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In this work we study how CPT-odd Maxwell-Carroll-Field-Jackiw (MCFJ)electrodynamics as well as a dimension-5 extension of it affect the opticalactivity of continuous media. The starting point is dimension-3 MCFJelectrodynamics in matter whose modified Maxwell equations, permittivitytensor, and dispersion relations are recapitulated. Corresponding refractiveindices are achieved in terms of the frequency and the vector-valued backgroundfield. For a purely timelike background, the refractive indices are real. Theirassociated propagation modes are circularly polarized and exhibitbirefringence. For a purely spacelike background, one refractive index isalways real and the other can be complex. The circularly polarized propagatingmodes may exhibit birefringence and dichroism (associated with absorption).Subsequently, we examine a dimension-five MCFJ-type electrodynamics, previouslyscrutinized in the literature, in a continuous medium. Following the sameprocedure, we find the refractive indices from a sixth-order dispersionequation. For a purely timelike background, three distinct refractive indicesare obtained, one of them being real and two being complex. They are associatedwith two circularly polarized propagating modes that exhibit birefringence ordichroism, depending on the frequency range. Scenarios of propagation andabsorption analogous to those found in dispersive dielectrics are also observedfor spacelike background configurations. We conclude by comparing thedimension-three and five results and by emphasizing the richer phenomenology ofthe propagating modes in the higher-derivative model. Our results areapplicable in the realm of Weyl semimetals.

Effects of CPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter