Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 6

DEP =+ e 0 C m

- 2

(1.4)

This definition is totally general, applying to all materials, in particular to all
biological materials. It indeed holds for materials in which [3]:

1. The polarization vector has not the same direction as the vector electric
field, in which case the material is anisotropic .
2. The polarization can be delayed with respect to the variation of elec-
tric field, as is the case in lossy materials . All physical materials are
lossy, so this is a universal property. It is neglected, however, when the
losses are reasonably small, which is not always the case in biological
tissues.
3. The polarization is not proportional to the electric field, in which case
the material is nonlinear .

In all other cases, that is, when the material is isotropic , lossless , and linear ,
the definition (1.4) can be written

DEE
r

= ee = e (1.5)

0

which combines the applied and induced fields, hence the external source field
and the induced polarization, into the definition of e (F m -1 ), permittivity of
the material, product of the permittivity of vacuum e 0 (F m -1 ) and the relative
permittivity e r (dimensionless) of the material. The electric susceptibility c e is
related to the relative permittivity by the expression

e =+ 1 c

(1.6)

r e

It should be stressed that the use of permittivity, relative permittivity, and sus-
ceptibility is limited to isotropy, losslessness, and linearity, which is far from
being always the case, in particular in biological tissues.
Dielectric polarization is a rather complicated phenomenon [4]. It may be
due to a variety of mechanisms, which can be summarized here only briefly.
The simplest materials are gases, especially when they are rarefied. The sim-
plest variety is formed of nonpolar gases , in which the molecules have no elec-
tric dipole at rest. When an electric field is applied, an electric dipole is
induced. This is a simple case for which a simple model can be used for cor-
rectly calculating the polarization. The next category is that of polar gases ,in
which an electric dipole does exist at rest. When an external electric field is
applied, the dipole orientation is modified; it essentially rotates. For such a
polar rarefied gas, which is still a very simple case, the relationship between
polarization and applied field is already found to be nonlinear. When the
density increases, modeling becomes much more difficult, and classical physics
yields wrong models for compact gases, liquids, and of course solids, in