Design of a Tunable Multi-Band Transmitting and Band-Stop Photonic Crystal IR Filter Utilizing Lucas Numbers

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.