04ElectromagneticWavesinAnisotropic-DispersiveMedia.pdf

4 Electromagnetic Waves in Anisotropic-Dispersive Media In Chapters 1 and 3, we examined the basic theory of magnetism and devel- oped a model for the magnetic susceptibility tensor of a saturated ferro- or ferrimagnetic insulator. In this chapter, we will examine the properties of elec- tromagnetic waves traveling in media characterized by frequency-dependent electric and magnetic susceptibilities. We then combine this formalism with the Polder susceptibility tensor to obtain the properties of electromagnetic waves in saturated magnetic insulators. 4.1 Maxwell’s Equations1 The fundamental equations governing electromagnetic fields are Maxwell’s equations: ∂D ∇ × H = + J, (4.1) ∂t ∂B ∇ × E = − , (4.2) ∂t ∇ · D = ρ, (4.3) ∇ · B = 0. (4.4) Here, all of the field quantities are assumed to depend explicitly on time. Although we have encountered some of these quantities in previous chapters, we define them all here for convenience: H is the magnetic field intensity (A/m); D is the electric flux density (C/m2 ); J is the electric volume current density (A/m2 ); E is the electric field intensity (V/m); 1 Standard text books by Jordan and Balmain [1], Kraus and Fleisch [2], and Cheng [3] serve as good sources of introductory material on Maxwell’s equations. D.D. Stancil, A. Prabhakar, Spin Waves, DOI 10.1007/978-0-387-77865-5 4 111 c Springer Science+Business Media, LLC 2009 112 4 Electromagneti