Vector theory of diffraction by gratings made of a uniaxial dielectric-magnetic material exhibiting negative refraction

Ricardo A. Depine, Marina E. Inchaussandague, Akhlesh Lakhtakia

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Diffraction of linearly polarized plane electromagnetic waves at the periodically corrugated boundary of vacuum and a linear, homogeneous, nondissipative, uniaxial dielectric-magnetic material is formulated as a boundary-value problem and solved using the differential method. Attention is paid to two classes of diffracting materials: those with negative definite permittivity and permeability tensors and those with indefinite permittivity and permeability tensors. The dispersion equations turn out to be elliptic for the first class of diffracting materials, whereas for the second class they can be hyperbolic, elliptic, or linear, depending on the orientation of the optic axis. When the dispersion equations are elliptic, the optical response of the grating is qualitatively similar to that for conventional gratings: a finite number of refraction channels are supported. On the other hand, hyperbolic or linear dispersion equations imply the possibility of an infinite number of refraction channels. This possibility seriously incapacitates the differential method as the corrugations deepen.

Original languageEnglish (US)
Pages (from-to)514-528
Number of pages15
JournalJournal of the Optical Society of America B: Optical Physics
Volume23
Issue number3
DOIs
StatePublished - Jan 1 2006

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magnetic materials
refraction
gratings
permeability
diffraction
tensors
permittivity
boundary value problems
electromagnetic radiation
optics
vacuum

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Atomic and Molecular Physics, and Optics

Cite this

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title = "Vector theory of diffraction by gratings made of a uniaxial dielectric-magnetic material exhibiting negative refraction",
abstract = "Diffraction of linearly polarized plane electromagnetic waves at the periodically corrugated boundary of vacuum and a linear, homogeneous, nondissipative, uniaxial dielectric-magnetic material is formulated as a boundary-value problem and solved using the differential method. Attention is paid to two classes of diffracting materials: those with negative definite permittivity and permeability tensors and those with indefinite permittivity and permeability tensors. The dispersion equations turn out to be elliptic for the first class of diffracting materials, whereas for the second class they can be hyperbolic, elliptic, or linear, depending on the orientation of the optic axis. When the dispersion equations are elliptic, the optical response of the grating is qualitatively similar to that for conventional gratings: a finite number of refraction channels are supported. On the other hand, hyperbolic or linear dispersion equations imply the possibility of an infinite number of refraction channels. This possibility seriously incapacitates the differential method as the corrugations deepen.",
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Vector theory of diffraction by gratings made of a uniaxial dielectric-magnetic material exhibiting negative refraction. / Depine, Ricardo A.; Inchaussandague, Marina E.; Lakhtakia, Akhlesh.

In: Journal of the Optical Society of America B: Optical Physics, Vol. 23, No. 3, 01.01.2006, p. 514-528.

Research output: Contribution to journalArticle

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AB - Diffraction of linearly polarized plane electromagnetic waves at the periodically corrugated boundary of vacuum and a linear, homogeneous, nondissipative, uniaxial dielectric-magnetic material is formulated as a boundary-value problem and solved using the differential method. Attention is paid to two classes of diffracting materials: those with negative definite permittivity and permeability tensors and those with indefinite permittivity and permeability tensors. The dispersion equations turn out to be elliptic for the first class of diffracting materials, whereas for the second class they can be hyperbolic, elliptic, or linear, depending on the orientation of the optic axis. When the dispersion equations are elliptic, the optical response of the grating is qualitatively similar to that for conventional gratings: a finite number of refraction channels are supported. On the other hand, hyperbolic or linear dispersion equations imply the possibility of an infinite number of refraction channels. This possibility seriously incapacitates the differential method as the corrugations deepen.

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