Additional waves and additional boundary conditions in local quartic metamaterials

Additional electromagnetic waves and additional boundary conditions (ABCs) in non-local materials attract a lot of attention. Here we report the possibility of additional propagating and evanescent waves in local anisotropic and bi-anisotropic linear materials if non-reciprocity is present. We also show that additional waves cannot propagate in local reciprocal bi-anisotropic materials. We investigate the possible options for ABCs and describe how to complement the conventional 4 Maxwell’s boundary conditions in the situations when there are more than 4 waves that need to be matched at the boundary of local and linear quartic metamaterials. We show that these ABCs must depend on the properties of the interface and require the introduction of the additional effective material parameters describing this interface, such as surface conductivities.