Electromagnetic constitutive properties can be extended by judiciously combining component materials to form a composite material. Provided that the granular dimensions of the composite material are much smaller than the electromagnetic wavelengths involved, the composite material may be regarded as a homogenized composite material (HCM). There are many ways in which the characteristics of HCMs can extend beyond those of the component materials; for examples, gain and loss, group speed, and weak nonlinearity may each be enhanced via homogenization. There even are many ways in which HCMs can exhibit characteristics that are not at all exhibited by their component materials; for examples, anisotropy and bianisotropy, Voigt-wave propagation, and negative phase velocity may be supported by HCMs whose component materials do not support these properties. The combination of active and dissipative component materials can yield HCMs that are neither wholly active nor wholly dissipative; such HCMs are can support plane-wave propagation, as well as surface-wave propagation, that is amplified for certain propagation directions but attenuated for other propagation directions.