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Chapter 8:
Photonic Crystals: From Fundamentals to Functional Photonic Opals
Controlling the flow of light is one of the major challenges in modern optics. With optical telecommunication and computing technologies becoming increasingly important, there is an ever-growing need for devices that will be able to control and manipulate lightwave signals. Guiding of light over large distances with ultralow losses has revolutionized the communications industry, allowing for fiber optic transmission of information. Therefore, it is certainly conceivable that the control of light flow on a microscopic scale may equally well open a new era in the realms of computation, quantum electronics, photonics, optical chips, and functional devices. Classic means for controlling light signals are Bragg mirrors, waveguides, resonators, and beam splitters. However, considering that the diversity of modern optical devices has dramatically increased, there is now a plethora of new challenges in our quest for new ways of controlling light. An example of desired lightwave-based functionality is optically switchable windows, whose appearance can be switched on demand (e.g., from opaque to totally transparent and vice-versa). It is thus clear that such sorts of applications fundamentally entail an exploration and pursuit of new ideas, designs, and photonic devices that will enable us to mould the flow of light beyond current constraints. Photonic crystals (PCs) are engineered structures that have a photonic functionality on the materials level, enabling the complete prohibition or allowance of the propagation of light in certain directions and at certain frequencies. They accomplish this feat by means of a periodic modulation of the refractive index of a suitable host medium. Within these three-dimensionally periodic structures, the distribution of electromagnetic modes and their accompanying dispersion relations differ dramatically from those of bulk media. PCs are, in this regard, highly attractive because they allow the design and manipulation of their photonic properties based on a so-called “band-structure engineering.” In particular, it swiftly turns out from a pertinent modal analysis that PCs possess photonic band gap (PBG) regions, i.e., regions in which the propagation of photons is forbidden and the density of allowed electromagnetic states vanishes. These regions can be designed to exist in one-, two- or three-dimensional structures, depending on whether the dielectric constant is periodic along one direction and homogeneous in the others (1D PCs), periodic in a plane and homogeneous in the third direction (2D PCs), or periodic in all three directions (3D PCs). Although 1D PCs have been known and well-studied for decades in the form of highly reflecting dielectric (Bragg) mirrors, the idea of constructing a 2- or 3D PC is no more than about two decades old. From the start, 3D PCs have attracted enormous attention by scientists, owing to the prediction that they posses highly unusual features, such as full 3D PBGs, and also because of the conceivable applications of these structures. Some of the best known 3D PCs are the Yablonovite structure, the “layer-by-layer” structure, the silicon woodpile structure, and the opal and inverse-opal PC structures.
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