Notes on waves with negative phase velocity

Negative refraction is a wave phenomenon beyond geometrical optics-it depends on the way waves behave when their phase velocity reaches a zero. Various forms of linear wave processes in media can be concisely described in one wave equation that is inspired by the interpretation of a medium as an effective space-time geometry. Depending on the conformal factor of the effective metric, the waves may show positive or negative refraction. For electromagnetic waves in two-dimensional dielectrics the conformal factor corresponds to the impedance.