Reflection and Refraction at Isotropic and Anisotropic Media in Coordinate-Invariant Treatment

Abstract

The article develops coordinate-invariant methods to calculate reflection and refraction of plane monochromatic waves at the plane boundary between two isotropic and an isotropic and an anisotropic medium. The vectorial wave equation for the electric field is used to determine polarization vectors to known refraction vectors and this is applied to uniaxial media. Then it is shortly shown how the boundary conditions can be derived using the Heaviside step function and its derivatives which are the delta function and its derivatives. As preparation to the anisotropic case, there are calculated in coordinate-invariant way the amplitude relations for the reflection and refraction between two isotropic media and then in analogous way, the case of reflection and refraction between an isotropic and an anisotropic medium. This is then specialized for perpendicular incidence. It is shown that negative refraction such as discussed in last twenty-five years is impossible.