Band - Gap Engineering and Defect Modes in Photonic Crystals with Rotated Hexagonal Holes

During recent years, we have observed a rapidly growing interest in the design and fabrication of novel types of photonic-crystal structures possessing large absolute band gaps. The study of various geometries of three-dimensional photonic crystals and different ways to enlarge their absolute band gaps is a key issue in the physics of periodic dielectric structures, where different polarizations of light are coupled together and, therefore, the existence of an absolute band gap is crucially important for various applications of three-dimensional photonic crystals in optics (see. e.g., [1] and references therein). However, for two-dimensional (2D) photonic crystals , Maxwell equations are known to decouple effectively for two polarizations, so that the study of a particular photonic band gap of such periodic structures can be carried out independently for both E-polarized and H-polarized electromagnetic waves. Accordingly, two types of photonic band gaps are usually distinguished to exist for different polarizations. When the band gaps for two different polarizations overlap, they create the combined band gap known as an absolute bandgap. One of the main reasons to enlarge the absolute band gaps and to study the band-gap properties of 2D periodic photonic structures is the attractive possibility of creating novel types of tunable waveguides and circuits for applications of photonic crystals in integrated optics. In particular, the existence of a large absolute band gap would allow us to design waveguides in pla-nar structures which can support propagating modes of both polarizations in the same frequency domain. To date, a number of different approaches have been suggested for the enlargement of the absolute band gaps of 2D photonic-crystal structures. One of these approaches relies on the idea of using the photonic crystals created by a 2D lattice of noncircular holes and exploring the symmetry-reducing properties of 2D photonic crystals for the band-gap enlargement [2–12]. In particular, Wang et al. [11] demonstrated that the absolute band gap becomes maximal in the case of air holes of the same symmetry as the lattice symmetry. For example, the band gap takes a maximum value for a triangular lattice of rotated hexagonal holes. However , Qui et al. [10] suggested that a band gap as large as that demonstrated in [11] can be achieved in 2D pho-tonic crystals created by air holes of more complex noncircular shape without any rotation. In spite of many studies of the absolute band gaps of photonic crystals created by a lattice of …