Negative Index in Chiral Metamaterials under Conductive Loss and First Order Material Dispersion Using Lorentzian, Condon and Drude Models
The aim of this paper is to explore the emergence of negative index (NIM) in chiral materials with conductive loss using standard dispersive models (Lorentzian, Condon and Drude) for the material parameters. Expanding to first order, results are derived for phase and group velocities, and corresponding indices, thereby finding appropriate sideband ranges. As expected, in the NIM region the phase index is negative and group index is positive, it is also found that NIM may occur both for positive and negative sidebands. OCIS codes: (160.1585) chiral media; (160.3918) metamaterials; (260.2030) dispersion 1. General constitutive relations for isotropic chiral media In metamaterials the relationships between the fields (the electric field E and the electric field displacement D and also the magnetic field B and the inductive magnetic field H are not parallel, and electric and magnetic vectors are coupled [1] In particular, the following form is convenient in solving many wave propagation problems in a reciprocal chiral medium [2] D E j H (1) B H j E (2) where is the chirality parameter, is the electric permittivity, and is the magnetic permeability. 2. Derivation of dispersive and lossy chiral wavevectors and phase and group velocities via spectral analysis Starting with expansions of the material parameters up to the first order, one may express the frequency dependent chirality parameter p electric permittivity p the magnetic permeability p and the conductivity p as first order Taylor expansions assuming monochromatic, sinusoidal phasor analyses to be valid [3,4] 0 0 0 0 0 0 0 0 0 po p p p po p p p p p po p p p p p (3) where p p p p are the material parameters of interest expressed as functions of the sideband frequency (O) of the propagating field, and p is the chiral wavenumber which has the dimension rad m 1 More details about calculating the chiral wavevectors in a material with conductive losses may be found in Ref. [3] 2.1 Wavevector solution under conductive losses and plane wave propagation We have introduced complex conductivity into the electromagnetic problem thereby implying that the material has (here) only conductive losses; it is found that in this case the chiral wavevector becomes complex as follow: 3 z k j (4) where the conductivity is equal to 0 0 0 0 0 0 0 0 p p p p r p i p p r p i j j After significant algebra, the complex wavevector (choosing the 3 rd of three possible solutions) in a lossy metamaterial as described can be expressed to first order as follows: