Epsilon-near-zero or mu-near-zero materials composed of dielectric photonic crystals

We theoretically demonstrate that at certain frequencies two-dimensional dielectric photonic crystals (PCs) may be regarded as either epsilon-near-zero or mu-near-zero materials. We show that the transmission through a slab of such materials upon normal incidence is normally non-unity and decays with slab thickness. However, when the incident angle increases slightly, the transmittance experiences a dramatic increase due to the Brewster effect. The combination of the tunneling and resonance effects makes such materials good candidates for almost perfect bending waveguides and cloaking in waveguides. The zero index also enables applications of focusing and directive emission. At last, the distinction between the single-zero and double-zero media is discussed. In all of the above results, the numerical simulations perfectly match with theoretical predictions from the effective medium analysis.