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Location and Topology of the Fundamental Gap in Photonic Crystals

Thomas Christensen1,*, Hoi Chun Po1,2, John D. Joannopoulos1, and Marin Soljačić1

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China

  • *tchr@mit.edu
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Phys. Rev. X 12, 021066 – Published 27 June, 2022

DOI: https://doi.org/10.1103/PhysRevX.12.021066

Abstract

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly constrained by symmetry, this problem cannot be addressed directly with conventional band-symmetry analysis due to the existence of a photonic polarization vortex at zero frequency. We develop an approach for overcoming the associated symmetry singularity by incorporating fictitious, auxiliary longitudinal modes. Our strategy also enables us to extend recent developments in symmetry-based topological analysis to the fundamental gap of three-dimensional photonic crystals. Exploiting this, we systematically study the topology of the minimal fundamental gaps. This reveals the existence of topological gap obstructions that push the fundamental gap higher than what a conventional analysis would suggest. Our work demonstrates that topology can play a crucial role in the opening of the fundamental photonic gap and informs future theoretical and experimental searches for conventional and topological band gaps in three-dimensional photonic crystals.

Physics Subject Headings (PhySH)

Popular Summary

A defining property of photonic crystals—periodic arrangements of refractive material, repeating on a scale comparable to wavelengths of light—is their ability to support photonic band gaps, that is, frequency ranges in which light cannot propagate. While research in photonic crystals has pursued the properties of photonic band gaps for decades, fundamental questions remain. Here, we provide a full answer to one such question: Where can the first photonic band gap above zero frequency be opened?

It is well known that structural symmetry strongly influences the achievable sizes of photonic band gaps. Similarly, symmetry also constrains where photonic band gaps can be opened in the first place, i.e., how many bands must exist below the first gap. Here, we adapt symmetry-based tools from topological band theory to answer this question for every possible type of crystalline symmetry. Not only do we determine where the first photonic band gap can be opened, we also discover a novel topological obstruction to its opening in certain symmetry settings.

Our work paves the way for comprehensive symmetry-based diagnosis of photonic topology.

Article Text

Supplemental Material

References (82)

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Phys. Rev. X 12, 021066– Published 27 June, 2022
  • Received 9 July 2021
  • Accepted 3 May 2022
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