Transition from photonic crystals to dielectric metamaterials

Dielectric metamaterials create a low-loss platform for a variety of applications in photonics involving a complex manipulation of the amplitude, polarization, and phase of light. However, for many applications it is important to understand how an artificial periodic system operating as a photonic crystal with the properties dominated by the Bragg scattering can transform into a metamaterial described by effective parameters. This chapter provides a comprehensive overview of the transitions between photonic crystals and metamaterials. As an example, we consider the structures composed of dielectric rods arranged in a periodic lattice. The metamaterial regime is defined by a polariton-like feature in the photonic bandgap diagram below all Bragg stop-bands created by the periodicity. This definition makes it possible to introduce the concept of a photonic phase diagram for the metamaterial and photonic crystal regimes as a function of the geometric parameters and dielectric rod permittivity. Transition between the photonic crystal and metamaterial “phases” is accompanied by a dramatic modification of the electromagnetic field patterns in the wave scattering. In addition, we describe the existence of epsilon-near-zero regime, stability of the metamaterial bandgap spectra in the presence of disorder, experimental studies of dielectric metamaterials for the microwave frequencies, and also discuss practical realizations of silicon-based metamaterials operating in the visible frequency range.