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semiconductors, which puts an energy level in the energy gap. A wave guide is like a pipe that confines electromagnetic energy, enabling it to flow in one direction. An mteresting feature of this wave guide is that the light in the photonic crystal guide can turn very sharp comers, unlike light traveling in a fiberoptic cable. Because the frequency of the light in the guide is in the forbidden gap, the tight cannot escape into the crystal. It essentially has to turn the sharp corner. Fiberoptic cables rely on total internal reflection at the inner surface of the cable to move the light along. If the fiber is bent too much, the angle of incidence is too large for total internal reflection, and light escapes at the bend.

A resonant cavity can be created in a photonic crystal by removing one rod, or changing the radius of a rod This also puts an energy level into the gap. It turns out that the frequency of this level depends on the radius of the rod, as shown in Fig. 6.33. The air and dielectric bands discussed above are indicated on the figure. This provides a way to tune the frequency of the cavity. This ability to tune die light and concentrate it in small regions gives photonic crystals potential for use as filters and couplers in lasers. Spontaneous emission is the emission of light that occurs when an exited state decays to a lower energy state. It is an essential part of the process of producing lasing. The ability to control spontaneous emission is

Figure 6.33. Dependence of frequency of localized states in the band gap formed on the radius rof a single rod in the square lattice. The ordinate scale is the frequency I multiplied by the lattice parameter a divided by the speed of light c. [Adapted from J. D. Joannopoulos, Nature 386,143 (1997).]

necessary to produce lasing. The rate at which atoms decay depends on the coupling between the atom and the photon, and the density of the electromagnetic modes available for the emitted photon. Photonic crystals could be used to control each of these two factors independently.

Semiconductor technology constitutes the basis of integrated electronic circuitry. The goal of putting more transistors on a chip requires further miniaturization. This unfortunately leads to higher resistances and more energy dissipation. One possible future direction would be to use light and photonic crystals for this technology. Light can travel much faster in a dielectric medium than an electron can in a wire, and it can carry a larger amount of information per second. The bandwidth of optical systems such as fiberoptic cable is terahertz in contrast to that in electron systems (with current flowing through wires), which is a few hundred kilohertz. Photonic crystals have the potential to be the basis of future optical integrated circuits.

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