Physical Background

Starting from the equations of macroscopic electromagnetism, we derive the geometric optics regime as a limiting case. We discuss the different types of anisotropy possible and then focus on the optical indicatrix in uniaxial and biaxial media. From the optical indicatrices, we show how to obtain the Fresnel surfaces for the ordinary and extraordinary waves and how this relates to the classical Eikonal equation. The permittivity \(\varepsilon \) can be written in terms of appropriate refractive indices and director fields by using the constitutive relation \(\mathbf {D} = \varepsilon \mathbf {E}\) , where \(\mathbf {D}\) is the electric flux density and \(\mathbf {E}\) is the electric field. Finally, the definition of light ray is explored; in the case of anisotropic media, it is necessary to distinguish between the direction of propagation of light rays and the direction of propagation of energy flux.