Green's function method for waveguide and single impurity modes in 2D photonic crystals: H-polarization

Khazhinsky, M.G.; McGurn, Arthur R.

doi:10.1016/s0375-9601(97)00842-6

Cited by 16 publications

(7 citation statements)

References 13 publications

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“…Thus, we have a straight-forward numerical scheme to calculate the transmission amplitude in the presence of an impurity: for a given impurity arrangement we compute equation (13).…”

Section: Impurity Effects In the Transmissionmentioning

confidence: 99%

“…In this paper we investigate these questions for various types of single defects. We compare experimental results with those obtained by the transfer matrix calculations, equation (13), and point out the most prominent and typical transport features.…”

Section: Introductionmentioning

confidence: 95%

“…There are several calculational methods for the treatment of impurities in photonic crystals. These are based on plane wave expansion of the fields [9]; finite-difference time-domain algorithms [10,7]; variational methods [8]; R-matrix methods [11]; transfer-matrix methods [12], combined, if necessary, with finite element methods; super-cell [13], Green-function, and tight-binding methods (see, e. g. Ref. [5]).…”

Section: Introductionmentioning

confidence: 99%

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Impurity effects on the band structure of one-dimensional photonic crystals: experiment and theory

et al. 2008

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We study the effects of single impurities on the transmission in microwave realizations of the photonic Kronig-Penney model, consisting of arrays of Teflon pieces alternating with air spacings in a microwave guide. As only the first propagating mode is considered, the system is essentially one dimensional obeying the Helmholtz equation. We derive analytical closed form expressions from which the band structure, frequency of defect modes, and band profiles can be determined. These agree very well with experimental data for all types of single defects considered (e. g. interstitial, substitutional) and shows that our experimental set-up serves to explore some of the phenomena occurring in more sophisticated experiments. Conversely, based on the understanding provided by our formulas, information about the unknown impurity can be determined by simply observing certain features in the experimental data for the transmission. Further, our results are directly applicable to the closely related quantum 1D Kronig-Penney model.

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“…Thus, we have a straight-forward numerical scheme to calculate the transmission amplitude in the presence of an impurity: for a given impurity arrangement we compute equation (13).…”

Section: Impurity Effects In the Transmissionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Impurity effects on the band structure of one-dimensional photonic crystals: experiment and theory

et al. 2008

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] These are waveguide structures formed in photonic crystals by the addition of a line of site impurities to the photonic crystal. Electromagnetic waveguide modes then propagate along the line of site impurities.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the Green's function method can be easily applied to waveguide channels formed from different dielectric materials or materials that have a number of different interconnecting waveguide channels all formed from different types of dielectric materials. In this approach, Green's functions techniques are applied 3, [9][10][11][12][13][14] to particular types of photonic crystal waveguides for which the equations describing the propagation of light in the waveguide channels reduce to a set of difference equations. These difference equations are treated using standard methods to obtain analytic closed-form expressions for the propagation characteristics of photonic crystal circuits.…”

Section: Introductionmentioning

confidence: 99%

Photonic crystal circuits: A theory for two- and three-dimensional networks

McGurn

2000

Phys. Rev. B

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A discussion is given of waveguides in photonic crystals and branching network geometries of waveguides formed by joining several waveguide channels into conducting circuits for the transmission of light in photonic crystals. We shall refer to these structures in general as photonic crystal circuits. These conducting networks, which transport light, are an optical analogy to electrical circuits, which transport electrons through electrical networks. Photonic crystal circuits, however, unlike most electrical circuits, exhibit a variety of interference effects in their transport properties. The interference effects are related to the nondiffusive nature of the optical transport. The transport properties of light in a variety of circuit geometries are studied. Emphasis is placed on network geometries, which include barriers formed by the addition of dielectric materials to waveguide channels, bends in waveguide channels, closed loops, and interconnecting branched networks. Results for the transmission and reflection properties of photonic circuit modes are presented as functions of the mode frequencies and the dielectric constants of the materials forming the waveguide channels. A comparison is made of the properties of photonic crystal circuits with those of layered optical systems.

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DNLS with Impurities

Cuevas

Palmero

2009

Springer Tracts in Modern Physics

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Green's function method for waveguide and single impurity modes in 2D photonic crystals: H-polarization

Cited by 16 publications

References 13 publications

Impurity effects on the band structure of one-dimensional photonic crystals: experiment and theory

Impurity effects on the band structure of one-dimensional photonic crystals: experiment and theory

Photonic crystal circuits: A theory for two- and three-dimensional networks

DNLS with Impurities

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