Propagation of short pulses through ${\mathrm{Cu}}_2\mathrm{O}$ crystal containing Rydberg excitons is studied with the use of the density matrix formalism and the finite difference time domain method. Effects of the so-called Rydberg blockade are studied extensively, exploring not only a reduction of absorption (bleaching) but also power-dependent changes of dispersive properties of the medium. The role of an exciton lifetime and coherent population oscillations in the dynamics of the system are investigated. A pump-probe setup with two pulses is also studied, showing a good agreement with recent experimental results. Calculations are performed for Rydberg states, both for low $n<10$ and high $n\sim 20$ principal quantum numbers.

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• Excitons
• Light propagation, transmission & absorption
• Density matrix methods
• Finite-difference time-domain method
• Monte Carlo methods