2026-08-14 –, Room 3
Periodic structures create band gaps that restrict electromagnetic and elastic wave propagation. These gaps enable control of light and sound at the wavelength scale. PhoXonic.jl is the first pure Julia tool computing both photonic and phononic dispersion relations through a unified interface using plane wave expansion. It supports 1D, 2D, and 3D with dense and sparse solvers, and includes topological invariant analysis. Results reproduce published literature.
Photonic and phononic crystals are periodic structures that exhibit band gaps—frequency ranges where electromagnetic or elastic waves cannot propagate. These materials enable precise control over light and sound at the wavelength scale, with applications ranging from optical fibers and lasers to acoustic filters and vibration isolation. When a single structure simultaneously exhibits both photonic and phononic band gaps, it is called a phoxonic crystal, enabling coupled optomechanical interactions. Existing tools such as MPB focus on photonic crystals only and require C++/Scheme.
PhoXonic.jl is the first pure Julia tool computing both photonic and phononic dispersion relations using plane wave expansion (PWE). It offers:
- Unified API across 1D, 2D, and 3D: The same workflow for photonic and phononic crystals—define materials, geometry, and wave type, then compute band structures.
- Multiple solver backends: Dense eigensolvers for small systems, Krylov methods for large-scale problems, and LOBPCG with warm-start acceleration for efficient band structure sweeps.
- Green's function method and supercell supports: Density of states (DOS) and local density of states (LDOS) calculations for defect mode analysis. Point and line defect simulations via supercell construction.
- Transfer matrix method: Exact solutions for 1D multilayer structures, including transmission/reflection spectra, oblique incidence with TE/TM polarization, and support for lossy materials.
- Topological Invariant Analysis: The ability to compute the 2D Wilson loop spectrum and winding number enables its use as a research tool in topological photonics/phononics.
Validation / Features / Future Directions
The accompanying figure formation of phoxonic bandgap reproducing the paper by Maldovan & Thomas (2006).
PhoXonic.jl has been validated against:
- (Photonic bandgap) MIT Photonic Bands (MPB) and textbook examples from Joannopoulos.
- (Phononic bandgap) Published results from [Kushwaha et al.]
(https://doi.org/10.1103/PhysRevLett.71.2022) for phononic crystals
- Tanaka et al. for phononic crystals with void inclusions
- Dobrzynski et al., "Phononics" textbook (2017, Elsevier, Ch.5) for Si/Epoxy and C/Epoxy phononic crystals (circular and square cross-section inclusions, examples 216--218)
This package is open to contributions and designed for extensibility.
Links
- PhoXonic.jl: https://github.com/hsugawa8651/PhoXonic.jl, DOI: 10.5281/zenodo.18055170
- Docs: https://hsugawa8651.github.io/PhoXonic.jl/dev/
- Colab: https://colab.research.google.com/gist/hsugawa8651/6e19b5d1c083e925aa1642a2fab6f0fc/colab_demo.ipynb
Hiroharu Sugawara is an associate professor in the Graduate School of Systems Design at Tokyo Metropolitan University, Tokyo, Japan. He received his Ph.D. in electronic engineering from the University of Tokyo in 1994.
His research focuses on eco-friendly semiconductor functional materials.
He has been a Julia user since Julia 0.5.
He has been teaching a programming exercise course using the Julia language for university freshmen in the Department of Mechanical Systems Engineering every year since the 2018 academic year.
He translated Tanmay Bakshi's "Tanmay Teaches Julia for Beginners" into Japanese (ISBN 978-4807920211) in 2022.