When wave propagates in a complex heterogeneous medium, it cannot “feel” the fine micro-structures of the medium if its wavelength is much larger than the size of the micro-structure.  The wave behaves as if it is traveling in a homogenized medium.  The property of the homogenized medium is determined by the micro-structures and their relation is characterized by effective medium theories.   We applied the coherent potential approximation, multiple-scattering theory methods to derive effective medium theories for photonic/phononic crystals and metamaterials. In particular, we studied:

  • finite frequency behavior of a metamaterial: effective parameters are related to the scattering coefficients
  • tight-packing limit of a phononic crystal: higher order filling ratio terms are non-negligible in the effective mass-density
  • anisotropic property for rectangular and rhombus structures: the anisotropy only appears in mass-density


​Prof. Zhaoqing Zhang, Prof. Ping Sheng, Prof. Zhengyou Liu, Prof. Jun Mei, Prof. Yun Lai


  1. ​Jun Mei, Ying Wu, and Zhengyou Liu, “Effective medium of periodic fluid-solid composites” Europhys. Lett. 98, 54001 (2012)
  2. Ying Wu, Jun Mei, and Ping Sheng, “Anisotropic dynamic mass density for fluid–solidcomposites” Physica B: Condensed Matter 407, 4093 (2012) (Invited proceedings of conference: Wave Propagation)
  3. Ying Wu and Zhao-Qing Zhang “Dispersion relations and their symmetry properties for electromagneticand elastic metamaterials in two dimensions”  Phys. Rev. B 79, 195111(2009)
  4. Ying Wu, Yun Lai, and Zhao-Qing Zhang, “Effective mediumtheory for elastic metamaterials in two dimensions” Phys. Rev. B 76, 205313 (2007)
  5. Ying Wu, Jensen Li, Zhao-Qing Zhang and C. T. Chan, “Effectivemedium theory for magnetodielectric composites: Beyond the long-wavelengthlimit”  Phys. Rev. B 74, 085111(2006)