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## Multiscale methods for engineering double negative metamaterials. (2013)

Venue: | Photonics and Nanostructures Fundamentals and Applications, |

Citations: | 1 - 1 self |

### Citations

574 |
The electrodynamics of substances with simultaneously negative values of ε and µ
- Veselago
- 1968
(Show Context)
Citation Context ...nges. 1 Introduction A compelling aspect of metamaterials research is the quest for new sub-wavelength microstructures that deliver both negative bulk dielectric constant and bulk magnetic permeability across prescribed frequency intervals. Double negative materials offer great potential for applications in biomedical imaging, optical lithography and data storage. Such media support electromagnetic waves for which the phase velocity is antiparallel to the direction of energy flow as well as other unusual electromagnetic effects such as the reversal of the Doppler effect and Cerenkov radiation [41]. Double negative metamaterials are characterized by sub-wavelength microstructure and control radiation through a delicate combination of local and global resonances. This approach to controlling wave propagation is distinct from approaches using photonic materials which control radiation through multiple diffraction implemented by structuring the medium along the same length scale as the wave length of the incident radiation. Pendry [29] demonstrated that unconventional properties can be derived from sub-wavelength configurations of different conventional materials. It was shown that a cubic... |

465 | Magnetism from conductors and enhanced nonlinear phenomena
- Pendry, Holden, et al.
- 1999
(Show Context)
Citation Context ...ated that unconventional properties can be derived from sub-wavelength configurations of different conventional materials. It was shown that a cubic lattice of metal wires exhibited behavior associated with negative bulk dielectric constant near the plasma resonance of the structure. This resonance frequency is intrinsic to the lattice and lies in the microwave regime six decades below the plasma resonance of the metal used to make the lattice. Subsequently non-magnetic metallic split-ring resonators were constructed to deliver negative effective magnetic permeability at microwave frequencies [28]. In more recent work Smith et al. [39] experimentally demonstrated that arrays of metallic posts and split ring resonators could also support resonances at microwave frequencies and deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency d... |

390 |
Composite medium with simultaneously negative permeability and permittivity
- Smith, Padilla, et al.
- 2000
(Show Context)
Citation Context ... be derived from sub-wavelength configurations of different conventional materials. It was shown that a cubic lattice of metal wires exhibited behavior associated with negative bulk dielectric constant near the plasma resonance of the structure. This resonance frequency is intrinsic to the lattice and lies in the microwave regime six decades below the plasma resonance of the metal used to make the lattice. Subsequently non-magnetic metallic split-ring resonators were constructed to deliver negative effective magnetic permeability at microwave frequencies [28]. In more recent work Smith et al. [39] experimentally demonstrated that arrays of metallic posts and split ring resonators could also support resonances at microwave frequencies and deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude ... |

377 | Experimental verification of a negative index of refraction - Shelby, Smith, et al. |

269 | The theory of composites - Milton - 2002 |

107 | Optical negative-index metamaterials
- Shalaev
(Show Context)
Citation Context ...gime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the article is to introduce a multi-scale method for exploring the universe of sub-wavelength microstructures that links the geometry of the microstructure to the actual dispersion relations for the medium without making use of any simplifying approximation (e.g. the dipole approximation). Here we consider periodic arrays of nonmagnetic scatterers made from two distinct materials. We present a systematic... |

74 |
Low frequency Plasmons in thin-wire structures, J.Phys.: Condens
- Pendry, Holden, et al.
- 1998
(Show Context)
Citation Context ...iparallel to the direction of energy flow as well as other unusual electromagnetic effects such as the reversal of the Doppler effect and Cerenkov radiation [41]. Double negative metamaterials are characterized by sub-wavelength microstructure and control radiation through a delicate combination of local and global resonances. This approach to controlling wave propagation is distinct from approaches using photonic materials which control radiation through multiple diffraction implemented by structuring the medium along the same length scale as the wave length of the incident radiation. Pendry [29] demonstrated that unconventional properties can be derived from sub-wavelength configurations of different conventional materials. It was shown that a cubic lattice of metal wires exhibited behavior associated with negative bulk dielectric constant near the plasma resonance of the structure. This resonance frequency is intrinsic to the lattice and lies in the microwave regime six decades below the plasma resonance of the metal used to make the lattice. Subsequently non-magnetic metallic split-ring resonators were constructed to deliver negative effective magnetic permeability at microwave fre... |

65 | Negative index of refraction in optical metamaterials
- Shalaev, Cai, et al.
- 2005
(Show Context)
Citation Context ...the plasma resonance of the metal used to make the lattice. Subsequently non-magnetic metallic split-ring resonators were constructed to deliver negative effective magnetic permeability at microwave frequencies [28]. In more recent work Smith et al. [39] experimentally demonstrated that arrays of metallic posts and split ring resonators could also support resonances at microwave frequencies and deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs cont... |

30 |
Homogenization of metamaterials by field averaging,
- Smith, Pendry
- 2006
(Show Context)
Citation Context ...effective magnetic permeability together with conditions for generation of negative effective permeability are developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effective negative permeability on the propagation of Bloch waves inside high contrast dielectrics [18], the generation of negative permeability inside metallic - dielectric resonators [36], and for concentric coated cylinder assemblages generating a double negative media [13]. 2 Power series representations We start with a metamaterial crys... |

28 |
Low-loss negative-index metamaterial at telecommunication wavelengths
- Dolling, Enkrich, et al.
- 2006
(Show Context)
Citation Context ...the plasma resonance of the metal used to make the lattice. Subsequently non-magnetic metallic split-ring resonators were constructed to deliver negative effective magnetic permeability at microwave frequencies [28]. In more recent work Smith et al. [39] experimentally demonstrated that arrays of metallic posts and split ring resonators could also support resonances at microwave frequencies and deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs cont... |

26 | Transport properties of regular arrays of cylinders, - Perrins, Mckenzie, et al. - 1979 |

25 |
Homogenization near resonances and artificial magnetism from dielectrics,
- Bouchitte, Felbacq
- 2004
(Show Context)
Citation Context ...ngth periodic arrangements of nonmagnetic infinitely long parallel coated cylinders immersed in a nonmagnetic host. In what follows the period of the lattice is denoted by d. The coated cylinders are parallel to the x3 axis and made from a frequency independent high dielectric core and a frequency dependent dielectric plasmonic coating (Figure 1). The host medium containing the coated rods has relative dielectric permittivity equal to unity. To generate effective magnetic properties the material comprising the core of the rod is chosen to be a high contrast dielectric material ǫR = γ/d 2 see, [9]. The dielectric coating is frequency dependent and characterized by single oscillator model that includes dissipation. The approach taken here solves the Maxwell equations directly and explicitly with no approximations made. The solution is given by a power series with each term iteratively defined by the solution of an auxiliary problem that is simpler than the original Maxwell system. In what follows we apply the power series method to identify the dispersion relation for TE modes with magnetic field parallel to the cylinders. The leading order term in the power series for the dispersion re... |

24 |
Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,
- Zhang, Fan, et al.
- 2005
(Show Context)
Citation Context ...the plasma resonance of the metal used to make the lattice. Subsequently non-magnetic metallic split-ring resonators were constructed to deliver negative effective magnetic permeability at microwave frequencies [28]. In more recent work Smith et al. [39] experimentally demonstrated that arrays of metallic posts and split ring resonators could also support resonances at microwave frequencies and deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs cont... |

19 |
Experimental observation of left-handed behavior in an array of standard dielectric resonators,
- Peng, Ran, et al.
- 2007
(Show Context)
Citation Context ...deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the article is to introduce a multi-scale method for exploring the universe of sub-wavelength microstructures that l... |

18 |
Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns
- Huangfu, Ran, et al.
(Show Context)
Citation Context |

15 |
Engineering the electromagnetic prop- erties of periodic nanostructures using electrostatic resonances,
- Shvets, Urzhumov
- 2004
(Show Context)
Citation Context ... negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the article is to introduce a multi-scale method for exploring the universe of sub-wavelength microstructures that links the geometry of the microstructure to the actual dispersion relations for the medium without making use of any simplifying approximation (e.g. the dipole approximation). ... |

15 |
AllDielectric Rod-Type Metamaterials at Optical Frequencies
- Vynck, Felbacq, et al.
- 2009
(Show Context)
Citation Context ...deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the article is to introduce a multi-scale method for exploring the universe of sub-wavelength microstructures that l... |

14 |
Homogenization of Maxwell’s equations in a split ring geometry,
- Bouchitte, Schweizer
- 2010
(Show Context)
Citation Context ...egative intervals for several choices of inner and outer radii of the rod coating and compare these with the dispersion curves for the imaginary part of the wave number versus frequency. From this we can identify which design delivers a double negative interval associated with the least attenuation of average electromagnetic energy flow (4.3) see, Figure 4 of section 3 and the following discussion. We conclude the introduction noting that formulas for frequency-dependent effective magnetic permeability together with conditions for generation of negative effective permeability are developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic ... |

14 |
Negative refraction in periodic and random photonic crystals,
- Bouchitte, Felbacq
- 2005
(Show Context)
Citation Context ...egative intervals for several choices of inner and outer radii of the rod coating and compare these with the dispersion curves for the imaginary part of the wave number versus frequency. From this we can identify which design delivers a double negative interval associated with the least attenuation of average electromagnetic energy flow (4.3) see, Figure 4 of section 3 and the following discussion. We conclude the introduction noting that formulas for frequency-dependent effective magnetic permeability together with conditions for generation of negative effective permeability are developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic ... |

14 | Magnetism and homogenization of micro- resonators,
- Kohn, Shipman
- 2008
(Show Context)
Citation Context ...egative intervals for several choices of inner and outer radii of the rod coating and compare these with the dispersion curves for the imaginary part of the wave number versus frequency. From this we can identify which design delivers a double negative interval associated with the least attenuation of average electromagnetic energy flow (4.3) see, Figure 4 of section 3 and the following discussion. We conclude the introduction noting that formulas for frequency-dependent effective magnetic permeability together with conditions for generation of negative effective permeability are developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic ... |

12 | The effective conductivity of strongly heterogeneous composites, - Bruno - 1991 |

12 |
Coated non-magnetic spheres with a negative index of refraction at infrared frequencies,
- Wheeler, Aitchison, et al.
- 2006
(Show Context)
Citation Context ...ays of metallic posts and split ring resonators could also support resonances at microwave frequencies and deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the artic... |

10 |
First-principles homogenization theory for periodic metamaterials,” Phys
- Alù
- 2011
(Show Context)
Citation Context ...dent effective magnetic permeability together with conditions for generation of negative effective permeability are developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effective negative permeability on the propagation of Bloch waves inside high contrast dielectrics [18], the generation of negative permeability inside metallic - dielectric resonators [36], and for concentric coated cylinder assemblages generating a double negative media [13]. 2 Power series representations We start with a metamateria... |

9 |
Negative effective permeability in polaritonic photonic crystals,
- Huang, Povinelli, et al.
- 2004
(Show Context)
Citation Context ...deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the article is to introduce a multi-scale method for exploring the universe of sub-wavelength microstructures that l... |

9 |
Bounds and exact theories for the transport properties of inhomogeneous media,
- McPhedran, Milton
- 1981
(Show Context)
Citation Context ...d spectra is a type of electrostatic spectra associated with a three phase medium and is global and intrinsic to the structural geometry. This spectra is associated with the configuration of the periodic structure and the relative position of the scatterers with respect to each other. Both spectral problems emerge naturally from the power series method and are not part of any imposed hypotheses. Electrostatic spectra for two phase materials has been recognized as useful in characterizing electromagnetic properties of periodic nano structures see, for example [37]. Earlier pioneering work [4], [23], identified electrostatic modes and showed how their use allows for the separation of the dielectric properties of the component materials from underlying geometric effects due to the structure of two-phase composites. Numerical methods for computation of electrostatic spectra for complex two-phase structures are developed in [24] For the problem at hand we apply the strategy developed by the authors in [12] and [11] to express the complex effective dielectric constant in terms of a new type of three phase electrostatic spectra. The effective dielectric constant is expressed in a spectral rep... |

7 |
The dielectric constant of a simple cubic array of identical spheres,
- Bergman
- 1979
(Show Context)
Citation Context ...second spectra is a type of electrostatic spectra associated with a three phase medium and is global and intrinsic to the structural geometry. This spectra is associated with the configuration of the periodic structure and the relative position of the scatterers with respect to each other. Both spectral problems emerge naturally from the power series method and are not part of any imposed hypotheses. Electrostatic spectra for two phase materials has been recognized as useful in characterizing electromagnetic properties of periodic nano structures see, for example [37]. Earlier pioneering work [4], [23], identified electrostatic modes and showed how their use allows for the separation of the dielectric properties of the component materials from underlying geometric effects due to the structure of two-phase composites. Numerical methods for computation of electrostatic spectra for complex two-phase structures are developed in [24] For the problem at hand we apply the strategy developed by the authors in [12] and [11] to express the complex effective dielectric constant in terms of a new type of three phase electrostatic spectra. The effective dielectric constant is expressed in a spectr... |

6 |
Tunable double negative band structure from non-magnetic coated rods,
- Chen, Lipton
- 2010
(Show Context)
Citation Context ...etamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effective negative permeability on the propagation of Bloch waves inside high contrast dielectrics [18], the generation of negative permeability inside metallic - dielectric resonators [36], and for concentric coated cylinder assemblages generating a double negative media [13]. 2 Power series representations We start with a metamaterial crystal characterized by a period cell containing a centered coated cylinder with plasmonic coating and high dielectric core. The core radius and the coating radius are denoted by a and b respectively (Figure 2). The cylinder is parallel to the x3 axis and is periodically o x1 x2 d 2 H P R G θ a b r Figure 2: The period cell: R represents the high dielectric core, P the plasmonic coating and H denotes the connected host material. arranged within a square lattice over the transverse x = (x1, x2) plane. The period of the lattice is de... |

5 |
Homogenization of wire mesh photonic crystals embdedded in a medium with a negative permeability,
- Felbacq, Bouchitte
- 2005
(Show Context)
Citation Context |

5 | Sub-wavelength plasmonic crystals: dispersion relations and effective properties,
- Fortes, Lipton, et al.
- 2009
(Show Context)
Citation Context ...e developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effective negative permeability on the propagation of Bloch waves inside high contrast dielectrics [18], the generation of negative permeability inside metallic - dielectric resonators [36], and for concentric coated cylinder assemblages generating a double negative media [13]. 2 Power series representations We start with a metamaterial crystal characterized by a period cell containing a centered coated cylinder with plasmonic coating and high diel... |

5 |
Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors,
- Milton
- 2010
(Show Context)
Citation Context ...gy flow (4.3) see, Figure 4 of section 3 and the following discussion. We conclude the introduction noting that formulas for frequency-dependent effective magnetic permeability together with conditions for generation of negative effective permeability are developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effective negative permeability on the propagation of Bloch waves inside high contrast dielectrics [18], the generation of negative permeability inside metallic - dielectric resonators [36], and for... |

5 | On the influence of obstacles arranged in rectangular order upon the properties of a medium - Strutt - 1892 |

4 |
Homogenization of finite metallic fibers and 3D-effective permittivity tensor,
- Bouchitte, Bourel
- 2010
(Show Context)
Citation Context ...nary part of the wave number versus frequency. From this we can identify which design delivers a double negative interval associated with the least attenuation of average electromagnetic energy flow (4.3) see, Figure 4 of section 3 and the following discussion. We conclude the introduction noting that formulas for frequency-dependent effective magnetic permeability together with conditions for generation of negative effective permeability are developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effect... |

4 |
Resonance and Double Negative Behavior in Metamaterials
- Chen, Lipton
(Show Context)
Citation Context ...y of the band structure of the metamaterial. Each branch of the dispersion relation is given by power series in the ratio of period to wave number. The leading order term in the expansion is the effective complex index of refraction for the medium. Figures displaying the real and imaginary parts of the leading order dispersion relation for several different bands are displayed in section 3 see, Figures 4(a) through 4(d). The higher order terms in the series involve corrections for spatial dispersion. When the media is assumed lossless the power series for each branch is shown to converge, see [12]. This is also true for lossy materials. This expansion provides the rigorous and explicit connection between microgeometry and dispersion. It provides the opportunity for the systematic design of sub-wavelength structures for control of dispersion based on the shape and topology of the inclusions used in the microgeometry. This is taken up in section 3 where several simulations exhibiting the sensitivity of the dispersion relations to the underlying geometry of the scatterers is presented. The methodology provides a way to systematically identify the location of the center frequency and band ... |

4 |
Artificial magnetism and anticrossing interaction in photonic crystals and split-ring structures,
- Chern, Felbacq
- 2009
(Show Context)
Citation Context |

4 |
Power series for waves in micro-resonator arrays,
- Shipman
- 2010
(Show Context)
Citation Context ...loped in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effective negative permeability on the propagation of Bloch waves inside high contrast dielectrics [18], the generation of negative permeability inside metallic - dielectric resonators [36], and for concentric coated cylinder assemblages generating a double negative media [13]. 2 Power series representations We start with a metamaterial crystal characterized by a period cell containing a centered coated cylinder with plasmonic coating and high dielectric core. The core radius and the coating radius are denoted by a and b respectively (Figure 2). The cylinder is parallel to the x3 axis and is periodically o x1 x2 d 2 H P R G θ a b r Figure 2: The period cell: R represents the high dielectric core, P the plasmonic coating and H denotes the connected host material. arranged within ... |

4 |
Negative refractive index in the near-UV from Au-coated CuCl nanoparticle superlattices,
- Yannopapas
- 2007
(Show Context)
Citation Context ...ays of metallic posts and split ring resonators could also support resonances at microwave frequencies and deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the artic... |

3 | Convergent power series for fields in positive or negative high-contrast periodic media,
- Fortes, Lipton, et al.
- 2011
(Show Context)
Citation Context ...electric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effective negative permeability on the propagation of Bloch waves inside high contrast dielectrics [18], the generation of negative permeability inside metallic - dielectric resonators [36], and for concentric coated cylinder assemblages generating a double negative media [13]. 2 Power series representations We start with a metamaterial crystal characterized by a period cell containing a centered coated cylinder with plasmonic coating and high dielectric core. The core radius and the coating radius are denoted by a and b respectively (Figure 2). The cylinder is parallel to the x3 axis and is periodically o x1 x2 d 2 H P R G θ a b r Figure 2: The period cell: R represents the high dielectric cor... |

3 |
Next Wave of metamaterials hopes to fuel the revolution,
- Service
- 2010
(Show Context)
Citation Context ...ptical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the article is to introduce a multi-scale method for exploring the universe of sub-wavelength microstructures that links the geometry of the microstructure to the actual dispersion relations for the medium without making use of any simplifying approximation (e.g. the dipole approximation). Here we consider periodic arrays of nonmagnetic scatterers made from two distinct materials. We present a s... |

3 |
Artificial magnetism and negative refractive index in three-dimensional metamaterials of spherical particles at near-infrared and visible frequencies,
- Yannopapas
- 2007
(Show Context)
Citation Context ...ays of metallic posts and split ring resonators could also support resonances at microwave frequencies and deliver negative effective negative refractive 1 index for a range of microwave frequencies. Subsequent work has delivered several new configurations of metallic resonators for double negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the artic... |

3 |
Negative-zero-positive refractive index in a prism-like omega-type metamaterial,
- Zhang, Potet, et al.
- 2008
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3 |
Resonant condition of unitary dendritic structure with overlapping negative permittivity and permeability,
- Zhou, Zhao
- 2007
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2 |
Dynamical theory of artifical optical magnetism produced by rings of plasmonic nanoparticles,
- Alu, Engheta
- 2008
(Show Context)
Citation Context ...ouble negative behavior [15, 19, 34, 46, 47, 48]. New designs for generating double negative properties in the optical regime rely on Mie resonances. One scheme employs coated rods made from a high dielectric core coated with a frequency dependent dielectric plasmonic or Drude type behavior at optical frequencies [43, 44, 45]. Other schemes employ small particles made from dielectric materials with large permittivity, [20, 30, 42]. Alternate strategies for generating negative bulk dielectric permeability at infrared and optical frequencies use special configurations of plasmonic nanoparticles [1], [37]. The list of metamaterial designs continues to grow and recent reviews of the subject can be found in [32] and [33]. In this article we focus on a class of simple microstructures and investigate the range of double negative behavior that one can engineer using lossy nonmagnetic materials. The main point of the article is to introduce a multi-scale method for exploring the universe of sub-wavelength microstructures that links the geometry of the microstructure to the actual dispersion relations for the medium without making use of any simplifying approximation (e.g. the dipole approximat... |

2 | Double Negative Dispersion Relations from Coated Plasmonic Rods, SIAM, Multiscale Modeling and Simulation,
- Chen, Lipton
- 2013
(Show Context)
Citation Context ...for two phase materials has been recognized as useful in characterizing electromagnetic properties of periodic nano structures see, for example [37]. Earlier pioneering work [4], [23], identified electrostatic modes and showed how their use allows for the separation of the dielectric properties of the component materials from underlying geometric effects due to the structure of two-phase composites. Numerical methods for computation of electrostatic spectra for complex two-phase structures are developed in [24] For the problem at hand we apply the strategy developed by the authors in [12] and [11] to express the complex effective dielectric constant in terms of a new type of three phase electrostatic spectra. The effective dielectric constant is expressed in a spectral representation formula that explicitly links the configuration of the scatters to effective properties. Similarly the Dirichlet spectra delivers a representation formula for the magnetic permittivity. This formula agrees with the representation formula for the magnetic permittivity developed in the work of [9] for periodic arrays of high dielectric rods. In this article we provide explicit power series for the associated... |

2 | Advances in the Rayleigh multipole method for problems in photonics and phononics, - McPhedran, Nicorovici, et al. - 2001 |

2 | Transport properties of a 3 phase composite material: the square array of coated cylinders, - Nicorovici, McPhedran, et al. - 1993 |

1 |
Causality relations in the homogenization of metamaterials,
- Alu, Yaghjian, et al.
- 2011
(Show Context)
Citation Context ...dependent effective magnetic permeability together with conditions for generation of negative effective permeability are developed in [7, 8, 9, 14, 16, 21]. For periodic arrays made from metal fibers a homogenization theory delivering negative effective dielectric constant [6] has been established. A novel method for creating metamaterials with prescribed effective dielectric permittivity and effective magnetic permeability at a fixed frequency is developed in [26]. New methodologies and issues for computing homogenized 3 properties for metamaterials using top down approaches are presented in [2], [3], [38]. Earlier work on the power series approach to sub-wavelength analysis has been developed and applied in [17] for characterizing the dynamic dispersion relations for Bloch waves inside plasmonic crystals. It has also been applied to assess the influence of effective negative permeability on the propagation of Bloch waves inside high contrast dielectrics [18], the generation of negative permeability inside metallic - dielectric resonators [36], and for concentric coated cylinder assemblages generating a double negative media [13]. 2 Power series representations We start with a metama... |

1 | Bohren and D.H.Huffman, Absorption and Scattering of Light by Small Particles, - F - 2004 |

1 |
Intrinsic resonant behavior of metamaterials by finite element calculations, Physical Review B,
- Mejdoubi, Brosseau
- 2006
(Show Context)
Citation Context ...e power series method and are not part of any imposed hypotheses. Electrostatic spectra for two phase materials has been recognized as useful in characterizing electromagnetic properties of periodic nano structures see, for example [37]. Earlier pioneering work [4], [23], identified electrostatic modes and showed how their use allows for the separation of the dielectric properties of the component materials from underlying geometric effects due to the structure of two-phase composites. Numerical methods for computation of electrostatic spectra for complex two-phase structures are developed in [24] For the problem at hand we apply the strategy developed by the authors in [12] and [11] to express the complex effective dielectric constant in terms of a new type of three phase electrostatic spectra. The effective dielectric constant is expressed in a spectral representation formula that explicitly links the configuration of the scatters to effective properties. Similarly the Dirichlet spectra delivers a representation formula for the magnetic permittivity. This formula agrees with the representation formula for the magnetic permittivity developed in the work of [9] for periodic arrays of h... |