The aim of this tutorial chapter is to cover the elements of the new optical science of negative refraction. We make no claim to exhaustive coverage. Our aim is rather to cover the material in such a way as to make this exciting field accessible to enthusiastic and well prepared undergraduates, as well as to new researchers in the field. Modern-day interest in negative refraction was sparked by Smith et al., who showed in 2000 that it was possible to make a structure that exhibited a negative index of refraction for microwaves. The novel property of their metamaterial was that the crests of the microwaves travelled in the direction opposite to which the energy was flowing. This led to the term "negative phase velocity" being applied to such media. Previously Schuster, Mandelshtam, and Veselago had explored the implications of light's phase velocity being negative. The key characteristics of a medium that allows light to propagate freely with a negative phase velocity are that both the permittivity Ïµ and the permeability Î¼ must be negative. The property of having the crests of an electromagnetic wave move from the receiver toward the source is the result of the intervening medium having a negative magnetic permeability. Such waves associated with microwave fields in magnetic materials are called backward waves and have been known for more than half a century. The improvement offered by also having the permittivity negative is that these backward waves propagate without appreciable attenuation.
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