Application of the general Jacobi diagonalization method to the optical properties of a medium perturbed by an external field

摘要

An analytical approach is presented for studying the convergence of the general Jacobi method applied to diagonalizing the second-rank tensors that describe the optical properties of a medium subjected to an external field. This approach utilizes the fact that the components of such tensors are usually given in field-free principal axes as power series in the field strength, neglecting terms beyond a chosen power of the field. It is shown that for a biaxial or uniaxial medium, the finite number of iterations, which guarantees exact reduction of all the initial terms up to the required power in the series expansions of all off-diagonal elements, can always be found. Moreover, a fixed sequence of rotations in the Jacobi algorithm can be predicted. These findings allow one to derive analytical formulas in noniterative form for a given highest order of the effects being considered and also to optimize numerical iterative diagonalization procedures. Formulas for eigenvalues and eigenvectors applicable to biaxial and uniaxial mediums perturbed by the linear and quadratic effects are presented. Illustrations are given of the electro-optic and piezo-optic effects for the point group 3m. Conditions for biaxial and uniaxial perturbation of a uniaxial crystal are discussed.