Near-zero-index media as electromagnetic ideal fluids

Abstract

Near-zero-index (NZI) supercoupling, the transmission of electromagnetic waves inside a waveguide irrespective of its shape, is a counterintuitive wave effect that finds applications in optical interconnects and engineering light–matter interactions. However, there is a limited knowledge on the local properties of the electromagnetic power flow associated with supercoupling phenomena. Here, we theoretically demonstrate that the power flow in two-dimensional (2D) NZI media is fully analogous to that of an ideal fluid. This result opens an interesting connection between NZI electrodynamics and fluid dynamics. This connection is used to explain the robustness of supercoupling against any geometrical deformation, to enable the analysis of the electromagnetic power flow around complex geometries, and to examine the power flow when the medium is doped with dielectric particles. Finally, electromagnetic ideal fluids where the turbulence is intrinsically inhibited might offer interesting technological possibilities, e.g., in the design of optical forces and for optical systems operating under extreme mechanical conditions.

Complex Analytic Dependence on the Dielectric Permittivity in ENZ Materials: The Photonic Doping Example

“…In particular, we find that when k = 0, we recover the ideal fluid analogy in EMNZ materials discovered in [14]. The interest in Corollary 2.6 is that, the ideal fluid analogy for the electric field distribution, in materials for which the magnetic permeability is nonzero, admits a simple modification-rather than obtaining a divergence free Poynting vector, one obtains a Poynting vector with constant divergence.…”

“…Our next corollary generalizes the so-called "Ideal Fluid Analogy" introduced in [14]. In that paper, the authors consider the setting in which both the dielectric permittivity ε δ and the magnetic permeability (k 2 = ω 2 µ in the notation of the introduction), both vanish in the ENZ region.…”

“…As explained in the introduction, our next corollary clarifies and complements the result in two ways: first, of course, it describes corrections to the leading order theory recalled in the introduction due to nonzero δ (e.g., via the presence of losses), and second, it is not restricted to the case of vanishing magnetic permeability. In order to state this corollary, we recall the notion of the Poynting vector, as the authors in [14] formulate their ideal fluid analogy in terms of the Poynting vector. It is defined as the function…”

“…Since the Poynting vector involves both the magnetic field ⃗ H and the electric field ⃗ E, this requires understanding both fields in the limit δ → 0. For ENZ waveguides, this was the focus of [14]; we are not aware of a similar study in the photonic doping setting. Some related literature.…”

Momentum considerations inside near-zero index materials

“…In the past decade materials with near-zero refractive index have received a lot of attention because of their unusual optical properties, such as supercoupling 17 , 18 , enhanced nonlinearities 19 – 22 and fluorescence 23 – 25 , control of dipole-dipole interactions 26 , 27 , geometry-invariant resonant cavities 28 , photonic doping 29 and propagation of the light power flow akin to ideal fluids 30 . The refractive index of a material is near zero when at least one of the two constitutive parameters of the refractive index — the relative electric permittivity ε ( ω ) or the relative magnetic permeability μ ( ω ) — is close to zero 31 , 32 .…”