Pre-Quantum Electrodynamics

Let's quickly pause to give a classification of the types of responses that might be expected from materials. \subsubsection*{Permanent polarization:} here, \({\bf P} \neq 0\) even if \({\bf E} = 0\). These are the {\bf electrets}.

\subsubsection*{Nonlinear dielectrics:} \[ P_i = \sum_j \alpha_{ij} E_j + \sum_{jk} \beta_{ijkl} E_j E_k E_l + ... \] (even-order terms usually absent, but could be there in principle). \subsubsection*{Linear dielectrics:} only linear term is there. Most general: \[ P_i = \varepsilon_0 \chi_{ij} E_j \label{Gr(4.38)} \] where \({\bf \chi}\) is the {\bf electric susceptibility tensor} (it's a tensor of rank 2), which cannot depend on \({\bf E}\) (otherwise we go back to the nonlinear case). Common in crystals, leading to for example double refraction. \subsubsection*{Linear isotropic dielectrics:} at a given point, the electrical properties of the dielectric are independent of the direction of \({\bf E}\) (isotropy). Liquids fall into this category. We here have