Analysis of the contributions of magnetic susceptibility to effective refractive indices of photonic crystals at long-wavelength limits

Since the magnetic susceptibility of materials is significant for low-wavelength regions, we investigated magnetic effects on refractive indices for long-wavelength electromagnetic waves propagating in photonic crystals (PCs). The PCs consisted of triangularly arrayed long rods, and were made of either dielectric or magnetic material, with air as the interstitial medium. According to calculated photonic band structures, the magnetism of rods plays a role in TM modes. Instead of using complicated calculating processes for band structures to find long-wavelength refractive indices, an analytic method was developed to estimate the effective refractive indices of long-wavelength TM modes. The refractive indices obtained through the band structures and the analytic method were consistent with each other. This demonstrates the validity of the analytic method, which we used to further clarify the physical mechanism involving the effects of rod magnetism on the refractive indices of long-wavelength TM modes propagating along magnetic PCs.