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.
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.
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.
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.
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.
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.