Electromagnetic Wave Propagation and Radiation in Chiral Media

Abstract

Propagation and radiation of electromagnetic waves in a lossless, reciprocal, chiral medium is studied in this thesis. Such a medium is described electromagnetically by the constitutive relations D = eE + iγB and H = iγE + (1/µ)B. The constants e, µ, γ are real and have values that are fixed by the size, shape, and the spatial distribution of the elements that collectively compose the medium. The plane wave propagation in an unbounded chiral medium is considered. The propagation constants are obtained and the polarization properties of electromagnetic waves in such a medium are discussed in detail. The problem of reflection from, and transmission through a semi-infinite chiral medium is solved by obtaining the Fresnel equations. The conditions for the total internal reflection of the incident wave from the interface, and the existance of the Brewster angle are obtained. The effects of the chirality on the polarization and intensity of the reflected wave from the chiral half-space are discussed and illustrated by employing the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence. The radiation emitted by an oscillating dipole in an unbounded, lossless, chiral medium is calculated. From the constitutive relations and from the time-harmonic Maxwell equations ∇ x E = iωB and ∇ x H = J - iωD, it is seen that the wave equation for such a medium is given by ∇ x ∇ x E - ω2µeE - 2ωµγ∇ x E = iωµJ where the source term J is the current density of the oscillating dipole and where E is the electric vector of the radiated field. The desired solution of this wave equation is found by the dyadic Green's function method, that is, by first constructing the dyadic Green's function Γ and then evaluating the expression E = iωµ∫Γ(r,r')•J(r')dV'. The dyadic Green's function Γ and the components of the radiated electric field E are obtained in closed form. The components of the radiated B, D, and H fields can be derived from knowledge of E by using the Maxwell equation B = (1/iω)∇ x E and the constitutive relations. The wave impedance of the medium and the radiation resistance of the dipole are also obtained. The effects of the chiral medium on the polarization and intensity of the dipole radiation are discussed.