Investigation of the spectral response of graphene-dielectric (SiO 2 )-based periodic structure was made in the far-infrared (IR) to the mid-IR frequency range, and the effects of different parametric and operational conditions on the transmission characteristics were explored. The presence of stop-bands, followed by Bragg reflection harmonics, in the low-frequency regime was observed exploiting the bilayer graphene (BLG) sheets. The width of stop-bands could be tuned by altering the number of periods as well as the chemical potential of BLG. The formation of a stop-band (with a transmission dip positioned at ~16 THz) having a span of ~3 THz was noticed, which is possibly a very large stop-bandwidth reported so far. The structure was also analyzed upon introducing a defect layer of MgF 2 having a thickness smaller than the dielectric medium. This results in shifting the position of stop-bands of the structure. The characteristics of transmission spectra were found to be greatly depending on the chemical potential (of BLG) and other operating conditionsthe feature that triggers the usefulness of the proposed structure in the design of optical modulators, tunable narrow-band filters and broad-band reflectors.