Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction

The effective properties associated with the propagation of electromagnetic waves in photonic crystals (PCs) are analyzed for one dimensional photonic crystals to illustrate the difference in those properties between infinitely extended and finite size photonic crystals (along the wave propagation direction). It is shown that the multiple reflections at the two end surfaces of a PC result in oscillations in transmittance, phase velocity, group velocity, as well as effective refractive indexes n _eff, which are often determined experimentally from the transmitted or reflected wave. At the frequencies far away from the bandgap, the oscillation in both the transmittance and n _eff can be modeled by treating the PC as an effective medium with the effective properties derived from the dispersion curves of the corresponding infinitely extended PC. As the frequencies approaching the band edges, however, the oscillations in both transmittance and n _eff are markedly enhanced due to the reflections from the internal interfaces in the PC. The results clearly demonstrate the importance of the two end faces on the effective properties of a finite size PC, which can be quite different from those deduced for an infinitely extended PC.