Internal conical refraction in biaxial media and graphical plane constructions deduced from Möhr’s method

Abstract

Following a recent alternative method based on the local properties of the permittivity tensor and on Möhr’s plane graphical construction, propagation of locally plane light waves in biaxial media are studied. The method is applied to re-obtain and synthesize in a very simple and compact manner some geometrical properties of a monochromatic locally plane wave in these media. Likewise, detailed studies for the case when the wave vector lies in the plane of optic axes or is close to these axes have been carried out. Then, phenomenon of internal conical refraction is easily explained and the aperture angle of internal conical refraction can be obtained graphically by means of simple procedures from the known eigenvalues of the dielectric tensor. Then, two graphical constructions to determine the ray direction are also proposed. The former is used when the electric field direction is known. The latter follows from the knowledge of the direction of propagation and uses an alternative tensor based on the relative dielectric permittivity one.