Understanding laser stabilization using spectral hole burning

The theoretical understanding of such laser stabilization exists for the case of cavities, while it is not very well developed for the case using spectral holes. Our contribution is to provide such a theory in the case of using spectral holes. The main difficulty is the requirement to calculate the coherent response of the atomic reference material to the incoming laser radiation. These calculations are inherently non-linear, but we develop a linearized, analytical theory, which is valid in the frequency stabilized condition.