Quantum investigation of electromagnetic field energies in the presence of metamaterials

We ýstudy ýquantum ýnature ýof ýmetamaterials ýin ýthe ýpresence ýof ýelectromagnetic ýfield. Starting from a Lagrangian, the ýelectromagnetic ýfield ýýisý canonically ýquantized in ýthe ýpresence ýof ýthe metamaterialsý. The equations of motion for the canonical variables are solved using Laplace technique. In the large-time limit, the vector potential operator is found and expressed in terms of the medium operators. In a global thermal state, finite temperature two-point correlation functions of the electromagnetic field are calculated. The electromagnetic energy flux and energy density and absorbed energy in metamaterials are obtained by considering the special case of thermal equilibrium and using Noether's theorem. ý