We show how to compute the optical functions when Rydberg excitons appear, including the effect of the coherence between the electron-hole pair and the electromagnetic field. We use the real density matrix approach (RDMA), which, combined with the Green's function method, enables one to derive analytical expressions for the optical functions. Choosing the susceptibility, we performed numerical calculations appropriate to a ${\mathrm{Cu}}_{2}0$ crystal, being a semiconductor with an indirect gap. The effect of the coherence is displayed in the line shape. We also examine in detail and explain the dependence of the oscillator strength and the resonance placement on the state number. We report good agreement with recently published experimental data. We also show that the presented method can be applied to semiconductors with a direct gap.

• Received 9 December 2015
• Revised 24 January 2016

DOI:https://doi.org/10.1103/PhysRevB.93.075206