  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.
