Quantization of the electromagnetic field at the presence of two dielectric slabs and application to the Casimir effect
- 59 Downloads
The three dimensional formalism of the Green function method of the electro-magnetic field quantization is extended to quantize the electromagnetic field, at the presence of two dispersive and dissipative dielectric slabs. It is shown that the system decomposes into a singlet and a doublet parts. The singlet system corresponds to the normal polarization state of the electric field and the doublet system corresponds to the sum of parallel and longitudinal polarization states. Each part is quantized separately and vector potential operator of the each part is derived in terms of rightward and leftwards annihilation and creation operators. By using the assuming commutation properties of the noise current density, the equal time canonical commutation relations between the vector potential operator and its conjugate generalized momentum are verified for each part. Finally as an application, the explicit form of field operators are used to obtain an expression for the Casimir force between the two slabs via Maxwell stress tensor.
- 1.W. Vogel, D.G. Welsh, S. Wallentowitz, Quantum Optics: An Introduction (Wiley-VCH, 2001)Google Scholar
- 17.M. Amooshahi, B. Nasr Esfahani, Ann. Phys. 325, (2010) 1913–1930Google Scholar
- 34.C. Cohen-Tannoudji, J. Dupont-Roc, G. Gryberg, Photons and Atoms (Wiley, New York, 1980)Google Scholar
- 35.L. Landau, E. Lifshitz, L. Pitaevskii, Electromagnetic of Continuous Media (Pergamon, Oxford, 1984)Google Scholar