwell equations yield unphysical results for certain phenomena. We propose a fully invariant formulation, based on the use of invariant molecular polarizability tensors in the quantum-mechanical expressions for expectation values of molecular multipole moments induced by harmonic, plane electromagnetic waves. We show that expressions for the invariant polarizabilities can be discerned from the partially invariant theory, and we discuss the uniqueness of our procedure. C 2012 American Institute of Physics. [doi:10.1063/1.3677767] the theory describes origin-independent observables is encapsulated in the following statement:To each multipole order (that is, electric dipole; electric quadrupole-magnetic dipole; electric octopole-magnetic quadrupole; etc), the theory forms a linear combination of various origin-dependent polarizabilities 26 in such a way that the overall expression for an observable is invariant due to cancellation − among the terms of that order − of changes produced by a shift in the molecular coordinate origin.(In view of its antecedence, it seems appropriate to refer to (II) as the Van Vleck-Buckingham condition.) These studies present a satisfying picture: theoretical expressions for observables that are expected to be origin independent are found to be so, and consequently their experimental values can be quoted without reference to a molecular coordinate origin. 27 However, we have shown that a notable exception occurs in the case of the macroscopic electromagnetic response fields D and H for a linear, homogeneous, anisotropic medium interacting with harmonic, plane electromagnetic waves. Here, the dynamic material constants (the permittivity, inverse permeability, and magnetoelectric coefficients) in the constitutive relations D(E,B) and H(E,B) are macroscopic observables whose experimental values are not linked to any coordinate origin. On the other hand, a direct calculation yields multipole expressions for these observables that are origin dependent 28, 29 (see also Secs. V and VII). This unacceptable result produces other unphysical features such as origin dependence of the energy flow 30 (the time average of the instantaneou...

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“…9 As can be seen, in the regions where the wavenumber are purely imaginary, so too is the transverse impedance (as one would expect). 10 We can understand the differences between the regions of real, imaginary, and complex by noting the value of equivalent sheet reactance in each region. In the first region, the sheet reactance (see Figure 4) is large and negative-this implies the x-component of wavenumber will be purely real.…”

Section: Wire Mediamentioning

confidence: 99%

“…In such regions, there is 9 The transverse impedance for the wave associated with the wavenumber is evaluated at the midpoint between the adjacent elementary planes. 10 Because of the granularity of the data, it appears that at certain points the impedance might be complex, however this is only a plotting artifact. The transverse impedance is either purely real or purely imaginary.…”

Section: Wire Mediamentioning

confidence: 99%

“…Recent research efforts in designing artificial complex material have introduced some unusual inclusions intended to achieve interesting electromagnetic features; as an example, inclusions intended to produce artificial material with similar characteristics as optically active (chiral) media have received much attention (e.g., [9,10,11]). Along with advances in inclusion design, researchers have proffered improved polarizability models (e.g., [12,13,14,15,16,17]) and mixing formulas (e.g., [18,19,20,21]).…”

Section: Introductionmentioning

confidence: 99%

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Electromagnetic wave propagation in the wire medium: a complex medium with long thin inclusions

Moses

Engheta

2001

Wave Motion

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The wire medium is a type of complex artificial material we conceptually envision as many identical finitelength, parallel, thin wire inclusions embedded within a host medium. It is representative of a class of novel artificial materials characterized by long thin inclusions. Unlike some conventional artificial material, the inclusions of this class are not necessarily electrically short. Here, we present our theoretical analysis for wire media and by studying certain salient features of plane-wave propagation through these media, introduce equivalent medium parameters that depend, among other parameters, on the direction of wave propagation. The approach we use separates the artificial material into its elementary planes and then uses periodic moment method techniques to individually characterize each elementary plane. Analytic formulas from periodic structure theory are then used to determine the effective wavenumber for the overall medium and the transverse impedance at the midpoint between adjacent elementary planes. Our examples show that some realizations of these media are spatially dispersive and may exhibit interesting features such as "angular windows of propagation" and other properties that are dependent on the polarization, frequency and direction of wave propagation. Disciplines Electrical and Computer Engineering AbstractThe wire medium is a type of complex artificial material we conceptually envision as many identical finite-length, parallel, thin wire inclusions embedded within a host medium. It is representative of a class of novel artificial materials characterized by long thin inclusions. Unlike some conventional artificial material, the inclusions of this class are not necessarily electrically short. Here we present our theoretical analysis for wire media and, by studying certain salient features of plane wave propagation through these media, introduce equivalent medium parameters that depend, among other parameters, on the direction of wave propagation. The approach we use separates the artificial material into its elementary planes and then uses periodic moment method techniques to individually characterize each elementary plane. Analytic formulas from periodic structure theory are then used to determine the effective wavenumber for the overall medium and the transverse impedance at the midpoint between adjacent elementary planes.Our examples show that some realizations of these media are spatially dispersive and may exhibit interesting features such as "angular windows of propagation" and other properties that are dependent on the polarization, frequency, and direction of wave propagation.

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The optical activity of an artificial non-magnetic uniaxial chiral crystal at microwave frequencies

Cited by 32 publications

References 20 publications

An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability

An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability

On the transition from microscopic to macroscopic electrodynamics

Electromagnetic wave propagation in the wire medium: a complex medium with long thin inclusions

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