A theoretical study of some properties of light propagation in Rudin–Shapiro one-dimensional photonic heterostructures is presented. Particular attention is paid to hybrid periodic–quasiperiodic–periodic systems that include the Rudin–Shapiro sequence design in the non-periodic regions. Features such as omnidirectional reflection, spatial mode localization and full photonic band gap are discussed for different cases. The calculation tool employed is the transfer matrix/scattering matrix technique. The proposed hybrid heterostructure then are used as unitary cells of a photonic crystal which shows wide omnidirectional full gaps in the infrared regions of work. In some of the structures investigated, the proposal involves different pattern of dielectric contrast appears for the periodic part and for the quasiperiodic part. © 2024 Elsevier Inc.