Electromagnetic wave propagation in left-handed materials and metallic photonic crystals

Theoretical study of the light propagation in the materials of a new type, which have simultaneously negative electric permittivity ϵ and magnetic permeability μ in the same frequency range and are known as Left-Handed Materials (LHM), is presented. It is shown that in spite of widespread opinion, the refractive index n of the LHM is not necessarily negative. The first and the second thermodynamic laws for electromagnetic field are shown to give two inequalities that are different in the LHM and in the regular materials (RM). Namely, the product Re[n]Im[n] is positive in the RM and negative in the LHM. The second inequality reads that the group velocity is positive in RM and negative in the LHM. Both conditions are quadratic in n, so that the sign of n can be chosen in either way. Moreover, it is shown that if the negative sign is chosen one should change some general electrodynamics definitions. The most important property of the LHM is negative refraction of light at the interface of the RM and the LHM. Russian scientist Victor Veselago has proposed a unique lens for the three-dimensional (3D) imaging based upon this property. The theory of diffraction in the LHM is presented to show that the image of this lens has a usual wavelength smearing though many recent authors claim that this lens is a perfect one.; A new lens based upon the LHM is proposed, which is a modification of the Veselago lens. The new lens should be easier to manufacture, it has multiple foci and can image an object located at any large distance from the lens. The new lens might be useful for the 3D imaging.; The first LHM has been recently created by the San Diego group. It is based upon the low-frequency (GHz) mode in metallic photonic crystal (MPC). This mode has been interpreted by this group as a plasmon that creates a negative ϵ at low frequencies. An analytical theory of the low frequency modes in the MPC has been presented. It has been shown that the mode under study is not a plasmon but a cutoff mode of electromagnetic spectrum of the MPC. This mode cannot propagate in a medium with negative μ. Therefore all the interpretation of the above experiment should be reconsidered.; The high frequency behavior of a two-dimensional (2D) MPC has been also studied (ωτ >> 1, where τ is a relaxation time of electrons in the metal). In this frequency regime the 2D MPC has a complicated spectrum of EMW due to three different plasma modes. Spectrum of the plasma waves, electromagnetic waves, reflection and refraction are considered.