Design of a Tunable Multi-Band Transmitting and Band-Stop Photonic Crystal IR Filter Utilizing Lucas Numbers
Mathematics, vol.14, no.12, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 12
- Publication Date: 2026
- Doi Number: 10.3390/math14122232
- Journal Name: Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: golden ratio, Lucas sequence, multilayer, photonic crystal, transfer matrix method
- Hacettepe University Affiliated: Yes
Abstract
In this study, a novel aperiodic photonic crystal (PC) structure is designed using the golden ratio-based Lucas sequence, and its infrared (IR) transmission characteristics are investigated. Transmission behavior demonstrates a strong dependence on the number of unit cells and parity (even or odd) of the defect layer repetitions, enabling the formation of a predetermined number of resonant modes around the operating wavelength and broad photonic stopbands at longer wavelengths with sharp defect modes. With its high spectral tunability, the proposed new Lucas sequence-based structure represents a viable candidate for the design of high-performance optical filters and components. These findings indicate that novel Lucas sequence-based PC designs will provide new opportunities for manipulating light–matter interactions in future studies.