General formula for phonon-assisted n-photon absorption in solids

A general formula for phonon-assisted n-photon absorption in solids is obtained by (n+1)-th order perturbation technique. The complicated calculation process for transition element of n-photon absorption is simply demonstrated by a diagram approach that is proposed in this work. We find that the transition element for the n-photon absorption has a simple form, i.e., it is just the first term of the n-th order fist kind Bessel function.