Material parameters of metamaterials (a Review)
TL;DR: In this article, a theory of the homogenization of a certain class of metamaterials is stated, and a more widespread method of determining the material parameters of met amaterials based on the extraction of the refractive index and the characteristic impedance from the scattering matrix of the plate of the metammaterial is discussed.
Abstract: A theory of the homogenization of a certain class of metamaterials is stated. These metamaterials are volume lattices of electric and magnetic dipoles that are resonant with frequencies that are considerably lower than that of the first Bragg resonance of the lattice. It was shown that, for plates of a metamaterial, which are described by bulk material parameters, transition layers play an important role, and the known Drude notion of transition layers is significantly revised. The paper also discusses a more widespread method of determining the material parameters of metamaterials based on the extraction of the refractive index and the characteristic impedance from the scattering matrix of the plate of the metamaterial. The physical meaning of the material parameters obtained in this way is clarified, and the concept of Bloch lattices related to it is discussed. It is shown that the bulk material parameters and the parameters of transition layers can also be extracted from components of the scattering matrix of plates.
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TL;DR: In this paper, an accurate homogenized description of periodic metamaterials made of magnetodielectric inclusions was derived, highlighting and overcoming relevant limitations of standard homogenization methods.
Abstract: We derive from first principles an accurate homogenized description of periodic metamaterials made of magnetodielectric inclusions, highlighting and overcoming relevant limitations of standard homogenization methods. We obtain closed-form expressions for the effective constitutive parameters, pointing out the relevance of inherent spatial dispersion effects, present even in the long-wavelength limit. Our results clarify the limitations of quasistatic homogenization models, restore the physical meaning of homogenized metamaterial parameters, and outline the reasons behind magnetoelectric coupling effects that may arise also in the case of centersymmetric inclusions.
306 citations
TL;DR: In this paper, the problem of characterization of metamaterials with spatial dispersion effects is addressed and the role of transition layers (perhaps transition sheets) in the characterization is explained.
Abstract: In this overview paper the trends in the modern literature concerning the characterization of linear electromagnetic properties of nanostructured metamaterials are briefly discussed. Electromagnetic characterization of bulk and surface metamaterials is discussed. The problem of characterization of metamaterials with spatial dispersion effects is addressed. It is shown that for bulk metamaterials formed as orthorhombic dipole lattices experimental electromagnetic characterization (retrieval of material parameters) becomes possible. However, standard schemes of material parameter retrieval contain pitfalls even for this kind of material. To clarify these pitfalls the concept of characteristic material parameters is suggested which is clearer and more restrictive that the concept of effective material parameters. For a special but important class of metamaterials (called Bloch lattices by the author) bulk material parameters are obtained which probably fit the concept of electromagnetic characterization because they satisfy basic physical limitations. Further, the problem of the violation of Maxwell boundary conditions for a macroscopic field at the physical boundary of the metamaterial lattice is discussed. The role of transition layers (perhaps transition sheets) in the characterization of metamaterials is explained. Finally, a relevant numerical example is presented as an illustration of the theory.
210 citations
TL;DR: In this paper, a 2D periodic nanoparticle arrays (metasurfaces) that support lattice resonances near the Rayleigh anomaly due to the electric dipole and magnetic dipole (MD) resonant coupling between the nanoparticles Silicon and core-shell particles are considered.
Abstract: To achieve efficient light control at subwavelength dimensions, plasmonic and all-dielectric nanoparticles have been utilized both as a single element as well as in the arrays Here we study 2D periodic nanoparticle arrays (metasurfaces) that support lattice resonances near the Rayleigh anomaly due to the electric dipole (ED) and magnetic dipole (MD) resonant coupling between the nanoparticles Silicon and core-shell particles are considered Our investigations are carried out using two independent numerical techniques, namely, the finite-element method and the method of coupled-dipole equations based on the Green function approach We numerically demonstrate that choosing of lattice periods independently in each mutual-perpendicular direction, it is possible to achieve a full overlap between the ED-lattice resonance and MD resonances of nanoparticles in certain spectral range and to realize the resonant lattice Kerker effect (resonant suppression of the backward scattering or reflection) At the effect conditions, the strong suppression of light reflectance in the structure is appeared due to destructive interference between electromagnetic waves scattered by ED and MD moments of every nanoparticle in the backward direction with respect to the incident light wave Influence of the array size on the revealed reflectance and transmittance behavior is discussed The resonant lattice Kerker effect based on the overlap of both ED and MD lattice resonances is also demonstrated
184 citations
TL;DR: The scattering-parameter extraction method of metamaterial homogenization is reviewed to show that the only ambiguity is that related to the choice of the branch of the complex logarithmic function (or the complex inverse cosine function).
Abstract: The scattering-parameter extraction method of metamaterial homogenization is reviewed to show that the only ambiguity is that related to the choice of the branch of the complex logarithmic function (or the complex inverse cosine function). It is shown that the method has no ambiguity for the sign of the wavenumber and intrinsic impedance. While the method indeed yields two signs for the intrinsic impedance and thus the wavenumber, the signs are dependent. Moreover, both sign combinations lead to the same permittivity and permeability, and are thus permissible. This observation is in distinct contrast to a number of statements in the literature where the correct sign of the intrinsic impedance and wavenumber resulting from the scattering-parameter method is chosen by imposing additional physical requirements, such as passivity. The scattering-parameter method is reviewed through an investigation of a uniform plane wave normally incident on a planar slab in free space. The severity of the branch ambiguity is illustrated through simulations of a known metamaterial realization. Several approaches for proper branch selection are reviewed, and the suitability to metamaterial samples is discussed.
141 citations
TL;DR: In this paper, the authors study 2D periodic nanoparticle arrays that support lattice resonances near the Rayleigh anomaly due to the electric dipole and magnetic dipole (MD) resonant coupling between the nanoparticles and demonstrate that, choosing of lattice periods independently in each mutual-perpendicular direction, it is possible to achieve a full overlap between the ED-lattice resonance and MD resonances of nanoparticles in a certain spectral range and to realize the resonant lattice Kerker effect.
Abstract: To achieve efficient light control at subwavelength dimensions, plasmonic and all-dielectric nanoparticles have been utilized both as a single element as well as in the arrays. Here we study 2D periodic nanoparticle arrays (metasurfaces) that support lattice resonances near the Rayleigh anomaly due to the electric dipole (ED) and magnetic dipole (MD) resonant coupling between the nanoparticles. Silicon and core-shell particles are considered. We demonstrate for the first time that, choosing of lattice periods independently in each mutual-perpendicular direction, it is possible to achieve a full overlap between the ED-lattice resonance and MD resonances of nanoparticles in certain spectral range and to realize the resonant lattice Kerker effect (resonant suppression of the scattering or reflection). At the effect conditions, the strong suppression of light reflectance in the structure is appeared due to destructive interference between electromagnetic waves scattered by ED and MD moments of every nanoparticle in the backward direction with respect to the incident light wave. Influence of the array size on the revealed reflectance and transmittance behavior is discussed. The resonant lattice Kerker effect based on the overlap of both ED and MD lattice resonances is also demonstrated.
119 citations
References
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Book•
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01 Jan 1959
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,815 citations
[...]
01 Oct 1999
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,503 citations
TL;DR: The authors' simulations show that a version of the lens operating at the frequency of visible light can be realized in the form of a thin slab of silver, which resolves objects only a few nanometers across.
Abstract: Optical lenses have for centuries been one of scientists’ prime tools. Their operation is well understood on the basis of classical optics: curved surfaces focus light by virtue of the refractive index contrast. Equally their limitations are dictated by wave optics: no lens can focus light onto an area smaller than a square wavelength. What is there new to say other than to polish the lens more perfectly and to invent slightly better dielectrics? In this Letter I want to challenge the traditional limitation on lens performance and propose a class of “superlenses,” and to suggest a practical scheme for implementing such a lens. Let us look more closely at the reasons for limitation in performance. Consider an infinitesimal dipole of frequency v in front of a lens. The electric component of the field will be given by some 2D Fourier expansion,
10,974 citations
TL;DR: These experiments directly confirm the predictions of Maxwell's equations that n is given by the negative square root ofɛ·μ for the frequencies where both the permittivity and the permeability are negative.
Abstract: We present experimental scattering data at microwave frequencies on a structured metamaterial that exhibits a frequency band where the effective index of refraction (n) is negative. The material consists of a two-dimensional array of repeated unit cells of copper strips and split ring resonators on interlocking strips of standard circuit board material. By measuring the scattering angle of the transmitted beam through a prism fabricated from this material, we determine the effective n, appropriate to Snell's law. These experiments directly confirm the predictions of Maxwell's equations that n is given by the negative square root of epsilon.mu for the frequencies where both the permittivity (epsilon) and the permeability (mu) are negative. Configurations of geometrical optical designs are now possible that could not be realized by positive index materials.
8,477 citations