Research Research Overview 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 Metamaterials - 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/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 - 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 - 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 - 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.
