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.

Type of Study: Research |
Subject:
General

Received: 2017/08/6 | Revised: 2019/01/5 | Accepted: 2017/11/11 | Published: 2018/12/12

Received: 2017/08/6 | Revised: 2019/01/5 | Accepted: 2017/11/11 | Published: 2018/12/12

1. W. Greiner and J. Reinhardt, Quantum Electrodynamics, Springer-Verlag Berlin, Heidelberg, 4th Ed. 2009. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, World Scientic, Singapore, 5th Ed. 2009.

2. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, World Scientic, Singapore, 5th Ed. 2009.

3. W. Vogel and D. G. Welsch, Quantum Optics , Wiley- VCH Verlag GmbH and Co. Weinheim, 3rd Ed. 2006.

4. M. Amooshahi, "Canonical quantization of electromagnetic field in the presence of absorbing bi-anisotropic multilayer magnetodielectric media," Eur. Phys. J. D, Vol. 69, PP. 66-88, 2015.

5. R. Nawaz and M. Ayub, "Closed form solution of electromagnetic wave diffraction problem in a homogeneous bi‐isotropic medium," Math. Method Appl. Sci. Vol. 38, PP. 176-187, 2016.

6. M.A. Kaliteevski, V.A. Mazlin, K. A. Ivanov, and A. R. Gubaydullin, "Quantization of electromagnetic field in an inhomogeneous medium based on scattering matrix formalism (S-quantization)", Opt. Spectrosc. Vol. 119, PP. 832-837, 2015.

7. S.A.R. Horsley, "Canonical quantization of the electromagnetic field interacting with a moving dielectric medium," Phys. Rev. A, Vol. 86, PP. 023830 (1-14), 2012.

8. F. Kheirandish and S. Salimi, "Quantum field theory in the presence of a medium: Green's function expansions," Phys. Rev. A, Vol. 84, PP. 062122 (1-9), 2011.

9. M. F. Maghrebi, R. Golestanian, and M. Kardar, "Scattering approach to the dynamical Casimir effect," Physical Review D, Vol. 87, PP. 025016 (1-15), 2013.

10. F. Kheirandish and M. Jafar "A perturbative approach to calculating the Casimir force in fluctuating scalar and vector fields," Phys.Rev. A, Vol. 86, PP. 022503 (1-20), 2012.

11. R. Golestanian and M. Kardar,"Path-integral approach to the dynamic Casimir effect with fluctuating boundaries," Physical Review A, Vol. 58, PP. 1713-1722, 1998.

12. B. Kiani and J. Sarabadani, "Repulsive Casimir interaction between conducting and permeable corrugated plates," Phys. Rev. A, Vol. 86, PP. 022516 (1-6), 2012.

13. R. Guerout, A. Lambrecht, K. A. Milton, and S Reynaud, "Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors," Phys. Rev. E, Vol. 93, PP. 022108 (1-7), 2016.

14. J S. Høye, I. Brevik, and K. A. Milton, "Casimir friction between polarizable particle and half-space with radiation damping at zero temperature," J. Phys. A: Math. Theor. Vol. 84, PP. 36-51, 2016.

15. E. Amooghorban and F. Kheirandish, "Relativistic and Non-Relativistic Quantum Brownian Motion in an Anisotropic Dissipative Medium," Int. J. Theor. Phys. Vol. 53, PP. 2593 (1-27), 2014.

16. A. Refaei and F. Kheirandish, "Dissipative Scalar Field Theory: A Covariant Formulation," Int. J. Theor. Phys. Vol. 55, PP. 432-439, 2016.

17. F. Kheirandish and V. Ameri, "Electromagnetic field quantization in the presence of a rotating body," Phys. Rev. A, Vol. 89, PP. 032124 (1-14), 2014.

18. M. Amooshahi, "Canonical quantization of electromagnetic field in an anisotropic polarizable and magnetizable medium," J. Math. Phys, Vol. 50, PP. 062301 (1-22), 2009.

19. W. Greiner and J. Richardt, Field quantization, Springer-Verlag, Berlin, Heidelberg, 1996. [DOI:10.1007/978-3-642-61485-9]