Phase space analysis of metamaterial-based optical systems

•Slabs or lenses with positive/negative indices are analyzed in phase space.•ABCD matrices in the paraxial case are used and full ray tracing otherwise.•Shearing direction of Wigner distribution function changes in the metamaterial slab.•Spherical aberrations occur through planar lenses in the non-paraxial case.•Ideal lensing effect requires equal absolute values of two refractive indices. Phase space analysis of light refraction in optical systems consisting of slabs or thin lenses from either metamaterials with negative refractive indices or common materials is performed with the aim of finding the conditions of perfect imaging for metamaterial-based optical systems. The analysis in the paraxial approximation uses ABCD matrices, whereas full ray tracing is employed in the non-paraxial case. The phase space analysis reveals that the ideality of planar metamaterial lenses only occurs when the absolute value of the refractive index in metamaterials is the same as in the surrounding medium.