Customizing longitudinal electric field profiles using spatial dispersion in dielectric wire arrays

Abstract

We show how spatial dispersion can be used as a mechanism to customize the longitudinal profiles of electric fields inside modulated wire media, using a fast and remarkably accurate 1D inhomogeneous model. This customization gives fine control of the sub-wavelength behaviour of the field, as has been achieved recently for transverse fields in simpler slotted-slab media. Our scheme avoids any necessity to run a long series of computationally intensive 3D simulations of specific structures, in order to iteratively converge (or brute-force search) to an empirical 'best-performance' design according to an abstract figure-of-merit. Instead, if supplied with an 'ideal waveform' profile, we could now calculate how to construct it directly. Notably, and unlike most work on photonic crystal structures, our focus is specifically on the field profiles because of their potential utility, rather than other issues such as band-gap control, and/or transmission and reflection coefficients.

Mode Profile Shaping in Wire Media: Towards An Experimental Verification

“…As we have already shown [1][2][3], such field profile customisation is even possible at the sub-wavelength scale, and does not require exhaustive brute-force computation. Further, for our spatially dispersive wire medium [3], we show this system can support shaped longitudinal electric fields. This field profiling is achieved by varying the radius of the wires in a carefully calibrated way.…”

“…In this article, we show that the field profiling of a longitudinal wave predicted in [3] can be numerically reproduced in an experimentally plausible system. In [3] we considered an infinite periodic array of infinite wires as shown in Figure 1, where the wire radius varied from 0.2 mm to 0.4 mm with a relative permittivity of = 1600.…”

“…This field profiling is achieved by varying the radius of the wires in a carefully calibrated way. In [3] the system was numerically modelled as an infinite periodic array of wires, so that the computation only required a single wire with periodic boundary conditions. In addition to periodicity, the simulated wire material had a very high permittivity and concomitantly small radius, features that would be problematic in experiment, both in terms of manufacture and fragility.…”

“…In [3] we considered an infinite periodic array of infinite wires as shown in Figure 1, where the wire radius varied from 0.2 mm to 0.4 mm with a relative permittivity of = 1600. As longitudinal electromagnetic waves (EM waves) are known to exist in guided wave systems we consider a 4 × 4 array of finite-wires, a single period long, and contained in a metallic waveguide closed at both ends, as depicted in Figure 2.…”

“…As longitudinal electromagnetic waves (EM waves) are known to exist in guided wave systems we consider a 4 × 4 array of finite-wires, a single period long, and contained in a metallic waveguide closed at both ends, as depicted in Figure 2. In the simulations reported here, our wire parameters are physically easier to realise than those used in [3], being based on a wire radius that varies from 0.5 mm to 0.7 mm, with a relative permittivity of = 50. The simulation of this system was undertaken using the frequency domain solver of the commercial software CST Microwave Studio (2018 Update, Framingham, MA, US).…”