This dataset contains the data presented in "Quantum Single-Photon Control, Storage, and Entanglement Generation with Planar Atomic Arrays", PRX Quantum 2, 040362 (2021). fig2a.csv contains the data in Fig. 2(a). The first column is the time in units 1/gamma, the second column is the energy in the case that no cavity photon is present, the third column the energy in mode one in the case that the cavity photon is present, and the fourth column the energy in mode two in the case that the cavity photon is present fig2b.csv contains the data in Fig. 2(b). The first column is the time in units 1/gamma, the second column is the incident power P_in, the third column the power in the case that no cavity photon is present, and the fourth column the power in the case that the cavity photon is present fig3a.csv contains the data in Fig. 3(a). The first column is the time in units 1/gamma, the second column is the energy in the case that no cavity photon is present, the third column the energy in the case that the cavity photon is present. fig3b.csv contains the data in Fig. 3(b). The first column is the time in units 1/gamma, the second column is the outgoing power in the case that no cavity photon is present, the third column the outgoing power in the case that the cavity photon is present. fig5a.csv is a 2D grid of the intensity data shown in Fig. 5(a). The columns correspond to regularly spaced sampling of x/lambda between -20/(2 pi) and 10/(2 pi). The rows are regularly spaced sampling of y/\lambda between -60/(2 pi) and 60/(2 pi). fig5b.csv is a 2D grid of the intensity data shown in Fig. 5(b), with the same spatial sampling as Fig. 5(a). fig6a.csv shows the data in Fig. 6(a). The first column is the detuning in units of gamma. The second column is the real part of the transmitted field, and the third column is the imaginary part. The absolute value and phase shown in the figure can be calculated from these as standard. fig6b.csv shows the data in Fig. 6(b). The first column is the detuning in units of gamma. The second column is the intensity of transmitted light. The third, fourth, and fifth columns are the Stokes parameters V, U, and Q, respectively. fig6br.csv is a 2D grid of the real part of the electric field shown in Fig. 6(c). The columns correspond to regularly spaced sampling of x/lambda between -40/(2 pi) and 100/(2 pi). The rows are regularly spaced sampling of y/\lambda between -70/(2 pi) and 70/(2 pi). For completeness, fig6bi.csv gives the imaginary part, which is not plotted. fig7.csv gives the data in Fig. 7, with time in units of 1/gamma in the first column, the purity of the full system Tr(rho^2) in the second, and the purity of the subsystem Tr(rho_s^2) in the third.