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Cited by 43Quantum Mechanics and Non-Hermitian PhysicsTopological Materials and PhenomenaMetamaterials and Metasurfaces Applications

Multi-dimensional band structure spectroscopy in the synthetic frequency dimension

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Cheng, Dali, Lustig, Eran, Wang, Kai, Fan, Shanhui·2023·Light: Science & Applications
DOI 10.1038/s41377-023-01196-1PMC PMC10300075
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Abstract

The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional physics. Many of these physics are characterized by band structures in more than one dimensions. Existing efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either one-dimensional Brillouin zones or one-dimensional subsets of multi-dimensional Brillouin zones. Here we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency dimension. We use a single photonic resonator under dynamical modulation to create a multi-dimensional synthetic frequency lattice. We show that the band structure of such a lattice over the entire multi-dimensional Brillouin zone can be measured by introducing a gauge potential into the lattice Hamiltonian. Using this method, we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian Hamiltonian. The measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one dimensions. Our results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension.

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  • Dirac points are common in two-dimensional systems.

    “Dirac points are common in two-dimensional systems [46][47][48].”

    From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [46]

    The Results section discusses two-dimensional band structures and non-Hermitian point-gap topology, not Dirac points. Searches for “Dirac points” and “Dirac cones and band crossings in two-dimensional systems” found no passage in our copy addressing whether Dirac points are common in two-dimensional systems. (LLM, conf=0.74)

    Experimental — accuracy not yet measured

  • In many existing works Dirac points are observed only at time-reversal-breaking wavevectors, such as the K- and K'-points in a honeycomb lattice.

    “However, in many existing works Dirac points are observed only at time-reversal-breaking wavevectors, such as the Kand K'-points in a honeycomb lattice [46][47][48].”

    From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [46]

    The Results section on two-dimensional non-Hermitian band structures discusses point-gap topology and time-reversal-invariant loops, not Dirac points. Searches for Dirac points, honeycomb lattices, and K/K′ wavevectors found no passage in our copy addressing where Dirac points have been observed in existing works. (LLM, conf=0.75)

    Experimental — accuracy not yet measured

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Research works printed but not linked: 48

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Authors
Cheng, D., Lustig, E., Wang, K., & Fan, S.
Affiliations
  • Stanford University (US)
  • McGill University (CA)
Corresponding author
Fan, Shanhui
ORCID
Venue
Light: Science & Applications
Publisher
Springer Science and Business Media LLC
Published
2023-06-27
Volume
12
Issue
1
Pages
158-158
ISSN
2047-7538 (ISSN-L)
DOI
10.1038/s41377-023-01196-1
PMC
PMC10300075
OpenAlex
W4382345200
Cited by
43
References
55
Citations by year
2026: 9 · 2025: 23 · 2024: 9 · 2023: 2
FWCI
4.99
Type
journal article
Language
en
Open access
Licence
Locations
  • Light Science & Applications (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Figshare (submittedVersion, cc-by)
  • arXiv (Cornell University) (cc-by)
Funders
United States Department of Defense | United States Air Force | AFMC | Air Force Office of Scientific Research (FA9550-18-1-0379, FA9550-22-1-0339)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
Keywords
synthetic dimensions, synthetic frequency dimension, photonic resonators, synthetic lattices, gauge potential, non-Hermitian Hamiltonian, point-gap topology, Brillouin zone

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