## Theory

The theoretical treatment of the electromagnetic properties of STFs can be divided essentially into two main tasks (Lakhtakia and Messier 2004): a description of the constitutive relations of the STF, and the solution of Maxwell's equations to describe the propagation of the electromagnetic wave. Once the description of the propagation of the wave has been obtained, various optical properties of the film such as reflectance, transmission, and optical rotation may be extracted easily.

### 15.3.1.1 Constitutive Properties

The width of the nanowires and voids in STFs are on the order of 50 nm, about an order of magnitude smaller than optical wavelengths. As described in many elementary texts (Jackson 1975), a composite medium, with a uniform composition and features much smaller than a wavelength, may be treated as a homogeneous material with average constitutive parameters. In fact, Maxwell's equations in materials represent such an averaging over atomic dimensions. On a larger scale, a thin layer of STF at a constant depth into the film may be considered a uniform composite of nanowire and void, since, at a given depth, all nanowires have the same morphology and orientation. Along the axis of inhomogeneity, however, the dimensions describing the STF features are on the order of an optical wavelength. Thus, in thin layers the STF may be treated as a homogeneous material; but the variation of parameters from one layer to the next necessitates treating the entire STF as a homogeneous material with constitutive parameters which vary continuously along the axis of inhomogeneity as the nature of the layer changes.

We will first look at finding average constitutive parameters of a single layer. As some applications of STFs involve infiltrating the void region with a fluid, the void region potentially has material in it. Assuming linear materials, the most general constitutive relations for the material in both naonowires and voids may be written in the form (Weiglhofer 2003)

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