Metamaterials from modified CPT-odd standard model extension and minimum length

Here we discuss the standard model extension in the presence of CPT-odd Lorentz violation (LV) sector and of a deformed Heisenberg algebra that leads to a non-commutative theory with minimum length (ML). We derive the set of Maxwell equations emerging from this theory and considered the consequences with respect to the usual effects of electromagnetic waves and material media. We then considered the set of modified equations in material media and investigate the metamaterial behaviour as a consequence of LV and ML. We show that a negative index refraction can be derived from the presence of a non-commutativity suitably tuned by the $\beta$ parameter, while in the presence of LV, we obtained the set of modified Maxwell equation in terms of the corresponding material fields with terms depending explicitly from the terms of interaction between the material fields depending on non-commutativity with the background field due to CPT-odd LV. We conclude that a new set of metamaterials can be derived as a consequence of CPT-odd LV and non-commutativity with minimum length.