Perfectly matched layer-absorbing boundary condition for left-handed materials

Dong, Xiaoting; Rao, X. S.; Gan, Yeow-Beng; Guo, Bin; Wang, Yin

doi:10.1109/lmwc.2004.827104

Cited by 78 publications

(47 citation statements)

References 11 publications

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“…The change of variable (11) with the particular choice (12), which corresponds to classical PMLs, transforms the dispersion relation (14) into…”

Section: A Necessary Stability Criterionmentioning

confidence: 99%

“…Theorem 1.3 (high-frequency necessary stability condition). For the non-dispersive model (1), the necessary stability condition for the PML system in the x direction (4) is that all the modes ω(k) solving the original dispersion relation (14) are forward in the x direction, i.e.…”

Section: A Necessary Stability Criterionmentioning

confidence: 99%

“…Since the 1990s, NIMs are the subject of intense researches due to their promising applications: superlens, cloaking, improved antenna, etc [10]. PMLs in such media have been already studied by the physics community [9,11,14,19] but, to our knowledge, without complete mathematical justification.…”

Section: Introductionmentioning

confidence: 99%

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Perfectly matched layers in negative index metamaterials and plasmas

Bécache¹,

Joly²,

Kachanovska³

et al. 2015

ESAIM: Proc.

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Abstract. This work deals with the stability of Perfectly Matched Layers (PMLs). The first part is a survey of previous results about the classical PMLs in non-dispersive media (construction and necessary condition of stability). The second part concerns some extensions of these results. We give a new necessary criterion of stability valid for a large class of dispersive models and for more general PMLs than the classical ones. This criterion is applied to two dispersive models: negative index metamaterials and uniaxial anisotropic plasmas. In both cases, classical PMLs are unstable but the criterion allows us to design new stable PMLs. Numerical simulations illustrate our purpose.Résumé. Ce travail porte sur la stabilité des Couches Absorbantes Parfaitement Adaptées (Perfectly Matched Layers, PMLs). La première partie est un récapitulatif de résultats antérieurs pour les milieux non dispersifs (construction et condition nécessaire de stabilité). La seconde partie concerne quelques extensions de ces résultats. Nous donnons un nouveau critère nécessaire de stabilité valable pour une grande classe de modèles dispersifs et pour des PMLs plus générales que celles classiques. Ce critère est appliquéà deux modèles dispersifs : les métamatériauxà indice négatif et les plasmas anistropiques uniaxiaux. Dans les deux cas, les PMLs classiques sont instables mais le critère nous permet de concevoir de nouvelles PMLs stables. Des simulations numériques illustrent notre propos.

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“…The change of variable (11) with the particular choice (12), which corresponds to classical PMLs, transforms the dispersion relation (14) into…”

Section: A Necessary Stability Criterionmentioning

confidence: 99%

Section: A Necessary Stability Criterionmentioning

confidence: 99%

See 1 more Smart Citation

Perfectly matched layers in negative index metamaterials and plasmas

Bécache¹,

Joly²,

Kachanovska³

et al. 2015

ESAIM: Proc.

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“…Overall, updating the components of E in the DNG-UPML requires three steps. First, obtaining the new values of the components of J according to (12): second, using these new J components to obtain the new values of the components of R according to (11): and third, using these new R components to obtain the new values of the E components according to (9).…”

Section: Upml For the Dng Mediummentioning

confidence: 99%

“…Since first introduced by Berenger in 1994 [8], the perfectly matched layer (PML) has become the most popular and efficient absorbing boundary condition. Unfortunately, standard versions of PML are inherently unstable when they are extended to truncate the boundary of DNG medium without any modification [9,10]. Recently, a nearly PML absorbing boundary condition for DNG medium is discussed, and 50-cell layers for NIMPML are used to truncate the DNG medium [10].…”

Section: Introductionmentioning

confidence: 99%

Uniaxial PML Absorbing Boundary Condition for Truncating the Boundary of DNG Metamaterials

Zheng¹,

Tam²,

Ge³

et al. 2009

PIER Letters

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Abstract-The conventional perfectly matched layer (PML) absorbing boundary condition is shown to be unstable when it is extended to truncate the boundary of the double negative (DNG) medium. It is a consequence of the reverse directions of the Poynting and phasevelocity vectors of plane waves propagating in such material. In this paper, a modified uniaxial PML (UPML), which is stable for the DNG medium, is derived. The auxiliary differential equation technique is introduced to derive the discrete field-update equations of DNG-UPML. Numerical results demonstrate the effectiveness and stability of the new UPML for the DNG medium.

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Study on transmission characteristics in photonic crystals with negative effective index of refraction

Shen¹,

Li²,

Ma³

et al. 2008

Cryst. Res. Technol.

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Transmission spectra from equivalent negative refractive photonic crystals (PCs) composed of a triangular array of air cylinders in a GaAs matrix are studied by finite-difference time-domain method in the paper. Mechanism of wave resonance is probed and propagation of optical waves in the PCs is described in terms of effective refraction index and Bloch waves. Our numerical results show that probability of spontaneous radiation would be enhanced extremely under the influence of Bloch resonance waves, stimulated emission and photon tunnel effect, resulting in the optical waves localized greatly in the PCs at particular frequencies. In addition, we find out that the position of transmission peaks, with values far greater than unit, can be controlled by tuning the central frequency of waveguide source. It means that photon current in the PCs also can be controlled to optimize transmission properties of PCs, so as to meet the requirements of novel optical devices based on PCs.

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Perfectly matched layer-absorbing boundary condition for left-handed materials

Cited by 78 publications

References 11 publications

Perfectly matched layers in negative index metamaterials and plasmas

Perfectly matched layers in negative index metamaterials and plasmas

Uniaxial PML Absorbing Boundary Condition for Truncating the Boundary of DNG Metamaterials

Study on transmission characteristics in photonic crystals with negative effective index of refraction

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