Fig. 3: Collective resonance excitation band structure and beam displacement for the \({{{J}}}=0\to {{{{J}}}}^{{\prime} }=1\) transition.
a 25-layer b 5-layer collective line shifts δ(j)(qy, qz = 0), in units of the single-atom linewidth γ, for atomic Bloch wave resonances across bands indexed by j, as a function of in-plane quasimomentum qy, indicative of the incident light’s tilting angle. The lattice spacing a = 0.45λ, in units of resonance wavelength λ. The colour coding indicates the collective resonance linewidth (see Methods), υ(j)(qy, qz = 0), on a logarithmic scale, normalised to γ. c 25-layer d 5-layer exact (scatter points) lateral displacement D(k∥, −δ(j)(ky, 0)), in units of λ, compared with approximate (solid lines) lateral beam displacement \(\tilde{D}({{{{\bf{k}}}}}_{\parallel},-{\delta}^{(j)}({k}_{y},0))={v}_{g,y}^{(j)}/{\upsilon }^{(j)}({k}_{y},0)\), derived from the group velocity \({v}_{g,y}^{(j)}=-\partial {\delta }^{(j)}({k}_{y},0)/\partial {k}_{y}\) along the y-axis for laser detuning Δ = −δ(j)(ky, 0) resonant with band j, considering the incident light’s wavevector y-component ky.
