Effect of Applied Fields on the Optical Properties of Color Centers

A theoretical analysis is made of the effect of an external perturbation, such as an electric field, magnetic field, or stress, on the optical properties of color centers. Our analysis is restricted to centers with orbital singlet ground states. It is especially applicable to centers with orbitally degenerate excited states which are interacting strongly with the lattice, such as the $F$ center in the alkali halides. We describe the changes in the optical properties by computing the changes in the moments of the optical absorption line shape that occur when the external perturbation is applied. The changes in the zeroth, first, second, and third moments may be computed quite simply. Although this does not give the detailed change in the line shape, it provides a precise method for evaluating parameters of the center, such as the spin-orbit coupling constant of the excited state of the $F$ center. We use our method of moments to analyze experiments on the circular dichroism, Faraday rotation, Stark effect, Voigt effect, and stress-induced dichroism of the $F$ center and the circular dichroism of the $A$ center. By analyzing the circular-dichroism or stress-induced-dichroism data for an $F$ band, we are able for the first time to evaluate the contributions to the broadening of the band by the cubic and noncubic lattice-vibrational modes. We have analyzed the data of Margerie and Romestain on the circular dichroism of the $F$ band in CsBr and CsCl. Our analysis resolves the discrepancy between their two methods of determining the spin-orbit splitting (measurement of the peak separation and measurement of the circular dichroism), and shows that the splitting arises from a combination of a large spin-orbit coupling and a large noncubic lattice-vibrational interaction.