Controlling electromagnetic fields with graded photonic crystals in metamaterial regime

Abstract

Engineering of a refractive index profile is a powerful method for controlling electromagnetic fields. In this paper, we investigate possible realization of isotropic gradient refractive index media at optical frequencies using two-dimensional graded photonic crystals. They consist of dielectric rods with spatially varying radii and can be homogenized in broad frequency range within the lowest band. Here they operate in metamaterial regime, that is, the graded photonic crystals are described with spatially varying effective refractive index so they can be regarded as low-loss and broadband graded dielectric metamaterials. Homogenization of graded photonic crystals is done with Maxwell-Garnett effective medium theory. Based on this theory, the analytical formulas are given for calculations of the rods radii which makes the implementation straightforward. The frequency range where homogenization is valid and where graded photonic crystal based devices work properly is discussed in detail. Numerical simulations of the graded photonic crystal based Luneburg lens and electromagnetic beam bend show that the homogenization based on Maxwell-Garnett theory gives very good results for implementation of devices intended to steer and focus electromagnetic fields.

3d Printed Lattices With Spatially Variant Self-Collimation

“…Excellent performance can even be obtained using materials with low dielectric constant (i.e., ε r < 3.0) that are usually less expensive and more commonly available than more exotic dielectrics with higher permittivity. Alternative techniques for spatial control of waves within a lattice include structures produced by transformation optics [45], waveguides [46,47], graded-index devices [48][49][50], introduction of defects [43], and graded photonic crystals [51][52][53][54][55]. Spatially-variant self-collimation is unique because it spatially varies the orientation of the unit cells within an otherwise monolithic and uniform lattice.…”

Design of a Pyramidal Horn Antenna With Low E-Plane Sidelobes Using Transformation Optics

“…The reduced parameter approximation does this by setting μ red = 1, to facilitate the material fabrication, and red = μ, to maintain the refractive index profile in the material. After employing these refinements, for the practical realization of the design, normal dielectrics, or dielectric rods with spatially varying radii [46] can be used. They have low loss, wide frequency band and are easy to implement.…”

“…They have low loss, wide frequency band and are easy to implement. In this work, in addition to using dielectrics to realize this refractive index distribution, the method presented in [46] is also applied, which is a general technique to realize isotropic GRIN media by two-dimensional graded photonic crystals.…”

“…They can be described with spatially varying effective index, so they can be regarded as low-loss broadband graded dielectric metamaterials. The Maxwell-Garnett effective medium theory is used to calculate the rods radii [46]. The designed non-dispersive refractive index distribution is approximated by a discrete form.…”

“…In this form, each ij-cell is a square of side d = 7.5 mm with the refractive index (n(x i , y i )) of n ij . For TM polarization, the rods radii can be calculated using [46]:…”