The last two equations are Gauss's Law and express the experimental facts of Coloumb's law and charge conservation. The simplest and most common case is Then where and As a result of the high frequencies and small wavelengths of optical fields, charge interactions with the optical field involve quantum mechanical effects which cannot accurately be analyzed by continuous models. In optical diffraction problems, is always neglected. In principle, J is also neglected, although the current density can be used formally to add a loss component to the pemitivitty, . We also note that the vectors E and D need not be colinear, meaning that may in general be tensor valued.
Most common materials are approximately homogeneous.
Media in which this is not the case include optical fiber, graded index lenses, and volume holograms. In homogeneous isotropic media, the wave equations are 2.4 Solutions to the Wave Equation Fields satisfying the wave equations are 4D disturbances in space-time. Since a wave disturbance propagates without dissipation, there are no spatially bounded solutions to the wave equation in source and absorber free space. Pulse packets in localized in space-time are potential solutions, but such solutions diffractively dissipate on propagation. There are no simple exact solutions of finite energy.