Our research foci are:

Numerical solutions to wave equation:

  • Wave functional materials:
    • Metamaterials: artificial materials engineered to have properties that may not be found in nature;
    • Photonic/phononic crystals: structured materials with periodic modulations in their physical parameters.
  • Effective medium theory:
    • Effective medium at finite frequencies: breaks the quasi-static limit and works for resonances;
    • Effective medium with "extreme" parameters: when the filling-ratio is extremely high.
  • Waves in random media:
    • Transport behavior: coherent and diffusive transition, energy equilibration;
    • Time reversal and imaging: locating an object by back propagating reversed signals.
  • Numerical solutions to wave equation:
    • Multiple-scattering or T-matrix: a method that takes all interactions between scatterers into account;
    • Algorithms: fast-multipole, sparse matrix canonical grid.

Current Research


We developed a new type of elastic metamaterial, which blurs the distinction between the fluids and solids over certain frequency regime and also exhibits super-anisotropic behavior at other frequencies.

Photonic crystals classical analogue of Dirac cones
Photonic/Phononic crystals: Classical analogue of Dirac cones

We offered a “selection rule” to examine the linearity of the dispersion, predicted the slope of the linear dispersion accurately, and clarified the concepts of the Dirac cone and the Dirac-like cone.

Phononic crystals Rotational modes
Phononic crystals: Rotational modes

We developed a lumped model for rotational modes in phononic crystals. It reveals the origin of the rotation modes, and provides a simple understanding of the mechanism.

Effective medium theory
Effective medium theory

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 the finite frequency behavior of a metamaterial, tight-packing limit of a phoXonic crystal, and anisotropic property for rectangular and rhombus structures.

Waves in random media and time reversal
Waves in random media and time reversal

We studied the diffusive behavior and energy equilibration in a randome elastic media. Developed the sparse matrix canonical grid method to deal with large-scale systems. We also investigated the imaging through complex media and explored the resolution limit.