In this dissertation, we study the electromagnetic (EM) wave propagation in optically active anisotropic media. Natural and induced optical activity (Faraday effect) are considered simultaneously. In addition, these media are considered lossless, homogeneous, linear, source-free and necessarily dispersive. They are described electromagnetically by the constitutive relations (CR) D= ε -ċE+iγ -ċH and D=-947; ≃ċE+µ -ċH.
We, first, derive the dispersion equation in a biuniaxial chiral medium that is placed in a constant magnetic induction field B othat is parallel to the axis of symmetry of the material, c. In this case, ε -, µ -and γ -, the permittivity, permeability and chirality tensors, respectively, are given in their dyadic representations as follow: ε -=ε 1I -+ (ε 2-ε 1)cc+iε x(c×I -), µ -= µ 1I -+ (µ 2-µ 1)cc+iµ x(c×I -), and γ -= #947; 1I -+(γ 2-γ 1)cc+γ x(c×I -)
We observe and discuss the important phenomenon of non-symmetrical values of the refractive indices, in the forward and backward directions of propagations.
We then study this phenomenon in more details in an isotropic chiral (γ -=γI -, ε 2=ε 1and µ 2=µ 1) medium that is subject to B o. In this case, we analyze the coupling effects of chirality and Faraday effect on the wave vector surface. We show that three different waves may propagate in one direction under certain circumstances. Moreover, c may acts as an optic axis for waves propagating in either the forward or backward direction. Conditions for linear polarization of the waves are determined. Then, expressions for the reflection and transmission coefficients at an isotropic-optically active interface are formulated for oblique and normal incidence. We observe the possibilities of linear or circular polarizations of the reflected wave, when the incident wave is either linearly or circularly polarized.
After that, we study the effects of the elements of the constant tensors ε -, µ -, and γ -by considering two special cases of only chiral media (ε x=0): (a) when ε -=ε I -, µ -=µI -, and γ -= γ 1I -+ (γ 2-γ 1)cc, and (b) when ε -= ε 1I -+(ε 2-ε 1)cc, µ -= µ 1I -+(µ 2-µ 1cc, and γ -= γ x(c×I -). In both of these cases, closed solutions for the refractive indices and their geometrical shapes are determined. Directions of the field vectors and the polarizations of the waves were determined in unbounded and semi-bounded media. In case (a), we observe the possibility of forming a conical section of optic axes on the index vector surface. In case (b) we observe that γ xpreserves the ellipticities of the two sheets of the index vector surface. It also preserves the linear polarization of the electric filed vector for one of the wave and the magnetic field vector for the other wave. However, the other field vectors become elliptically polarized with minor axes parallel to the wave vectors.
Finally, we consider isotropic chiral media. The reflections and transmission coefficients are studied in details when the incident wave is: (a) in an inactive medium, and (b) in a chiral medium. We show that it is possible for the velocity of light in a chiral medium to be higher than that of the vacuum. In addition, we show that it is possible to split any incident wave into its right- and left-hand circularly polarized components where one of them is completely transmitted while the other in completely reflected.