Low Frequency Dispersion Law for Two-Dimensional Metallic Photonic Crystals

摘要

Using the rigorous multiple-scattering theory, we study the dispersion relation of electromagnetic (EM) waves in two di- mensional dielectric photonic crystals (PCs) and metallic photonic crystals (MPCs) in the low-frequency limit. Analytic formula for the effective velocity of EM waves in PCs and MPCs is obtained. Accuracy of our formula is checked by comparing the results with rigorous calculations. For PCs, our result is exactly the same as the coherent potential approximation (CPA), which is accurate even when the filling fraction is high. But for MPCs, our approach demonstrates special advantages, while the CPA theory fails, in predicting the effective velocity of EM waves in MPCs at low frequency.