From this and Equation \(\eqref{Aquantum}\), we identify the corresponding classical field \[\mathbf{A}(\mathbf{r},t) = \sum_{\mathbf{k}\lambda} \Big(\mathcal{A}_{\mathbf{k}\lambda}\, e^{i(\mathbf{k}\...From this and Equation \(\eqref{Aquantum}\), we identify the corresponding classical field \[\mathbf{A}(\mathbf{r},t) = \sum_{\mathbf{k}\lambda} \Big(\mathcal{A}_{\mathbf{k}\lambda}\, e^{i(\mathbf{k}\cdot\mathbf{r} - \omega_{\mathbf{k}} t)} + \mathrm{c.c.}\Big)\, \mathbf{e}_{\mathbf{k}\lambda}, \quad \mathrm{where}\;\;\; \mathcal{C}_{\mathbf{k}\lambda} \alpha_{\mathbf{k}\lambda} = \mathcal{A}_{\mathbf{k}\lambda}.\] For each \(\mathbf{k}\) and \(\lambda\), Equations \(\eqref{Efield}\)–\(\eqref{B…