Deep-Microscopic Photonic Bandstructure of a Two-Dimensional Honeycomb Lattice
Abstract
Conventional descriptions of light in materials rely on macroscopic models that average the optical response over the microscopic lattice structures. These models are deployed in the semi-classical limit, where the collective local response over many lattice sites is adequate. However, they fail to capture the full spatial dispersion, which requires a lattice-resolved description of light. We address this limitation by formulating a deep-microscopic nonlocal theory of the photon based on the Maxwell Hamiltonian and its characteristic equation. The solution reveals the full spatial dispersion in the form of deep-microscopic photonic bandstructure, and corresponding real-space Bloch field textures. We demonstrate our theory for a two-dimensional (2D) tight-binding model of a gapped honeycomb lattice. Our framework thus extends photons to the same microscopic footing as electrons or phonons, providing a unified route to studying topology, dissipation, and quantum fluctuations of light in dispersive materials.
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BibTeX
@misc{das2026deepmicroscopic,
title = {{Deep-Microscopic Photonic Bandstructure of a Two-Dimensional Honeycomb Lattice}},
author = {Pronoy Das and Sathwik Bharadwaj and Wenbo Sun and Zubin Jacob},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33709},
eprint = {2610.33709},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33709},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Deep-Microscopic Photonic Bandstructure of a Two-Dimensional Honeycomb Lattice
AU - Pronoy Das
AU - Sathwik Bharadwaj
AU - Wenbo Sun
AU - Zubin Jacob
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33709
UR - https://arxiv.org/abs/2610.33709
AB - Conventional descriptions of light in materials rely on macroscopic models that average the optical response over the microscopic lattice structures. These models are deployed in the semi-classical limit, where the collective local response over many lattice sites is adequate. However, they fail to capture the full spatial dispersion, which requires a lattice-resolved description of light. We address this limitation by formulating a deep-microscopic nonlocal theory of the photon based on the Maxwell Hamiltonian and its characteristic equation. The solution reveals the full spatial dispersion in the form of deep-microscopic photonic bandstructure, and corresponding real-space Bloch field textures. We demonstrate our theory for a two-dimensional (2D) tight-binding model of a gapped honeycomb lattice. Our framework thus extends photons to the same microscopic footing as electrons or phonons, providing a unified route to studying topology, dissipation, and quantum fluctuations of light in dispersive materials.
ER -