3-3) Saleh & Teich Problem 5.2-1
5.2-1 Dielectric Media. Identify the media described by the following equations, regarding linearity, dispersiveness, spatial dispersiveness, and homogeneity. Assume that all media are isotropic.
(a) \(P = \epsilon_0 \chi \mathcal{E} - a \nabla \times \mathcal{E}\),
(b) \(P + aP^2 = \epsilon_0 \mathcal{E}\),
(c) \(a_1 \frac{\partial^2 P}{\partial t^2} + a_2 \frac{\partial P}{\partial t} + P = \epsilon_0 \chi \mathcal{E}\),
(d) \(P = \epsilon_0 \{a_1 + a_2 \exp[-(x^2 + y^2)]\} \mathcal{E}\),
where \(\chi, a, a_1,\) and \(a_2\) are constants.