Solution of refracted wave for monochromic plane wave incident on crystal interface

From Maxwells equations, with material constitutive relation of optically active crystal and boundary conditions of electric field on the boundary between isotropic media and crystal, through coordinate transformation, the formula of the direction of refracted wave for arbitrary direction incident monochromic plane wave was derived. Furthermore, based on the unit vector of direction of refracted wave, eigen waves of electric field, electric displacement vectors and direction of energy flow can be easily obtained. Based on wave optics and physical properties of crystal, its derivation involved no approximation, and the result is applicable for dual axes, single axis and isotropic crystal with or without optically active property.