High-frequency homogenization for dispersive materials of the Lorentz type #

Marie Touboul, R Assier, R Craster, S Guenneau, B Vial

11:10 Tuesday in 4Q05.

Part of the Multiple wave scattering session.

Abstract #

Classically, dynamic homogenization is understood as a low-frequency approximation to wave propagation in heterogeneous media. A particularly successful approach is the two-scale asymptotic expansion method and the notion of slow and fast variable. The idea of high-frequency homogenization, introduced in [1], is to use similar asymptotic methods to approximate how the dispersion relation and the media behave near a given point that satisfies the dispersion relation.

In the present work, we extend the high-frequency homogenization method to the case of dispersive media where the properties of the material depend on the frequency. More precisely, their dependence will be on the Lorentz (or Drude) type. Upon an expansion of these parameters, we get the approximations of band diagrams such as the ones studied in [2] with effective negative-n materials, or in [3] with metals in dielectrics, together with information on the nature of the effective equation for the wavefields.

[1] R. V. Craster, J. Kaplunov, A. V. Pichugin. High-frequency homogenization for periodic media, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, The Royal Society, 2010, 466, 2341-2362 [2] J. Li, L. Zhou, C. T. Chan, P. Sheng. Photonic Band Gap from a Stack of Positive and Negative Index Materials, Physical Review Letters, American Physical Society (APS), 2003, 90, 083901 [3] Y. Brûlé, B. Gralak, G. Demésy. Calculation and analysis of the complex band structure of dispersive and dissipative two-dimensional photonic crystals, Journal of the Optical Society of America B, 2016, 33