5 Negative Refraction in Photonic Crystals

The phenomenon of negative refraction (NR) by 2D photonic crystals (PCs) is demonstrated in microwave experiments. NR by PCs is observed in 2D parallel-plate waveguide and in 3D free space measurements. Results are in excellent agreement with band structure calculation and numerical simulation. The optical properties of isotropic materials that are transparent to electromagnetic (EM) waves can be characterized by a refractive index n. Given the direction of the incident beam θ 1 at the interface of vacuum and the material , the direction θ 2 of the outgoing beam can be determined using Snell's law, sin θ 1 = n sin θ 2. All naturally available transparent materials possess a positive refractive index, n > 0. Although we do know that materials with negative permittivity (ε) or negative permeability (µ) are available but do not allow light transmission, it was Veselago who in 1968 realized that double negative indices media with ε, µ < 0 are consistent with Maxwell's equations [1]. This idea was largely ignored till 2001 when it was demonstrated that certain composite metamaterials refract microwaves negatively (θ 2 < 0, θ 1 > 0) and consequently a negative index of refraction n < 0 can be assigned to such materials [2]. Negative refractive index materials (NIM) exhibit some unusual propagation characteristics of EM waves. The most striking property is that of left-handed electromagnetism (LHE). Since for a plane wave, the electric field E and the magnetic field H are related to each other through H = (c/µω)k × E and E = −(c/εω)k × H, thus E, H, and k form a left-handed triplet in a NIM. Consequently the Poynting vector S = E × H is antiparallel to the wave vector k, so that S · k < 0. A material possessing simultaneously negative permittivity ε < 0 and permeability µ < 0 can be shown to necessarily have n ≡ √ ε √ µ < 0 [1]. NIM are also referred to as left-handed meta-materials (LHM). In contrast E, H, k form a right-handed set corresponding