Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal

Kuzmiak, Vladimír; Maradudin, A. A.; McGurn, Arthur R.

doi:10.1103/physrevb.55.4298

Cited by 80 publications

(65 citation statements)

References 37 publications

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“…S λ (ω) is now an analytic extension of S ℓ (ω) into the complex λ plane which is regular in the vicinity of the positive real λ axis. Using Cauchy's theorem and by noting that inside the contour C the only singularities of the integrand in (22) are the integers, we can easily recover (11) from (22).…”

Section: Regge Poles and Surface Polaritonsmentioning

confidence: 99%

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Surface polaritons on left-handed cylinders: A complex angular momentum analysis

et al. 2005

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We consider the scattering of electromagnetic waves by a left-handed cylinder -i.e., by a cylinder fabricated from a left-handed material -in the framework of complex angular momentum techniques. We discuss both the TE and TM theories. We emphasize more particularly the resonant aspects of the problem linked to the existence of surface polaritons. We prove that the long-lived resonant modes can be classified into distinct families, each family being generated by one surface polariton propagating close to the cylinder surface and we physically describe all the surface polaritons by providing, for each one, its dispersion relation and its damping. This can be realized by noting that each surface polariton corresponds to a particular Regge pole of the S matrix of the cylinder. Moreover, for both polarizations, we find that there exists a particular surface polariton which corresponds, in the large-radius limit, to the surface polariton which is supported by the plane interface. There exists also an infinite family of surface polaritons of whispering-gallery type which have no analogs in the plane interface case and which are specific to left-handed materials.

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Section: Regge Poles and Surface Polaritonsmentioning

confidence: 99%

“…Recently, activity has focused particularly on the role of SP's in photonic crystal physics (see, for example, Refs. 18,19,20,21,22,23,24,25,26,27,28) as well as on their role in the enhanced transmission of light through periodic arrays of holes in a metal film 29 (see also Ref. 30 and references therein).…”

Section: Introductionmentioning

confidence: 99%

Surface polaritons on left-handed cylinders: A complex angular momentum analysis

et al. 2005

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“…In this case in electrodynamic terms a square grid of metallic cylinders is modelled as an equivalent grid of dielectric cylinders with a frequency dependent permittivity. The dispersion characteristics of such metallic systems are studied in [6][7][8][9] using the plane-wave expansion method, and the transmission characteristics are considered in [10,11] using the transfer matrix method [12]. All these methods can be successfully used for perfectly conducting cylinders also.…”

Section: Introductionmentioning

confidence: 99%

Dispersion and Reflection Properties of Artificial Media Formed By Regular Lattices of Ideally Conducting Wires

Belov¹,

Tretyakov²,

Viitanen³

2002

Journal of Electromagnetic Waves and Applications

181

135

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Abstract-An analytical theory of electromagnetic waves in artificial media formed by a rectangular lattice of thin ideally conducting cylinders using the local field approach is developed. As a result, the transcendental dispersion equation is obtained in closed form and solved numerically. Typical dispersion curves are calculated. Using these results, the reflection problem from an interface between a half space of wire medium and free space is solved for plane-wave excitation. In the low-frequency approximation a simple analytical formula for the frequency dependent effective dielectric permittivity is established.

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“…In recent papers dealing with photonic band structure of two-dimensional photonic crystals fabricated from metallic or semiconducting cylinders arrayed in a square lattice, a striking feature has been noted 1,5,8,9,10,11,12,13 , namely the existence of flat bands (i.e. dispersionless bands) in the frequency range in which ǫ(ω) < 0.…”

Section: Discussionmentioning

confidence: 99%

Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis

Ancey¹,

Décanini²,

Folacci³

et al. 2004

Phys. Rev. B

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We revisit scattering of electromagnetic waves from metallic and semiconducting cylinders in the framework of complex angular momentum techniques. We prove that "resonant surface polariton modes" are generated by a unique surface wave, i.e. a surface polariton, propagating close to the cylinder surface. This surface polariton corresponds to a particular Regge pole of the S-matrix of the cylinder. From the associated Regge trajectory we can construct semiclassically the spectrum of the complex frequencies of the resonant surface polariton modes which can be considered as Breit-Wigner-type resonances. Furthermore, by taking into account Stokes' phenomenon, we derive an asymptotic expression for the position in the complex angular momentum plane of the surface polariton Regge pole. We then describe semiclassically the surface polariton and provide analytical expressions for its the dispersion relation and its damping. All these features allow us to consider the photon-cylinder system as a kind of artificial atom where the photon plays the role of the electron. Finally, we briefly discuss the implication of our results for two-dimensional photonic crystals.

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Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal

Cited by 80 publications

References 37 publications

Surface polaritons on left-handed cylinders: A complex angular momentum analysis

Surface polaritons on left-handed cylinders: A complex angular momentum analysis

Dispersion and Reflection Properties of Artificial Media Formed By Regular Lattices of Ideally Conducting Wires

Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis

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