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

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