This research proposal develops a unified theoretical and experimental framework for acoustic and photonic analogues of spatially modulated sub-wavelength barrier lattices. Building upon the Kronig-Penney model and transfer matrix methods, the work aims to explore emergent topological regimes including Hofstadter butterfly spectra, Thouless pumping, and non-Hermitian skin effects. The methodology combines analytical theory with implementations using Helmholtz resonator arrays for acoustics and sub-wavelength dielectric structures for photonics. Anticipated outcomes include validated design rules for modulated barrier lattices and demonstration of topologically protected waveguiding across multiple wave physics domains.
Key findings
Development of a unified theoretical framework applicable to acoustic, photonic, and quantum mechanical systems.
Establishment of design principles connecting barrier modulation profiles to topological invariants and protected edge states.
Implementation of acoustic analogues using Helmholtz resonator arrays in the audible frequency range.
Implementation of photonic analogues using sub-wavelength dielectric waveguide structures.
Demonstration of topological protection, Thouless pumping, and non-Hermitian phenomena in both platforms.
Limitations & open questions
Currently a research proposal with experimental validation pending (proposed date March 2026).
No existing unified framework for arbitrary spatial modulation across different wave physics domains.
Simultaneous realization of acoustic and photonic implementations enabling direct comparison remains experimentally challenging.