Direct observation of ideal electromagnetic fluids

The study investigates whether electromagnetic power flow in near-zero-index (NZI) media behaves as an ideal electromagnetic fluid—specifically, whether vorticity in the Poynting vector field is intrinsically inhibited even in complex, obstacle-laden geometries. The context is the growing interest in NZI media, where decoupling of spatial and temporal field variations leads to geometry-invariant phenomena such as supercoupling and enhanced coherence. Prior experimental work largely characterized NZI behavior via scattering parameters and scalar images along straight waveguides, lacking direct, local, fully vectorial field measurements. The purpose of this work is to directly map and reconstruct the full vectorial electromagnetic fields inside a waveguide-emulated epsilon-near-zero (ENZ) medium at cutoff, and to experimentally test the predicted irrotational, vortex-free power flow akin to an ideal inviscid, incompressible, irrotational fluid, including robustness to waveguide deformations and dielectric inclusions.

NZI media exhibit counterintuitive wave phenomena due to effectively infinite wavelength and spatially static fields, enabling geometry-invariant effects such as supercoupling, deformable resonators, photonic doping, and enhanced spatial coherence. Applications span antennas, lenses, and nonlinear photonics. Experimental verifications traditionally rely on transmission/reflection spectra under geometry variations. Direct local field characterizations are scarce; exceptions include observation of phase-free (standing-wave-like) propagation and position-independent cathodoluminescence in straight NZI waveguides, both providing scalar amplitude information without full vectorial mapping or complex geometries. Theoretical work established an equivalence between the Poynting vector in 2D NZI media and the velocity field of ideal fluids, implying vanishing vorticity. The present study addresses the literature gap by providing fully vectorial, phase-resolved, subwavelength field mapping inside NZI/ENZ media with nontrivial geometries and inclusions.

- Platform: A rectangular waveguide structure emulating an epsilon-near-zero (ENZ) medium at the TE10 cutoff. Input/output waveguides are Teflon bricks coated with copper foil; the ENZ section is an air-filled aluminum cavity of height h = λ/2. - Simulation: Full-wave 3D simulations performed in ANSYS HFSS 18 with PEC approximation for aluminum and copper; 2D comparisons in COMSOL Multiphysics 5.5 validate that fields on the central plane replicate those of an ideal 2D ENZ medium. - Measurement challenge and solution: Direct internal probing would strongly perturb fields. Instead, the top metallic cover is replaced by a brass metal grid with electrically small square holes to minimally perturb the cavity while allowing access. Numerical comparisons (full vs perforated cover) show negligible impact on center-plane fields and transmission spectra. - Field sensing: An electrically small PCB loop B-field probe connected to a coaxial cable (Port 3) is inserted through grid holes to measure complex tangential magnetic field components on the top surface (z = h/2). During measurement, Port 2 is terminated with 50 Ω and S31 is recorded with a Keysight N9917A VNA. Probing both x and y components is achieved by orienting the loop accordingly. Coupling is weak (|S31| typically < −20 dB), indicating <1% power extraction and negligible perturbation. - Single-mode assumption: Waveguide dimensions ensure only the TE10 mode is present; higher-order modes decay rapidly. - Field reconstruction (semi-analytical): From measured surface tangential H(x,y,z=h/2) and boundary condition Etan=0 at the top surface: 1) Retrieve center-plane electric field E(x,y,0) via E(x,y,0) = (i ω μ0 / h) ∫₀^h Hz(x,y,z′) z′ dz′. 2) Retrieve center-plane magnetic field H(x,y,0) via H(x,y,0) = (1/(i ω μ0)) ∇xy × E(x,y,0). 3) Compute time-averaged Poynting vector S_R(x,y,0) = (1/2) Re[E(x,y,0) × H(x,y,0)]. The derivation assumes time dependence exp(−iωt) and treats the center plane as a 2D medium with Drude-type effective permittivity and μ = μ0. - Configurations and frequencies: Measurements performed for four cases: doped (dielectric inclusion) and undoped waveguides, each at 3.06 GHz (ENZ) and 3.9 GHz (conventional medium with effective εr ≈ 0.4). The dielectric dopant (JJD37-6, εr ≈ 37, tanδ = 0.001) acts as a photonic dopant to tune effective permeability and enhance transmission (supercoupling) while maintaining near-zero permittivity. - Validation: Agreement between simulated H-fields, simulated S31, and measured S31 along specific lines after normalization; phase and vector maps compared between simulation and reconstruction. Additional system and fabrication details are provided (CNC machined aluminum/brass, FR-4 probe, assembly tolerances).

- Direct mapping of the Poynting vector field in a waveguide-emulated ENZ medium shows irrotational, vortex-free power flow at the ENZ frequency (3.06 GHz), despite strong geometrical deformations and the presence of a dielectric dopant acting as an obstacle. - Outside the ENZ regime (3.9 GHz, effective εr ≈ 0.4), strong vortices appear in the power flow, with significant reflection and blockage due to the obstacle, confirming that vorticity is typical in conventional media and uniquely suppressed in NZI/ENZ media. - Spatially static electric field distributions (electrostatic-like patterns) and phase/magnitude uniformity of the magnetic field on the center plane are experimentally observed, confirming key electrodynamic signatures of 2D ENZ media. - Power flow intensifies within narrow channels around obstacles at ENZ, analogous to fluid acceleration in constricted pipes, and smoothly circumvents obstacles, including penetrable dielectrics that behave as effectively opaque to power flow. - Photonic doping enhances transmitted power: removing the dopant reduces power flow magnitude by >17 dB; maximum power flow in doped ENZ cases (Fig. 3a,b) is about 50× higher than in undoped ENZ cases (Fig. 4a,b). - Measurement method perturbs the fields negligibly (typical |S31| < −20 dB, i.e., <1% power coupled to the probe) and yields good agreement between simulated and reconstructed vector/phase maps. - Simulations and experiments consistently support the ideal electromagnetic fluid analogy, with ∇×S_R ≈ 0 at ENZ and vortical patterns present at non-ENZ frequency.

The findings directly address the central hypothesis that NZI/ENZ media support ideal electromagnetic fluid behavior: the Poynting vector field in the ENZ regime is irrotational and adapts smoothly to complex boundaries and inclusions without forming vortices. This demonstrates that optical turbulence is intrinsically inhibited in NZI media and that this property is robust to local geometry and topology changes, including the insertion of dielectric dopants. The experimental reconstruction provides fully vectorial, phase-resolved evidence of spatially static electric fields and uniform-phase magnetic fields—cornerstones of ENZ electrodynamics—bridging the gap between prior scattering-based measurements and local field observations. The observed acceleration of power flow in constrictions and obstacle circumvention further reinforces the fluid analogy and provides physical insight into supercoupling and impedance matching via photonic doping. Collectively, these results substantiate NZI media as platforms for deformation-robust wave transport and inspire fluid-mechanics-informed photonic designs.

This work introduces and validates a semi-analytical, minimally invasive technique to reconstruct full vectorial electromagnetic fields and Poynting vectors inside waveguide-emulated ENZ media, enabling the first direct observation of vortex-free, ideal-fluid-like power flow in complex geometries. It experimentally confirms spatially static electric fields and phase-uniform magnetic fields, and shows that the irrotational power flow is preserved in the presence of dielectric dopants and strong deformations, while conventional media exhibit pronounced vortices. The approach deepens physical insight into supercoupling and impedance matching in NZI media and provides a tool for probing subwavelength, fully vectorial field behavior. Future work could extend this methodology to optical frequencies, explore three-dimensional NZI configurations, investigate dynamic/tunable dopants and loss/dispersion effects, and apply the technique to broader classes of NZI phenomena and multiphysics devices inspired by fluid mechanics.

- Field equivalence to a 2D ENZ medium holds strictly on the center plane; measurements infer center-plane fields from surface data under the TE10 single-mode assumption. - The probe cannot access fields inside the dielectric dopant; measurements are limited to the hollow waveguide region. - Some phase inaccuracies near PEC walls occur where field magnitudes are very low; dielectric losses may be higher in experiments than in simulations, leading to small discrepancies (e.g., slight power flow toward the dopant). - Metal boundaries are modeled as PEC in simulations, neglecting ohmic losses; the grid-cover approximation, while validated, is still an idealization. - Frequency-specific demonstration at microwaves (3.06 GHz ENZ and 3.9 GHz non-ENZ); generalization to other bands/material platforms requires further study.