Light on a lattice
In this paper, we shall outline some of the theoretical techniques which have been employed over the last few years in the rapidly growing field of photonic materials. Although much of the work in this area has been motivated by the photonic crystal idea, which we will discuss, the field is actually much broader than that. What we are interested in is any situation where the interaction of light with matter is sufficiently complex that Maxwell's equations cannot be solved analytically. In that case, reliable, numerical schemes are vital if we are to obtain an understanding of the physical problem at hand. The problems treated so far have been diverse ranging from novel device physics and the design of efficient laser cavities, to surface physics and the scanning near-field optical microscope and the surface enhanced Raman effect. We will consider some of these and show how the techniques we have developed can be applied to them.
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