In the physics of continuous media, spatial dispersion is usually described as a phenomenon where material parameters such as permittivity or conductivity have dependence on wavevector. Normally, such a dependence is assumed to be absent for simplicity, however spatial dispersion exists to varying degrees in all materials.
The underlying physical reason for the wavevector dependence is often that the material has some spatial structure smaller than the wavelength of any signals (such as light or sound) being considered. Since these small spatial structures cannot be resolved by the waves, only indirect effects (e.g. wavevector dependence) remain detectable. An example of spatial dispersion is that of visible light propagating through a crystal such as calcite, where the refractive index depends on the direction of travel (the orientation of the wavevector) with respect to the crystal structure. In such a case, although the light cannot resolve the individual atoms, they nevertheless can as an aggregate affect how the light propagates. Another common mechanism is that the (e.g.) light is coupled to an excitation of the material, such as a plasmon.
Spatial dispersion can be compared to temporal dispersion, the latter often just called dispersion. Temporal dispersion represents memory effects in systems, commonly seen in optics and electronics. Spatial dispersion on the other hand represents spreading effects and is usually significant only at microscopic length scales. Spatial dispersion contributes relatively small perturbations to optics, giving weak effects such as optical activity. Spatial dispersion and temporal dispersion may occur in the same system.
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