Page 42 - Electromagnetics

temporal dispersion, have been studied primarily in the frequency domain. In this case
temporal derivative and integral operations produce complex constitutive parameters. It
is becoming equally important to characterize these effects directly in the time domain
for use with direct time-domain field solving techniques such as the finite-difference time-
domain (FDTD) method. We shall cover the very basic properties of dispersive media
in this section. A detailed description of frequency-domain fields (and a discussion of
complex constitutive parameters) is deferred until later in this book.
It is difficult to find a simple and consistent means for classifying materials by their
electromagnetic effects. One way is to separate linear and nonlinear materials, then cate-
gorize linear materials by the way in which the fields are coupled through the constitutive
relations:

1. Isotropic materials are those in which D is related to E, B is related to H, and
the secondary source current J is related to E, with the field direction in each pair
aligned.
2.In anisotropic materials the pairings are the same, but the fields in each pair are
generally not aligned.
3. In biisotropic materials (such as chiral media) the fields D and B depend on both
E and H, but with no realignment of E or H; for instance, D is given by the
addition of a scalar times E plus a second scalar times H. Thus the contributions
to D involve no changes to the directions of E and H.
4. Bianisotropic materials exhibit the most general behavior: D and H depend on both
E and B, with an arbitrary realignment of either or both of these fields.
In 1888, Roentgen showed experimentally that a material isotropic in its own station-
ary reference frame exhibits bianisotropic properties when observed from a moving frame.
Only recently have materials bianisotropic in their own rest frame been discovered. In
1894 Curie predicted that in a stationary material, based on symmetry, an electric field
might produce magnetic effects and a magnetic field might produce electric effects. These
effects, coined magnetoelectric by Landau and Lifshitz in 1957, were sought unsuccess-
fully by many experimentalists during the first half of the twentieth century. In 1959 the
Soviet scientist I.E. Dzyaloshinskii predicted that, theoretically, the antiferromagnetic
material chromium oxide (Cr 2 O 3 ) should display magnetoelectric effects. The magneto-
electric effect was finally observed soon after by D.N. Astrov in a single crystal of Cr 2 O 3
using a 10 kHz electric field. Since then the effect has been observed in many different
materials. Recently, highly exotic materials with useful electromagnetic properties have
been proposed and studied in depth, including chiroplasmas and chiroferrites [211]. As
the technology of materials synthesis advances, a host of new and intriguing media will
certainly be created.
The most general forms of the constitutive relations between the fields may be written
in symbolic form as

D = D[E, B], (2.14)
H = H[E, B]. (2.15)

That is, D and H have some mathematically descriptive relationship to E and B. The
specific forms of the relationships may be written in terms of dyadics as [102]

¯
¯
cD = P · E + L · (cB), (2.16)
¯
¯
H = M · E + Q · (cB), (2.17)

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