Determining angle of arrival of radio frequency fields using subwavelength, amplitude-only measurements of standing waves in a Rydberg atom sensor

TL;DR

Conventional AoA sensing often relies on phase references and large antenna arrays, limiting compactness and stability. The authors introduce a PEC-Rydberg cell that leverages subwavelength standing-wave imaging to infer AoA from amplitude ratios, removing the need for a local oscillator. They demonstrate LO-free AoA detection across 4.2–5.7 GHz with angular resolutions of about 1.7 deg for small polar angles and 4.1 deg overall, using a robotic LAPS system for precise positioning. This work delivers a compact, ultrawideband, subwavelength AoA sensor with potential field deployment on metallic surfaces and reduced sensitivity to environmental reflections, marking a practical advance in RF sensing.

Abstract

Deep subwavelength RF imaging with atomic Rydberg sensors has overcome fundamental limitations of traditional antennas and enabled ultra-wideband detection of omni-directional time varying fields all in a compact form factor. However, in most applications, Rydberg sensors require the use of a secondary strong RF reference field to serve as a phase reference. Here, we demonstrate a new type of Rydberg sensor for angle-of-arrival (AoA) sensing which utilizes subwavelength imaging of standing wave fields. By placing a metallic plate within the Rydberg cell, we can determine the AoA independent of the strength of incoming RF field and without requiring a secondary strong RF phase reference field. We perform precision AoA measurements with a robotic antenna positioning system for 4.2, 5.0, and 5.7 GHz signals and demonstrate a 1.7 deg polar angular resolution from 0 deg to 60 deg AoA and 4.1 deg over all possible angles.

Figures (9)

• Figure 1: The PEC-Rydberg antenna uniquely determines incoming angle-of-arrival (AoA) of an incoming RF field through amplitude-only, subwavelength RF imaging of standing wave field patterns. (a) Illustration of the PEC-Rydberg antenna. The PEC plate (orange) runs along a cylindrical vapor cell's major axis in the xz-plane. Two E-fields are measured through Rydberg Autler-Townes splitting along the two pink lines in the yz-plane. An E-field is incident with coordinates $(\theta, \phi, \chi)$, where $\theta$ is the rotation from the z-axis, $\phi$ is the rotation from the x-axis, and $\chi$ is the polarization defined as the angle from the plane of incidence. (b) The measured ratio of the electric field along Beams A and B, $E_A/E_B$, decreases monotonically with increasing $\theta$ from 4.2 to 5.7 GHz, thereby providing a unique determination of AoA at each frequency point.
• Figure 2: Analytical and numerical simulations indicate the ratio of two field strengths, $E_A/E_B$, measured inside the PEC-Rydberg cell can determine the incoming AoA. (a-d) The standing wave field pattern at a normalized distance, $z/\lambda_{RF}$, as a function of incoming angle-of-arrival (AoA), $\theta$, for an incident 1.0 V/m E-field incident on an infinite conducting plane polarized (a) parallel and (c) perpendicular to the plane of incidence. The laser beam locations we test for RF sensing are indicated by the dashed lines. E-fields along Beam A and B, $E_A$ and $E_B$, respectively, and the ratio of the fields, $E_A/E_B$, as a function of $\theta$, for fields polarized (b) parallel and (d) perpendicular to the plane of incidence. (e) Finite element simulation results showing the $E_{\parallel}$ field distribution in the the vapor cell in the yz-plane and xz-plane for three different angles of incidence. (f) Numerically determined average field strength along the length of the cell for varying $\theta$. Beam A and B location are denoted by the black dashed lines. (g) The field ratio, $E_A/E_B$, for varying frequency and $\theta$.
• Figure 3: Experimental setup for measuring the AoA of an incoming CW wave. (a) Cesium level diagram for RF detection. (b) Optical schematic: half-wave plate ($\lambda/2$), quarter-wave plate ($\lambda/4$), photodetector (PD), dichroic mirror (DM). Mirrors are indicated by diagonal lines and polarizing beam splitters by squares with an internal diagonal. (c) The vapor cell is shown on the portable optical setup inside the LAPS facility at NIST. The WR187 open-ended waveguide is at coordinates $(\theta, \phi, \chi)$ = (45$^{\circ}$, -45$^{\circ}$, 0$^{\circ}$) and at a distance of 20 cm. The inset shows a zoomed-in image of the vapor cell with the vertically aligned PEC plate (black line) and the two coupling beams (green spots).
• Figure 4: The AoA is uniquely determined by our PEC-Rydberg vapor cell from 4.2 to 5.7 GHz. (a) EIT traces in the PEC-Rydberg cell and reference cell. The cartoon to the right indicates the beam locations, A and B, with respect to the PEC plate and the incoming RF field. For Beam A and B, the EIT with Autler-Townes splitting is shown for a 5.044 GHz field with $\theta = 30 ^{\circ}$. (b) Normalized EIT signals in Beam A and B (rows) for $f_{RF}$ = 4.228 GHz, 5.044 GHz, and 5.711 GHz (columns) for varying $\theta$. (c) A one-to-one mapping exists between $\theta$ and $E_A/E_B$ for each tested frequency indicating the PEC-Rydberg cell can be calibrated to uniquely determining the incoming AoA.
• Figure 5: The maximum deviation from 5 GHz measurement repeats is 1.7$^{\circ}$ for $\theta \leq 60^{\circ}$ and less than 4.1$^{\circ}$ across all $\theta$. (a) Components of uncertainty as a function of incoming angle. (b) Three repeat measurements of 5.044 GHz were obtained and one measurement is used as a calibration to determine the AoA. The uncertainty bars are obtained from the square root of the sum of squares of the uncertainties in (a).