  A photonic realization of the Dirac oscillator (DO), i.e. of the relativistic
extension of the quantum harmonic oscillator, is proposed for light propagation
in fiber Bragg gratings. Transmission spectra clearly show the existence of
electron and positron bound states of the DO, corresponding to resonance modes
above and below the Bragg frequency, as well as the asymmetry of the energy
spectrum for electron and positron branches.
