Comparisons of the transmission and resonant tunneling between the superlattice composed of two alternating photonic crystals and its effective structure

摘要

Transmissions and resonant tunneling of superlattices composed of two alternating triangular photonic crystals (PhCs) and their corresponding effective one-dimensional (1D) superlattices are discussed. In the first case, below 0.40 (c/a), the transmissions of effective 1D superlattices calculated by the effective medium theory (EMT) match those of two-alternating-PhC superlattices calculated by the internal-field expansion method. No matter whether the propagating direction is along the symmetric (along K or M directions) or nonsymmetric axes (incident angle θ = 45?), the results hold very well. In the second case, resonant-tunneling phenomena and transmissions of the two-period superlattice composed of two alternating PhCs (the resonant-tunneling superlattice) can also be predicted by EMT below 0.20 (c/a). However, due to the evanescent waves at oblique incidence, the interface effect between two PhCs becomes explicit in the higher-frequency region and results in the deviations of resonant-tunneling frequencies in EMT calculations. By modifying the effective refractive indices of both PhCs, deviations are corrected and EMT calculations can exhibit resonant tunneling at right frequencies. Furthermore, the resonant-tunneling superlattice with larger background dielectric constant displays fewer modifications on the effective refractive indices.