Excitation theory for space-dispersive active media waveguides

Abstract

Abstract.A unified electrodynamic approach to the guided-wave excitation theory is generalized to the waveguiding structures containing a hypothetical space-dispersive medium with drifting charge carriers possessing simultaneously elastic, piezoelectric and magnetic properties. Substantial features of our electrodynamic approach are: (i) the allowance for medium losses and (ii) the separation of potential fields peculiar to the slow quasi-static waves which propagate in such active media independently of the fast electromagnetic waves of curl nature. It is shown that the orthogonal complementary fields appearing inside the external source region are just associated with a contribution of the potential fields inherent in exciting sources. Taking account of medium losses converts the usual orthogonality relation into a novel form called the quasi-orthogonality relation. Development of the mode quasi-orthogonality relation and the equations of mode excitation is based on the generalized reciprocity relation (the extended Lorentz lemma) specially proved for this purpose with allowing for specific properties of the space-dispersive active media and separating the potential fields. The excitation equations turn out to be the same in form whatever waveguide filling, including both the time-dispersive (bianisotropic) and space-dispersive media. Specific properties of such media are reflected in a particular form of the normalizing coefficients for waveguide eigenmodes. It is found that the separation of potential fields reveals the fine structure of interaction between the exciting sources and mode eigenfields: in addition to the exciting currents (bulk and surface) interacting with the curl fields, the exciting charges (bulk and surface) and the double charge (surface dipole) layers appear to interact with the quasi-static potentials and the displacement currents, respectively.

Biased Magnetic Materials in Ram Applications

“…In order to incorporate these interactions, the magnetic eld, H, is replaced by an e ective magnetic eld, H e , that includes other torque-producing contributions besides the external magnetic eld. The e ective magnetic eld can be modeled in the following way [3,8,27] H e = H + H an + H ex + H me (3.9) where the di erent terms are: 1) the classical magnetic eld, H, appearing in Maxwell's equations 2) the crystal anisotropy eld H an = −N c · M due to magnetocrystalline anisotropy of a ferro-or ferrimagnetic material, 3) the exchange eld H ex = λ ex ∇ 2 M due to non-uniform exchange interaction of the precessing spins 4) the magnetoelastic eld H me due to interaction between the magnetization and the mechanical strain of the lattice. The anisotropy tensor N c is assumed to be known, as well as the exchange constant λ ex .…”

Magnetic losses in composite materials

“…The field H is the classical magnetic field, which is the one appearing in Maxwell's equations, whereas the remaining fields are of microscopic (quantum mechanical) origin. The magnetocrystalline anisotropy field H an is due to the atomic lattice and can, to first order, be modelled with a symmetric tensor N c as H an = −N c M [19]. The exchange field H ex is due to the nonuniformity of the magnetization and can be modelled as [20].…”

“…Here j l (k ln r) denote the spherical Bessel functions and Y lm (θ, φ) are the spherical harmonics. Assuming that the magnetic field H 1 is uniform, inserting (19) into (17) and using the orthogonality of the M 1,nlm functions, it can be shown that all mode coefficients are zero for indices l, m = 0, and that the remaining ones are where M ± 1 = (x ± iŷ)/ √ 2, and x ln = k ln R are the roots of…”

The modified Poynting theorem and the concept of mutual energy

“…Application of reciprocity theorem and mutual energy theorem can also be found in the examples [26][27][28][29]. There are a few reference discussed the relationship between Poynting theorem and reciprocity theorem [30][31][32].…”