Modern application packages for rigorous solution of problems of light propagation in anisotropic layered media: II. Optically active crystals

Determination of the components of the gyration tensor of quartz by oblique incidence transmission two-modulator generalized ellipsometry

“…However, the more general case of oblique incidence requires solving the Maxwell equations with modified constitutive equations, significantly complicating the mathematics. To do so, several authors use the Berreman 4 × 4 matrix formulation of Maxwell equations, but, even so, different approaches appear in the literature since the choice of the constitutive relations is not unique [23]. We will use the propagation description first given by [24], which uses the constitutive equations given by Born [25].…”

“…We will use the propagation description first given by [24], which uses the constitutive equations given by Born [25]. This model is widely used in the literature [23,[26][27][28], particularly in experimental work, and gives the possible values of the refractive index n, for a given direction of the wave normal. Although this approach is only approximate, it has been shown to be accurate as long as the birefringence of the investigated crystal is not huge [29], as this model describes the phenomenon of optical activity within an accuracy of the product of the linear birefringence in the direction of observation by the gyrotropy parameters [28].…”

Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals

“…The optical activity tensor, g, emerging from this constitutive equation depends on the direction of the wave normal in the crystal. These equations are asymmetric, because a term has been added to the " " " vector but not to l. There seems to be consensus (Fedorov, 1973;Silverman, 1986;Lakhtakia, 2002;Konstantinova et al, 2002) that these constitutive equations and other asymmetric formulations present two deficiencies: they do not fulfill the energy and reciprocity requirements. A more suitable form of the constitutive equations was first given by Tellegen (1948):…”

“…To our knowledge these equations have never been described before. Konstantinova et al (2002) give the relations between the components of the optical activity tensors obtained on the basis of various constitutive equations for some crystal classes. We have checked that the relations that they provide for every specific crystal are in agreement with the optical rotation derived from equations (52).…”

Gyrotropic absorbing crystals of lower symmetries

“…The components of the eigenvectors are the x and y com ponents of the Е and Н vectors of the electric and magnetic fields in the crystal, respectively. The ratios E y /E x (or H y /H x ) are used to determine the azimuths and ellipticity of the natural waves propagating in the crystal [14,15]. In these calculations all tensors were reduced to the axes of the laboratory coordinate sys tem via successive rotations around the Z axis (by the angle ϕ), Y axis (by the angle θ), and X axis (by the angle ψ).…”