Trapping Defect Modes in a Quasi-Periodic Star Waveguide Structure Based on the Fibonacci Sequence

Understanding the interaction between electromagnetic wave propagation and the components of the photonic structure is crucial for developing advanced telecommunications systems. In this study, we investigate a one-dimensional Fibonacci quasiperiodic structure, consisting of periodic waveguides with resonators of varying lengths that depend on each other according to a Fibonacci sequence, attached to N evenly spaced sites. Our research reveals that the photonic bandgap of this structure is significantly influenced by the first two Fibonacci states, d_2in and d₂₁. Additionally, by introducing geometric defects at the resonators level, we enhance the structure’s ability to generate new permissible states within these gaps. The remarkably narrow width of these gaps confines defect modes to a very low-frequency range. Consequently, these defect modes emerge as distinct peaks in the transmission spectrum with optimal transmission and a very high-quality factor. Our results not only shed light on the core characteristics of photonic bandgaps, but also open up new possibilities for their practical use in telecommunications.