Two-Dimensional Photonic Crystal Waveguides

Abstract

In the last decades, a strong effort has been made to investigate and control the optical properties of materials, to confine light in specified areas, to prohibit its propagation, or to allow it to propagate only in certain directions and at certain frequencies. The introduction of components based on total internal reflection for light guidance, such as optical fibers or integrated ridge wave-guides, has already been a revolution in the telecommunication and optical industry. In parallel to that, another way of controlling light based on Bragg diffraction has already been used in many devices like dielectric mirrors. In 1987, the principle of dielectric mirrors leading to one-dimensional light reflection was generalized to two and three dimensions [1,2], founding a new class of materials: photonic crystals. Since then, this new field has gained continuously increasing interest [3]. Photonic crystals (PCs) are materials with a periodic dielectric constant. If the wavelength of light incident on the crystal is of the same order of magnitude as the periodicity, the multiple-scattered waves at the dielectric interfaces interfere, leading to a band structure for photons. If the difference between the dielectric constants of the materials composing the photonic crystal is high enough, a photonic band gap (i.e., a forbidden frequency range in a certain direction for a certain polarization) can occur. However, a complete photonic band gap (i.e., a forbidden frequency range in all directions for all polarizations) can occur only in three-dimensional (3-D) photonic crystals. Although these 3-D photonic crystals look very promising and have been theoretically widely studied, their experimental fabrication is still a challenge [4–7]. Therefore, a strong effort has been invested to study two-dimensional (2-D) photonic crystals, which are much easier to fabricate and which still present most of the interesting properties of their 3-D counterparts. In the ideal case, 2-D photonic crystals are infinitely extended structures with a dielectric constant that is periodic in a plane and homogeneous in the third dimension. However, experimental structures are always finite, leading to scattering losses in the third dimension [8]. More recently, the concept of photonic crystal slabs consisting of a thin 2-D photonic crystal surrounded by a lower-index material has emerged and is now widely studied, because it offers a compromise between two and three dimensions. Indeed, combining the index guiding in the vertical direction with the presence of the photonic crystal in the plane of periodicity, a 3-D control of light can be achieved [9–11]. Among the several interesting effects in photonic crystals that can be used for a multitude of applications, such as modification of spontaneous emission [12, 13] or effects based on the particular dispersion properties like birefringence [14], superprism effect, and negative refraction [15–17], one of the important effects relies on the existence of the band gap for waveguiding purposes. In this chapter, some properties of 2-D photonic crystals are studied, assuming first an infinite height (Section 2) and then a finite one (Section 3). Then, the influence of introducing a line defect into the photonic crystal lattice to build a waveguide is discussed, first in the case of infinite 2-D photonic crystals (Section 4) and finally in photonic crystal slabs (Section 5).