Probing the Firn Refractive Index Profile Using Antenna Response

The Radio Neutrino Observatory-Greenland (RNO-G, at Summit Station) experiment comprises an extensive fat-dipole antenna array deployed into ice boreholes over an eventual area of approximately 35 ${\rm km}^2$. Since the RNO-G experimental sensitivity depends on the radio-frequency properties of the firn, which are known to vary laterally on sub-km distance scales and vertically on sub-meter distance scales, a technique for quickly extracting information on firn ice properties with depth ($n(z)$) during drilling and deployment is desirable. Given that a dipole's resonant wavelength is fixed by geometry, the resonant frequency $f_{res}$ (measured as an S-parameter reflection coefficient [`$S_{11}$'] minimum) scales inversely with the local refractive index, allowing a translation of a depth-dependent $S_{11}$(z) profile into $n(z)$. $S_{11}$(z) data were initially taken in August, 2024 using a dipole lowered into a newly-drilled $98\pm 1$-mm diameter, 350-m deep borehole at Summit Station, Greenland, approximately 1 km from the site of the original GISP-2 core; improved measurements were subsequently made in May, 2025. We conclude that $S_{11}$(z) data can be used to estimate \RIP, on 50 cm vertical scales, at the per-cent level of accuracy required by experiments such as RN0-G.