Direct observation of ideal electromagnetic fluids

Near-zero-index (NZI) media exhibit counterintuitive phenomena due to their infinitely stretched wavelength and spatially static fields. Electrodynamics within NZI media lead to effects independent of system geometry, including supercoupling, deformable resonators, photonic doping, and enhanced spatial coherence of thermal fields. These properties enable applications in antennas, lenses, and components with boosted optical nonlinearities. The decoupling of spatial and temporal variations results in spatially static but temporally dynamic field distributions. Experimental verifications often focus on scattering parameters, but local and subwavelength field details remain less explored. Previous direct observations involved scalar amplitude measurements along straight waveguides. This research aims to characterize the vectorial nature (phase and amplitude) of field distributions within NZI media in nontrivial geometries, focusing on the local electromagnetic power flow, which is mathematically equivalent to the velocity field in an ideal fluid. This implies intrinsic inhibition of optical turbulence and the suppression of vorticity in the power flow. The study experimentally demonstrates this analogy at microwave frequencies using a dispersive rectangular waveguide at its cutoff frequency, emulating an epsilon-near-zero (ENZ) structure, a type of NZI medium. The chosen platform allows for complex geometries and the introduction of dielectric particles. A novel retrieval procedure allows direct mapping of fields with full vectorial information, based only on surface measurements, minimizing interference with the internal field.

The literature highlights the unique properties of near-zero index (NZI) media and their applications. Studies have explored supercoupling effects [2, 3], deformable resonators [3], and the use of photonic doping to modify the material properties and enhance specific phenomena [4-11]. The spatial coherence of thermal fields has also been shown to be affected by NZI materials [12]. Numerous technological applications have been proposed and in some cases demonstrated, including antennas [13-16], lenses [17-19], and nonlinear optical components [20-24]. Previous experimental studies have largely focused on measuring scattering parameters [26-28] or have provided scalar amplitude measurements of field distributions [29, 30], lacking the comprehensive vectorial information needed to fully understand the behavior of these materials. The theoretical framework connecting the electromagnetic power flow in NZI media to the behavior of an ideal fluid has been established [31], providing the foundation for this experimental investigation. The use of waveguides to emulate ENZ media, leveraging their lower losses compared to actual ENZ materials, has been explored [32-34].

The study employs a dispersive rectangular waveguide at its cutoff frequency to emulate a two-dimensional epsilon-near-zero (ENZ) medium. The waveguide, composed of a Teflon brick coated with copper foils and an air-filled aluminum case, allows for creating nontrivial geometries and introducing dielectric particles. A semi-analytical field retrieval technique is developed to map the internal fields without the need for intrusive probes. This technique relies on measuring the tangential components of the magnetic field on the top surface of the waveguide, which is modified to include a metal grid with small holes for probe access. The measurement is performed using an electrically small metal loop connected to a coaxial cable. The transmission coefficient from the input waveguide to the probe is measured using a vector network analyzer, providing the normalized magnitude and phase distribution of magnetic fields in both x and y directions. The electric field in the central plane is then retrieved using Equation (1), and the magnetic field in the central plane is subsequently retrieved using Equation (2). Finally, the Poynting vector field is calculated using Equation (3). This approach permits a full vectorial characterization of the electromagnetic field, encompassing both amplitude and phase information. Numerical simulations are performed using ANSYS HFSS 18 and COMSOL Multiphysics to validate the experimental results and explore the behavior of the waveguide under different conditions. The simulations model the waveguide structure in 3D, considering perfect electric conductor (PEC) boundary conditions for the aluminum and copper components. The dielectric particle is modeled using material parameters obtained from the literature [34]. Two specific frequencies are investigated: 3.06 GHz, where the waveguide exhibits an ENZ response, and 3.9 GHz, representing a conventional medium. The impact of a dielectric dopant on the field distribution and power flow is also studied, investigating the phenomenon of photonic doping.

The experimental results confirm the theoretical prediction that electromagnetic power flow in ENZ media behaves like an ideal fluid. The Poynting vector field is shown to be irrotational (∇ × S_R = 0), meaning it smoothly flows around obstacles and inclusions without forming vortices. This vortex-free behavior is observed at the ENZ frequency (3.06 GHz) even in the presence of significant waveguide deformations and dielectric inclusions. In contrast, measurements at a frequency outside the ENZ regime (3.9 GHz) show the presence of vortices in the power flow, demonstrating the unique characteristic of NZI media. The experimental retrieval procedure successfully maps the fields with full vectorial information (amplitude and phase). The electric field distribution resembles a spatially static field, while the magnetic field exhibits magnitude and phase uniformity. These characteristics are consistent with the theoretical properties of 2D ENZ media. The experiment also confirms the supercoupling effect—the enhanced field magnitude within the waveguide when a dielectric particle (photonic dopant) is introduced. Even with the inclusion of the dielectric particle, the power flow remains vortex-free, demonstrating the robustness of this ideal fluid behavior. The magnitude of the Poynting vector is significantly increased near the narrow channels created by the inclusion of the dielectric particle, analogous to fluid acceleration in narrow pipes. Comparisons between simulation and experimental results for the doped and undoped structures, at both ENZ and non-ENZ frequencies show good agreement, validating the experimental setup and the retrieval procedure.

The experimental observation of vortex-free power flow in ENZ media strongly supports the analogy between electromagnetic radiation in NZI media and an ideal fluid. The irrotational nature of the Poynting vector field, even in the presence of obstacles and topological changes, demonstrates the intrinsic inhibition of optical turbulence in these materials. This finding provides valuable insights into the supercoupling effect, as the enhanced transmission observed in the presence of photonic dopants does not introduce any disruption to the ideal fluid behavior. The development and successful application of the semi-analytical field retrieval technique represent a significant advance in the experimental characterization of NZI media. This technique enables direct, non-invasive observation of subwavelength field details, including full vectorial information, which was previously lacking. The results open perspectives for the design of new devices and systems that benefit from the unique properties of NZI media. Applications include robust optical systems protected against mechanical perturbations and systems inspired by fluid mechanics. The demonstration of spatially static electric field distributions and phase-uniform magnetic fields further confirms the fundamental electrodynamic characteristics of 2D ENZ media.

This work provides the first experimental validation of the ideal electromagnetic fluid analogy for near-zero-index media. The demonstration of vortex-free power flow, even with complex obstacles and topological changes, highlights the unique characteristics of these materials. The successful implementation of the novel field retrieval technique opens up new possibilities for characterizing subwavelength phenomena in NZI media. Future research could explore the extension of these principles to other frequency ranges and material platforms, and investigate the development of new devices that leverage the unique properties of electromagnetic ideal fluids.

The experimental setup is limited to microwave frequencies and a specific waveguide geometry. The retrieval technique relies on certain approximations and assumptions, such as the dominance of the TE₁₀ mode and the negligible effect of the measurement probes. The accuracy of the field retrieval could be influenced by imperfections in the fabrication and assembly of the waveguide structure. While the dielectric loss in the simulation is well estimated, it may differ slightly from the actual material used in the experiment, which may impact some details of the results, particularly those close to the dielectric particle.