### 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 language | English (US) |
---|---|

Pages (from-to) | 514-528 |

Number of pages | 15 |

Journal | Journal of the Optical Society of America B: Optical Physics |

Volume | 23 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2006 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of the Optical Society of America B: Optical Physics*,

*23*(3), 514-528. https://doi.org/10.1364/JOSAB.23.000514

}

*Journal of the Optical Society of America B: Optical Physics*, vol. 23, no. 3, pp. 514-528. https://doi.org/10.1364/JOSAB.23.000514

**Vector theory of diffraction by gratings made of a uniaxial dielectric-magnetic material exhibiting negative refraction.** / Depine, Ricardo A.; Inchaussandague, Marina E.; Lakhtakia, Akhlesh.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Vector theory of diffraction by gratings made of a uniaxial dielectric-magnetic material exhibiting negative refraction

AU - Depine, Ricardo A.

AU - Inchaussandague, Marina E.

AU - Lakhtakia, Akhlesh

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=33645746433&partnerID=8YFLogxK

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U2 - 10.1364/JOSAB.23.000514

DO - 10.1364/JOSAB.23.000514

M3 - Article

AN - SCOPUS:33645746433

VL - 23

SP - 514

EP - 528

JO - Journal of the Optical Society of America B: Optical Physics

JF - Journal of the Optical Society of America B: Optical Physics

SN - 0740-3224

IS - 3

ER -