The lateral shifts of the reflected and transmitted circularly polarized beams from a slab of nanocomposite structurally chiral medium are investigated at the edges of the photonic bandgaps of the structure using the transfer matrix method. The nanocomposite structurally chiral medium consists of the structurally chiral material with the silver nanoparticles randomly dispersed inside it. Due to the presence of metallic nanoparticles, this structure also contains an omnidirectional bandgap in addition to the conventional Bragg gap. By obtaining the co-polarized and cross-polarized reflection and transmission spectra of the structure, we show that only the reflected co-polarized right-handed circularly polarized beam has a considerable lateral shift at the edges of the Bragg gap. Moreover, we have shown that the circularly polarized beams do not have a significant lateral shift at the edges of the nanoparticles created bandgap. We also reveal that the reflected beam experiences a positive lateral shift at the lower edge of the Bragg gap and a negative lateral shift at the upper one. Then we examine the influences of the different parameters, such as the filling fraction of nanoparticles, incidence angle, tilt angle, and slab thickness on the lateral shift of the reflected co-polarized right-handed circularly polarized beam.
