Design of a high-performance four-color stopband photonic crystal filter based on mesoporous TiO₂ thin film

With the advancement of nanofabrication technology, the application of photonic crystals (PCs) as periodic structural filters in the visible light spectrum has become viable. To address the challenge of ensuring that the transmittance of each channel exceeds 90% in traditional multi-channel passband filters based on optical quantum well structures, this paper proposes and designs a novel structure for an efficient narrowband four-channel stopband filter utilizing mesoporous TiO2 films. By setting the period number of layers to 256 and the filling ratio to 0.04, narrower photonic band gaps (PBGs) for each channel and a reflectivity of over 98% were achieved. By adjusting the lattice constant a, an efficient four-channel stopband filter for different wavebands was successfully designed. Research has demonstrated that the impact of the incident light angle on PBGs differs based on the plane of incidence: in the Y-Z plane, as the incident angle increases, all PBGs only undergo a blue shift; In the X-Z plane, PBGs with even indices exhibit a blue shift as the incident angle increases, whereas those with odd indices develop multiple bandgaps. To ensure the stability of the filtering band of the mesoporous TiO2 film, for various lattice constants (290, 300, 310, and 320 nm), the incident light angle in the Y-Z plane must be maintained below 16.30°, 11.68°, 7.95°, and 14.19°, respectively. In the X-Z plane, the angles should be confined to 2.11°, 2.24°, 1.73°, and 1.73°, respectively. This study not only broadens the scope of PC research but also offers a robust theoretical foundation for the development of PC filters exhibiting high reflectivity and structural stability by elucidating their superior optical robustness under conditions of small incident angles.