Photonic Bandgap Expansion and Defect Mode Control in One-Dimensional Graded-Index Si/SiO₂ Photonic Crystals

Abstract

One-dimensional photonic crystals (1D-PhCs) have attracted considerable attention owing to their ability to manipulate electromagnetic wave propagation through photonic bandgap (PBG) formation. In conventional structures, the refractive indices of the constituent layers are assumed constant, which limits the flexibility in tailoring their optical response. In this study, a novel 1D-PhC incorporating a layer-to-layer graded refractive index profile and a central defect cavity is proposed and theoretically investigated. The structure consists of alternating silicon dioxide (SiO₂) layers with a fixed refractive index and silicon (Si) layers, whose refractive indices vary discretely according to the layer-to-layer refractive-index grading parameter, Δn. Moreover, a defect layer has been introduced at the center of the structure to generate a localized resonant mode within the PBG. The optical properties of the described structure were analyzed using the Transfer Matrix Method (TMM). The results showed that as Δn increased significantly, the PBG expanded from 393.7 to 747.4 nm, accompanied by a red shift of the defect resonance wavelength from 737.8 to 816.8 nm. However, the resonance line width decreased considerably, which enhanced the quality factor from 10³ to 5.1 × 10⁴. It was found that layer-to-layer refractive index grading could be an effective approach for PBG engineering and defect mode control, making the proposed structure a promising candidate for optical filters, resonators, and high-performance photonic devices.