Transfer-matrix analysis of resonance, phase, and spectral characteristics in a finite Si 3 N 4 /Air/TiO 2 photonic crystal

This work presents a theoretical investigation of a finite one-dimensional Si 3 N 4 /Air/TiO 2 photonic crystal operating in the visible spectral range using the transfer matrix method under oblique incidence. The optical response is examined through transmission, reflection, spectral phase, group delay, effective group index, electric-field localization and TE/TM angular dispersion. The multilayer exhibits narrow transmission resonances within highly reflective spectral regions, with resonance positions showing a progressive blue shift with increasing incidence angle and a red shift with increasing air-spacer thickness. Rapid phase variations near the dominant resonances produce moderate slow-light enhancement, with a maximum group delay of approximately 0.06 ps and an effective group index approaching 9–10. The calculated field profiles further reveal interference-assisted localization under resonant conditions. Structural robustness is evaluated through systematic thickness deviations, Monte-Carlo random-thickness perturbations and an effective surface/interface roughness model. The principal spectral features remain identifiable under moderate thickness variations, whereas increasing roughness reduces resonance contrast. These results demonstrate the potential of the finite Si 3 N 4 /Air/TiO 2 multilayer as a tunable theoretical platform for visible-range dielectric filtering, phase control and polarization-dependent spectral manipulation, while remaining subject to the limitations of idealized transfer-matrix modeling.