Topological photonics combines concepts from photonics, mathematics, and condensed matter physics to study wave propagation in structured materials. My current research focuses on the design and optimization of topological photonic crystals using semidefinite programming, finite element methods, and spectral analysis. Particular interests include spectral and band-gap optimization, Berry curvature, topological invariants, Chern-number computations, and valley-Hall photonic systems.
Research Topics
* Topological Photonic Crystals
* Band-Gap Optimization
* Berry Curvature and Berry Phase
* Topological Invariants (Chern Numbers)
* Valley-Hall Photonic Systems
* Spectral Analysis of Periodic Structures
* Bloch Wave Propagation
Research Methods
* Semidefinite Programming (SDP)
* Finite Element Methods (FEM)
* Numerical Optimization
* Spectral Theory
* Scientific Computing
* High-Performance Computing (HPC)
Current Research Applications
* Design of topological photonic crystals
* Shared spectral band-gap optimization
* Optimization of photonic wave propagation
* Valley-Hall edge-state engineering
* Numerical simulation of periodic electromagnetic structures
Current Research Highlights
* Shared spectral band-gap optimization of topological photonic crystals
* Semidefinite programming for photonic crystal design
* Finite element and spectral methods for electromagnetic wave propagation
* Berry-curvature and topological-invariant computation
* Valley-Chern analysis of photonic systems
Software and Computational Tools
* MATLAB
* CVX
* MOSEK
* SDPT3
* Gurobi
* Finite Element Analysis (FEM)
* High-Performance Computing (HPC)
Research Goal
To develop mathematical and computational frameworks for the design and optimization of topological photonic crystals with desirable spectral and topological properties, advancing applications in photonics, wave engineering, and scientific computing.