{
  "annotation_id": "6b7ae901-3728-4fe8-a785-dc1e46df7a87",
  "date_created": "2026-02-17T05:53:08.815000Z",
  "date_modified": "2026-02-17T05:53:08.815000Z",
  "file_hash": "7991d1369cf804ee12a1949ccd8ac841eba898a9e2c8555d9269d09728e8a270",
  "private": false,
  "record": {
    "abstract": "In this paper, we construct a one-dimensional photonic quasicrystal by combining two incommensurate spatial harmonics, where the ratio of their periods is the irrational number \\beta. We evaluate the photonic quasicrystal accurately by a generalized spectral method that embeds the quasiperiodic structure into a higher-dimensional periodic system. We study the spectral distribution of one-dimensional photonic quasicrystals and find some interesting phenomena. As the computational resolution N increases, there are more eigenvalues within finite frequency bandwidths, and the maximum localization always occurs at spectral gap edges for states near index N + 1. By varying \\beta within the range of (0,1), we present a butterfly-shaped spectral structure with abundant band gaps. We find that the spectral structure factor Q (defined as I_{mg}/N, where I_{mg} is the maximum gap index) exhibits different linear patterns as \\beta changes: Q = 1 - \\beta when \\beta \u003c \\beta c, while Q = \\beta when \\beta \u003e \\beta c, where \\beta c \\approx 0.424 is the transition point. This linear relationship holds robustly in the strong quasiperiodic regime (\\beta away from 0 or 1) and is independent of the specific type of irrational number used. The relationship disappears (weak quasiperiodic regime) near \\beta = 0 or \\beta = 1. It demonstrates that the intrinsic spectral properties of one-dimensional photonic quasicrystals are fundamentally governed by the magnitude of the irrational parameter \\beta.",
    "arxiv_id": "2601.06482",
    "authors": [
      "Hui Quan",
      "Wei Si",
      "Kai Jiang"
    ],
    "categories": [
      "physics.optics"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Spectral Distribution of one-dimensional Photonic Quasicrystals: The Role of Irrational Numbers",
    "url": "https://arxiv.org/abs/2601.06482",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2224cb2f-262e-48c6-9a83-59d52442a6fc",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}