Perturbative Approach to Calculating the Correlation Function of bi-isotropic Metamaterials

A bi-isotropic magneto-electric metamaterials is modeled by two independent reservoirs. The reservoirs contain a continuum of three dimensional harmonic oscillators, which describe polarizability and magnetizability of the medium. The paper aimed to investigate the effect of electromagnetic field on bi-isotropic. Starting with a total Lagrangian and using Euler-Lagrange equation, researcher could obtain a quantum Langevin type dissipative equation for electromagnetic field. Generating functional of the system is obtained by the path integral method and based on the perturbative approach. By generating functional, a series expansion in terms of susceptibility function of the bi-isotropic metamaterials is obtained for correlation function or two-point Green’s function. In special case, the close relationship between statistical mechanics and quantum field theory,which was reflected in the path integral methods, could obtain free energy of electromagnetic field for isotropic metamaterial using two-point Green’s function. As an example, the Casimir force of two polarizable metamaterial spheres by Lorentz susceptibilities was studied. Furthermore, Casimir force of two polarizable-magnetizable metamaterials was calculated.