2. The electrodynamic properties of matter interact strongly with microwaves

Microwaves interact with matter, microscopically, through its constituent atoms, conduction electrons if present, and atomic magnetic dipoles if present. Yet, macroscopically, the effects of microwaves on matter are well described by the four Maxwell equations and the electrodynamic properties of matter: ϵ (electric permittivity), μ (magnetic permeability), and σ (electrical conductivity).

The interactions of microwaves with matter are of many kinds. The general electrodynamic properties of matter, ϵ, μ, and σ, determine completely their behavior when microwaves "hit" them. More specifically, the electric permittivity, ϵ, carries information on the polarization of a dielectric specimen (water, vapor, clouds, wood, glass, and so on) and is related to the number of electric dipoles as χ = Nα/(ϵ<sup>0</sup> � Nαb) and P = (ϵ – ϵ0) E, and ϵ = (1 + χ) ϵ0, with P = ϵ0χE and α the molecular polarizability of the medium and is generally anisotropic, i.e., α<sup>x</sup> 6¼ α<sup>y</sup> 6¼ αz; hence χ in general is anisotropic and is represented by a tensor in matrix form. Electric dipoles absorb greatly microwaves because these cause the electric dipoles to execute damped oscillations at the GHz frequency. The damped motion brings with it a complex ϵ = ϵ' – i ϵ" which is also a function of frequency [27, 28], in which ϵ" takes account of the energy losses.

The magnetic permeability, μ, carries information on the magnetization capacity of a material that carries a number N of magnetic dipoles. They are related by μ = μ0(1 + χm), M = χmH, M = (μ<sup>r</sup> – 1)H, and M = ∑mi, where m<sup>i</sup> are microscopic, atomic magnetic moments (spin, S; orbital, m) [29, 30]. Magnetic dipoles absorb microwave energy because they precess with damping under the torques produced by the microwave's magnetic field; according to the Landau-Lifshitz [30] equation of motion: M'(t) = γM�H(ω) – αM�(M�H(ω)), in which H(ω) is the magnetic field component of the microwaves, γ is the gyromagnetic ratio, and α is the damping constant. The precession velocity and hence M<sup>0</sup> is different for different H (ω). The higher the frequency, the higher the losses. The damped precessions bring with them the loss of microwave energy making the magnetic permeability complex and frequency-dependent, μ(ω) = μ<sup>0</sup> (ω) � <sup>i</sup>μ″(ω). In addition, the response of <sup>M</sup> to H(ω) is almost always direction-dependent, i.e., given H in direction x produces Mx, but the same H applied along y or z produces My 6¼ Mz 6¼ Mx, and this responses are properly described with a tensor χm(ω), or tensor μ(ω). When the magnetic material is ferro- or ferrimagnetic and it is not magnetically saturated, its magnetic structure is comprised of domains and domain walls; the magnetization, Ma, within a domain, a, has a magnitude and a direction, a; the magnetization, Mb, within domain b, has another magnitude and another direction, b, and so on. The walls in between the domains have a considerable amount of magnetic energy [30, 31] and can move in translational or rotating dissipative and anisotropic motion following the LL damped equation of motion given above. An iconic set of magnetic materials that has been used in multiple microwave applications since its invention is the socalled microwave ferrites [11–15]. These materials present two magnetic structures and are very poor semiconductors; many authors approximate them as insulators. In any case, their conductivity is very small. However, metals have the largest conductivities and show particular interactions with microwaves. The conductivity of a metal, or conducting material, presents millions of "free" electrons to the actions of the electric, J = σE, and magnetic fields, qv�B, of the microwaves, and the Lorentz force makes them jiggle rapidly in the resistive medium they are, generating Joule losses and eventually heat. The higher the frequency of the microwaves, the conductivity can become frequency-dependent. In general, the responses ϵ(ω), μ(ω), and σ(ω) are heavily dependent on the frequency of the

The Interaction of Microwaves with Materials of Different Properties DOI: http://dx.doi.org/10.5772/intechopen.83675

microwaves. This is the dispersion characteristic of matter. As an example, clouds, water vapor, hot air, and sea water have quite different electrodynamic properties; that is why weather radar of longest wavelength (L-band, λ ≈ 1 m, ν ≈ 1.24 GHz) is used routinely to penetrate clouds, and weather radar of shorter wavelengths (C-band, λ ≈ 0.25 m, ν ≈ 3.2 GHz) is used to detect forests, and even X-band radar is used to measure altitude with respect to sea level due to its highest reflectivity on the surface of the ocean. The ϵ, the μ, and the σ of a material take away, absorb, energy any time they are microwave bathed, much the same way as when we heat coffee or meals in the microwave oven.

We describe here, in a nutshell form, the fundamental physics involved in the interactions of microwaves with matter with emphasis on magnetic matter. Today science and technology are able to produce, control, direct, and amplify microwaves in the laboratory and in devices and high-technology instruments and equipments [9, 11, 19, 21]. The electromagnetism of microwave devices and instruments is an integral part of today's technological world. And the electrodynamics of microwaves is governed by Maxwell's equations as applied to ϵ, μ, and σ materials. We present these equations and the partial differential wave equations that are obtained from them with the expressions of their solutions.
