Abstract
Spatially dispersive (also known as non‐local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the Floquet modes. A complete set of approximate solutions is calculated which are valid when the inhomogeneity is small. This is applied to inhomogeneous wire media. A new feature arises when considering spatially dispersive media, that is the existence of coupled modes.
Highlights
The standard method of calculating the Bloch modes for a given lattice is to prescribe the constitutive relations for each point within the unit cell
Usually the permittivity and permeability ε∼ and μ∼ of the materials used to construct the unit cell are considered to be only temporally dispersive, that is, they depend on the frequency1 ω
This approach is in contrast with most theoretical articles which consider inhomogeneous spatially dispersive media
Summary
The standard method of calculating the Bloch modes for a given lattice is to prescribe the constitutive relations for each point within the unit cell. In order to make sense of the arguments of ε∼ (ω, k, x) we no longer interpret ε∼ (ω, k, x) as the Fourier transform of the permittivity response function ε (t, x) but in terms of a differential equation [1] This is given in equation (3) below. An alternative interpretation of ε∼ (ω, k, x) is in terms of a susceptibility kernel [2, 3] This approach is in contrast with most theoretical articles which consider inhomogeneous spatially dispersive media. In the case of longitudinal modes, it is the plasma frequency kp given in (8) which is periodic in x, caused by a periodic variation in r In both the transverse and longitudinal cases, the goal in this article is to find solutions to the source free Maxwell equations, i.e. the dispersion relations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
