Order-<i>N</i>spectral method for electromagnetic waves

Chan, Che Ting; Yu, Qingliang; Ho, Kai‐Ming

doi:10.1103/physrevb.51.16635

Cited by 285 publications

(167 citation statements)

References 31 publications

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“…These periodic composites admit Bloch waves as solutions and many different numerical algorithms have been developed for calculating the dispersive properties of these waves. These include the popular plane wave expansion method [49], the finite difference time domain method [50], the multiple scattering method [51], variational methods [52,53], secondary expansions [54], etc.…”

Section: Dynamic Homogenizationmentioning

confidence: 99%

Elastic metamaterials and dynamic homogenization: a review

Srivastava

2015

International Journal of Smart and Nano Materials

120

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In this paper, we review the recent advances which have taken place in the understanding and applications of acoustic/elastic metamaterials. Metamaterials are artificially created composite materials which exhibit unusual properties that are not found in nature. We begin with presenting arguments from discrete systems which support the case for the existence of unusual material properties such as tensorial and/or negative density. The arguments are then extended to elastic continuums through coherent averaging principles. The resulting coupled and nonlocal homogenized relations, called the Willis relations, are presented as the natural description of inhomogeneous elastodynamics. They are specialized to Bloch waves propagating in periodic composites and we show that the Willis properties display the unusual behavior which is often required in metamaterial applications such as the Veselago lens. We finally present the recent advances in the area of transformation elastodynamics, charting its inspirations from transformation optics, clarifying its particular challenges, and identifying its connection with the constitutive relations of the Willis and the Cosserat types.

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Section: Dynamic Homogenizationmentioning

confidence: 99%

Elastic metamaterials and dynamic homogenization: a review

Srivastava

2015

International Journal of Smart and Nano Materials

120

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“…The density of states is obtained by an order (N) spectral method, which is discussed in detail elsewhere. 31 Briefly, the method integrates Maxwell's equations numerically in the time domain, and the spatial derivatives ͑the ''curls''͒ are determined by finite differences. The E and H fields are stored as time series, and when a sufficient number of time steps have been accumulated ͑which governs the resolution in the frequency domain͒, the field intensities are Laplace transformed from the time domain to the frequency domain to obtain the spectral intensities.…”

Section: ͑4͒mentioning

confidence: 99%

Localization of electromagnetic waves in two-dimensional disordered systems

et al. 1996

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We calculate the average transmission for s-and p-polarized electromagnetic ͑EM͒ waves and consequently the localization length of two-dimensional ͑2D͒ disordered systems which are periodic on the average; the periodic systems form a square lattice consisting of infinitely long cylinders parallel to each other and embedded in a different dielectric medium. In particular, we study the dependence of the localization length on the frequency, the dielectric function ratio between the scatterer and the background, and the filling ratio of the scatterer. We find that the gaps of the s-polarized waves can sustain a higher amount of disorder than those of the p-polarized waves, due to the fact that the gaps of the s-polarized waves are wider than those of the p-polarized waves. For high frequencies, the gaps of both types of waves easily disappear, the localization length is constant and it can take very small values. The optimum conditions for obtaining localization of EM waves in 2D systems will be discussed.

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“…This is carried out by solving the elastic wave equations by the finite-difference time-domain ͑FDTD͒ method. [15][16][17] The FDTD method is a popular numerical scheme for the solution of many problems in electromagnetics. It is especially effective for a large-scale simulation of a finite complex system, and has recently been applied to the study of both the transmission and frequency spectra of electromagnetic waves in photonic crystals.…”

Section: Introductionmentioning

confidence: 99%

Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch

2000

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The finite-difference time-domain method is applied to the calculation of dispersion relations of acoustic waves in two-dimensional ͑2D͒ phononic lattices, i.e., periodic solid-solid, solid-liquid, and solid-vacuum composites, for which the conventional plane-wave-expansion method fails or converges very slowly. Numerical examples are developed for 2D structures with polyethylene, mercury, and vacuum cylinders forming a square lattice in an aluminum matrix. The implication of the calculated dispersion relations for ultrasound transmission experiments is discussed.

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Order-Nspectral method for electromagnetic waves

Cited by 285 publications

References 31 publications

Elastic metamaterials and dynamic homogenization: a review

Elastic metamaterials and dynamic homogenization: a review

Localization of electromagnetic waves in two-dimensional disordered systems

Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch

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