Effective plasma frequency in tunable THz reflectors based on graphene and phosphorene

In this work, we show that a THz reflector made of a phosphorene (graphene)–dielectric multilayer can be analyzed through a simple effective plasma frequency model. We obtain the cutoff frequency, marking the beginning of the transmission region in terms of the effective plasma frequency, which depends on structural parameters of the multilayer and, more importantly, on the carrier density of phosphorene (graphene) layers. This implies that the cutoff frequency can be varied when considering carrier density tuning. We also show that the frequency regime, where cutoff frequency is obtained by carrier density tuning, goes through a wide range in the THz domain (3–25 THz), making the design of tunable reflectors in these frequencies possible through electrical doping. We numerically analyze the cutoff frequency as a function of carrier density and optical thickness of the multilayer, finding that the cutoff frequency and carrier density of phosphorene (graphene) have a very simple quadratic (quartic) relation. Our analysis allows us to obtain ranges where the effective analytical model fits better with the cutoff frequency computed from photonic bands for the multilayer periodic structure.