Hierarchical spectral control of porous silicon microcavities at 1.55µm via dielectric inclusion engineering and graphene tuning

We theoretically investigate hierarchical spectral control of a porous-silicon defect microcavity near 1.55 μm by combining dielectric inclusion engineering with graphene tuning. A transfer-matrix model incorporating effective-medium descriptions and Kubo-based graphene conductivity is used. Dielectric inclusions provide coarse spectral positioning, while a single graphene monolayer at the defect center enables fine electrical adjustment. The baseline cavity exhibits a resonance near 1.55 μm, a peak transmission of 0.994, and a quality factor of about 20. SiO₂, Al₂O₃, and TiO₂ inclusions produce substantial resonance shifts, while varying the graphene Fermi energy from 0.30 eV to 1.50 eV yields a tuning range of approximately 4.45 nm. This exceeds the calculated temperature-induced shift of 2.60 nm over 293 K to 373 K, highlighting graphene's potential for post-fabrication spectral calibration and potential future compensation of temperature-induced resonance drift. The results establish a hierarchical design strategy combining passive spectral positioning with active electrical trimming.