{"paper":{"title":"Hidden symmetries in $N$-layer dielectric stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.app-ph"],"primary_cat":"physics.optics","authors_text":"Haihao Liu, M. Shoufie Ukhtary, Riichiro Saito","submitted_at":"2017-05-26T11:27:28Z","abstract_excerpt":"The optical properties of a multilayer system of dielectric media with arbitrary $N$ layers is investigated. Each layer is one of two dielectric media, with thickness one-quarter the wavelength of light in that medium, corresponding to a central frequency. Using the transfer matrix method, the transmittance $T$ is calculated for all possible $2^N$ sequences for small $N$. Unexpectedly, it is found that instead of $2^N$ different values of $T$ at the central frequency ($T_0$), there are either $(N/2+1)$ or $(N+1)$ discrete values of $T_0$ for even or odd $N$, respectively. We explain the high d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09535","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"}