A sampling series representation of the gain and refractive-index formulas for a combined homogeneously and inhomogeneously broadened laser line

The well-known sampling theorem of communication theory and the associated sampling-series representation of a function are used to derive series representations for the gain and refractive index associated with a laser line that may, in general, be both homogeneously and inhomogeneously broadened. The representations obtained provide the basis for an efficient and highly accurate algorithm for computing numerical approximations to the gain and refractive-index integrals.