Photonic Crystals

Abstract

We start with an overview of what photonic crystals are and the basic principles behind their operation. We go on to discuss the design of the first photonic crystals in the microwave regime and their fabrication. We will then go on to look at photonic crystals in the optical regime their fabrication and their applications, including LEDs, lasers, reflectors, waveguides and circuits. Introduction and Basic Principles Photonic crystals offer an exciting new way to control the propagation of light. They promise many great applications, such as high efficiency light sources, low threshold lasers and waveguides into which we can introduce sharp bends. Photonic crystals are to photons, what semiconductors are to electrons, and it is hoped that they will offer as many applications. A photonic crystal is a dielectric containing a periodic arrangement of gaps of another material with a different refractive index. If the refractive index contrast is sufficiently high a band gap forms. This band gap is a set of photon energies which are forbidden from propagating in the material. As the wavelength of electromagnetic radiation is directly related to the photon energy by the equation λ = hc/E, we can say that the crystal blocks radiation of certain wavelengths. These wavelengths are of the order of the distance between gaps in the structure. The reason why this happens is similar to the reason for the existence of a bandgap in a semiconductor. A semiconductor consists of freely propagating electrons in a periodically varying electric field (due to the ions). A photonic crystal consists of photons propagating in periodically varying dielectric constant. One important thing to note is the effect that the crystal has on the emission of photons with energies inside the photonic bandgap in the material. These photons are not emitted and reabsorbed b h bl f h i i hi h h i i i i f bidd One other common feature of photonic crystals and semiconductors is the ability to introduce defect modes into the crystal. By breaking the periodicity of the crystal, either by adding or removing parts of the lattice, we can create energies inside the band gap at which photons are permitted to propagate. This is equivalent to the doping of semiconductors in order to create energy levels inside the semiconductor bandgap. Yablonovite The first photonic crystals were fabricated with a bandgap in the microwave region of the spectrum. This is because the long wavelength of microwaves means that the photonic structure is large enough to be machined. These crystals were produced in 1989 by Eli Yablonovitch at Bell Communications Research in New Jersey. [2, E. Yablonovitch et al, 1989] They machined a number of these crystals by drilling holes in a number of different dielectric materials with a range of dielectric constants. The holes were drilled in a face-centred-cubic arrangement because the theory suggested that this was the simplest structure that was likely to give the desired bandgap in all directions of propagation. The material which eventually showed a complete three-dimensional bandgap had a microwave refractive index of 3.5 The holes drilled were sufficiently large that they overlapped, with 86% of the material being drilled away. This work successfully demonstrated for the first time that a photonic bandgap could in fact be created. However, the development of photonic crystals in the optical regime is considerably more difficult.