Optical properties of a homogeneously broadened two-level system

For a homogeneously broadened two-level system described by the optical Bloch equations, we show that the photon-absorption cross section (A2) is not equal to the particle-excitation cross section (A2), where is the optical frequency and A2 is proportional to the intensity. We detail how conservation of energy accounts for this inequality. Analytic expressions for these cross sections for weak intensities and strong intensities (to obtain the lowest-order Bloch-Siegert shifts for and) are derived. We define an energy-loss cross section loss(A2) for the bath responsible for the homogeneous broadening, and show that it is proportional to the change of the index of refraction due to the optical transition, n(A2).