Spatially dispersive inhomogeneous electromagnetic media with periodic structure

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.

Mode Profile Shaping in Wire Media: Towards An Experimental Verification

“…This work is based on the understanding of wire media, a class of metamaterials consisting of a regular (rectangular) array of parallel wires or rods, whose radius is small compared to their spacing [13,14]. When the wire radii also vary, such three-dimensional inhomogeneous media are difficult to analyse in the absence of a simpler model for the system.…”

Electromagnetic mode profile shaping in waveguides

“…As stated in the introduction, this can be created with a wire medium, as described in more detail in [9].…”

“…It is natural to ask the meaning of a function depending on both k and z. This is addressed in [2,8,10,11]. The method, as described below, is to replace the permittivity function with a differential equation.…”

“…The method, as described below, is to replace the permittivity function with a differential equation. A wire medium [1,4,9,22,23] is naturally spatially dispersive, and by varying the radius of the wires periodically in z will naturally give it the correct spatial inhomogeneity ( …”

Subwavelength mode profile customization using functional materials

“…We show how we can use layered or varying material properties to sculpt an electric field profile along its propagation direction. Here we use sub-wavelength variation as a means of controlling the internal field profile [1,2], in contrast to the typical uses of layered [3] or chirped [4] 1D photonic crystals, whose focus is primarily on manipulating the band structure, reflectivity, or transmission properties. Up to now most of the work has concentrated on photonic band gaps in photonic crystals, and the transmission or reflection coefficients at various angles or frequencies of an incident wave [5].…”