{"paper":{"title":"On band gaps in photonic crystal fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Ilia Kamotski, Shane Cooper, Valery Smyshlyaev","submitted_at":"2014-11-02T10:32:08Z","abstract_excerpt":"We consider the Maxwell's system for a periodic array of dielectric `fibers' embedded into a `matrix', with respective electric permittivities $\\epsilon_0$ and $\\epsilon_1$, which serves as a model for cladding in photonic crystal fibers (PCF). The interest is in describing admissible and forbidden (gap) pairs $(\\omega,k)$ of frequencies $\\omega$ and propagation constants $k$ along the fibers, for a Bloch wave solution on the cross-section. We show that, for \"pre-critical\" values of $k(\\omega)$ i.e. those just below $\\omega (\\min\\{\\epsilon_0,\\epsilon_1\\}\\mu)^{1/2}$ (where $\\mu$ is the magnetic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0238","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}