Absorption of Light by Light

The mutual absorption of two nonparallel classical photon fields through the production of electron pairs is calculated. One of the photon fields is treated accurately in the sense that wave functions are employed which are solutions of the Dirac equation containing the potential of this photon field in the Hamiltonian. The second photon field is introduced as a first-order perturbation to the system containing the first field. An interesting feature is the appearance of an index related to the number of photons in the first field, though this field is not second-quantized. It is shown that the calculation of the absorption process reduces to known results in the limit of small field strength and in the limit of small energy of the photons in the first field. The general results of the theory can be applied to examine the validity of a perturbation expansion.