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Chapter 6:
Macroscopic Electromagnetism
Published: 2005
DOI: 10.1117/3.585322.ch6
The nanoengineered morphology of sculptured thin films having been discussed at length in Chapters 2-€“5, let us now turn our attention to the macroscopic electromagnetic characterization of these materials for optical purposes. The essence of electromagnetism comprises four partial differential equations: the so-called Maxwell equations. At microscopic length scales, these equations involve two vector fields along with two source densities, of which one is a scalar and the other is a vector. As these equations were born of experience with electromagnetic phenomenons [305], they are more appropriately named the Maxwell postulates. The two vector fields are the primitive fields, the adjective primitive not indicating a cultural judgment but the priority of existence instead. At macroscopic length scales, which concern us chiefly in this book, spatial averaging of the Maxwell postulates leads to the macroscopic Maxwell postulates. The four equations remain almost intact in form, except that averaged source densities are decomposed into two parts. Whereas one of the two parts can be externally applied, the other indicates the existence of matter. The matter-indicating part is combined with the averaged primitive fields to create two induction fields in two of the four Maxwell postulates. A set of equations is necessary to relate the macroscopic induction fields to the macroscopic primitive fields. These are the so-called constitutive relations, whose delineation has occupied much of the last 150 years [306, 307], but continues to remain a topic of great interest to engineers, scientists, and mathematicians [308, 309]. These equations are conjured from electromagnetic as well as non-electromagnetic considerations, but must be consistent with the structure of the Maxwell postulates [82]. This chapter is focused on two different routes to the macroscopic Maxwell postulates as well as on the constitutive relations of STFs.
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Maxwell's equations

Partial differential equations

Thin films

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