Versatile Spectral Tunability in One-Dimensional Graphene-Based Photonic Crystals via Thue–Morse Quasi-Periodic Chemical Potential Modulation

A one-dimensional Thue–Morse graphene photonic crystal (1D TMGPC) composed of alternating identical dielectric layers and graphene sheets is proposed, in which two distinct graphene chemical potentials are arranged according to a Thue–Morse quasi-periodic sequence. Using the transfer matrix method, we demonstrate that this structure effectively modulates terahertz waves and generates multiple abundant photonic bandgaps at both 20 K and 300 K. Notably, a novel splitting of low-frequency bandgaps produces two additional omnidirectional and polarization-insensitive bandgaps centered at approximately 1.45 THz and 1.95 THz. By analyzing the dispersion relations, reflection phase, photonic density of states, and electric field distributions, the boundary-driven modulation mechanism associated with the quasi-periodic chemical potential is elucidated. Furthermore, the proposed structure exhibits excellent multi-dimensional tunability. The bandgap properties can be dynamically tuned via the electrical control of graphene chemical potentials without altering the physical geometry. Structural tailoring provides an additional degree of freedom, as increasing the Thue–Morse sequence order induces passband splitting. Additionally, increasing the number of repeating periods yields comb-like multi-channel narrowband filtering responses. At a cryogenic temperature of 20 K, two distinct multi-channel narrowband comb filtering responses appear in the frequency ranges of 1.20–1.33 THz and 4.10–4.80 THz, with a minimum full width at half maximum (FWHM) of 1.10 GHz. At a room temperature of 300 K, the higher-frequency comb filtering response remains in the range of 4.10–4.80 THz, with a minimum FWHM of 5.70 GHz. Moreover, we evaluate the performance and stability of the structure when employed as filters and electro-optic switches, thereby providing useful insights for terahertz applications. With its simple geometry, abundant bandgaps, and flexible electro-structural tunability, the proposed 1D TMGPC is highly promising for broadband and electrically tunable terahertz devices.