🔭 astrophysics

What is new in NuRadioMC: Multilayer Analytic Raytracer

This paper introduces a new multilayer analytic raytracing method in the NuRadioMC framework that models complex, piecewise exponential refractive index profiles to enable realistic and computationally efficient simulation of radio signal propagation in diverse neutrino detector environments, including the atmosphere.

Original authors: Hannes Warnhofer, Sjoerd Bouma, Vital De Henau, Bryan Hendricks, Jakob Henrichs, Nils Heyer, Enrique Huesca Santiago, Annanay Jaitly, Philipp Laub, Anna Nelles, Martin Ravn, Felix Schlüter, Zeynep Su

Published 2026-09-07✓ Author reviewed ⓘ

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hannes Warnhofer, Sjoerd Bouma, Vital De Henau, Bryan Hendricks, Jakob Henrichs, Nils Heyer, Enrique Huesca Santiago, Annanay Jaitly, Philipp Laub, Anna Nelles, Martin Ravn, Felix Schlüter, Zeynep Su Selcuk, Karen Terveer, Christian Glaser, Christoph Welling, Philipp Windischhofer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep beneath the frozen surface of the Earth, in the vast sheets of ice that cover Antarctica and Greenland, scientists are listening for a ghostly whisper from the edge of the universe. These whispers are radio signals generated when ultra-high-energy neutrinos—particles so elusive they can pass through entire planets without stopping—collide with atoms in the ice. When such a collision happens, it creates a cascade of secondary particles that emit a brief flash of radio waves. To catch these flashes, researchers deploy arrays of antennas buried deep in the ice. However, the ice itself is not a uniform block of clear crystal; it is a complex, layered medium where the speed of light changes with depth. As a radio signal travels from the deep collision point up to an antenna, these changing conditions bend the signal's path, much like a straw looks bent when placed in a glass of water. To understand where a neutrino came from and how powerful it was, scientists must be able to trace these bent paths backward with extreme precision. If the map they use to trace the path is slightly wrong, the location of the cosmic event will be wrong too.

For years, the software used to simulate these journeys, known as NuRadioMC, relied on a simplified model of the ice. It treated the entire ice sheet as if it followed a single, smooth rule for how light slows down as it goes deeper. While this worked well enough for early experiments, measurements from real ice sheets showed that the reality is more complicated. The ice is made of distinct layers, each with slightly different properties, creating a jagged profile rather than a smooth curve. The old model could not capture these nuances, forcing scientists to choose between a fast but inaccurate simulation or a slow, computer-heavy calculation that took too long for the massive number of events needed for a full experiment.

In this new work, the team behind NuRadioMC has introduced a significant upgrade: a multilayer analytic raytracer. Instead of forcing the ice to fit a single, simple rule, this new method allows the simulation to describe the ice as a stack of different layers, where each layer follows its own specific rule for how light travels. The researchers did not just add this feature; they built a mathematical engine that can solve the path of the radio signal through these stacked layers almost instantly. By breaking the ice down into these manageable sections, the software can now calculate the exact route a signal takes, including how it bends at the boundaries between layers, without needing to run slow, step-by-step numerical calculations.

The results of this development are striking in their efficiency and accuracy. The new method can find the path of a signal through a three-layer model of the ice in about 0.4 milliseconds. This is roughly three times slower than the old single-layer method, but it is still fast enough to run millions of times in a single simulation run, a feat that was impossible with the more detailed models previously available. In contrast, the older, more flexible numerical methods that could handle complex ice structures took up to two seconds for a single path, making them too slow for large-scale studies. With this new tool, the team can now use realistic, multi-layered descriptions of the ice, such as those measured at Summit Station in Greenland, which show distinct changes in the ice structure at different depths.

The paper demonstrates that this approach does not just speed things up; it changes the picture of what the signals look like when they arrive. When the researchers compared the new multilayer model against the old single-layer model, they found noticeable differences in the time it took for signals to arrive and the angle at which they hit the antennas. These differences are critical because they directly affect how scientists reconstruct the original neutrino event. The new model also handles the transition from ice to air more realistically, allowing for a better description of signals that travel through the atmosphere. Furthermore, the software correctly identifies "shadow zones," areas where no signal can reach due to the bending of the rays, and "caustic pockets," where signals from different paths converge, creating complex patterns that the old model missed.

This advancement is part of a broader effort to refine the tools used by experiments like ARA, ARIANNA, and RNO-G, and it is planned for use in the future IceCube-Gen2 detector. By making the simulation of signal propagation both faster and more realistic, the researchers have removed a major bottleneck in the search for high-energy neutrinos. The software remains open-source and easy to use, requiring only standard computer libraries to run. It allows scientists to define an ice sheet with any number of layers or to select from pre-built models for specific locations like the South Pole or Moore's Bay. Ultimately, this work ensures that when a faint radio signal is detected in the deep ice, the map used to trace it back to its cosmic origin is as accurate as the data allows, bringing us one step closer to understanding the most energetic particles in the universe.

Technical Summary: NuRadioMC Multilayer Analytic Raytracer

Problem Statement
The simulation of ultra-high-energy neutrino detectors relies heavily on accurate modeling of radio signal propagation through complex media, such as glacial ice and the atmosphere. While the existing NuRadioMC framework offers flexible simulation capabilities, the choice of raytracing methods presents a trade-off between computational speed and physical realism. The standard numerical solver, radiopropa, handles complex medium definitions and discontinuities with high flexibility but is computationally expensive (up to 2 seconds per ray), rendering it infeasible for large-scale Monte Carlo productions. Conversely, the existing analytic raytracer is extremely fast (~0.15 ms) but relies on a single-layer exponential refractive index model. This simplified model fails to capture the nuanced, multi-layered refractive index profiles measured at real experiment sites (e.g., Summit Station, Greenland), potentially introducing inaccuracies in signal travel time and arrival angle calculations essential for reconstruction.

Methodology
To address this limitation, the authors developed a Multilayer Analytic Raytracer that extends the single-layer analytic approach. The core methodology retains the mathematical foundation of Fermat's principle and the analytic solution for exponential refractive index profiles ( $n(z) = n_{ice} - \Delta n \exp(z/z_0)$ ) but generalizes the medium description.

Layered Model: The refractive index profile is now described as a series of distinct exponential layers, where parameters ( $n_{ice}$ , $\Delta n$ , $z_0$ ) can vary between layers. This allows the model to approximate complex, non-smooth refractive index variations found in real ice and the atmosphere.
Analytic Continuity: Within each layer, the ray path is solved analytically. The algorithm ensures continuity across layer boundaries by iteratively calculating horizontal offset parameters ( $C_1$ ) for each layer, effectively stitching together the analytic solutions. Snell's law is naturally encoded at the interfaces.
Solution Finding: The algorithm identifies valid ray paths (direct, refracted, or surface-reflected) between a source and a receiver by minimizing the horizontal displacement difference ( $\Delta y$ ) at the receiver depth. It employs numerical minimization algorithms (scipy.optimize.root and scipy.optimize.brentq) to determine the invariant constant ( $C_0$ ) that defines the path.
Parameter Calculation: Once the path is determined, parameters such as travel time, viewing angles, and focusing factors are calculated via piecewise integration of analytic expressions. Attenuation remains the only parameter requiring numerical integration based on signal frequency.

Key Contributions

Implementation of Multilayer Raytracing: The primary contribution is the integration of a multilayer analytic raytracer into the NuRadioMC.SignalProp module. This class replaces the single-layer analytic raytracer when a medium of type IceModelExpLayers is selected.
Realistic Medium Modeling: The method enables the use of realistic refractive index models, such as the 3-layer model for Greenland (greenland_3exp), which better fits experimental data than the previous single-layer approximation.
Computational Efficiency: The new method maintains the speed advantage of analytic solutions. While the 3-layer model takes approximately 0.4 ms per path (roughly 3 times slower than the single-layer case), it remains orders of magnitude faster than the numerical radiopropa solver, making it suitable for large-scale Monte Carlo simulations.
Atmospheric Modeling: The framework supports modeling signal propagation through the atmosphere and across non-smooth refractive index changes, facilitating the simulation of signals that traverse the ice-air interface.

Results

Performance: The solution finding time scales roughly linearly with the number of layers ( $t \approx n_L \cdot 0.15$ ms). For a 3-layer model, the total time per path pair is approximately 0.4 ms, with parameter calculation taking ~15 $\mu$ s.
Accuracy: Comparisons with the single-layer analytic raytracer show exact agreement where the models overlap. Comparisons with radiopropa show minor deviations consistent with those observed in the single-layer case.
Physical Phenomena: The new model successfully reproduces complex ray path features, including shadow zones (regions with no geometric ray solutions) and caustic pockets (regions where more than two path solutions exist).
Impact on Observables: Applying the new greenland_3exp model reveals measurable differences in signal travel time and arrival angles compared to the older greenland_simple model, highlighting the importance of using realistic refractive index profiles for precision reconstruction.

Significance
The paper positions this development as a critical step toward more realistic and flexible simulations for in-ice radio neutrino detectors (such as ARA, ARIANNA, RNO-G, and the radio component of IceCube-Gen2). By bridging the gap between the speed of analytic methods and the physical fidelity of multi-layered models, the Multilayer Analytic Raytracer allows researchers to perform large-scale Monte Carlo simulations with improved accuracy regarding signal propagation. The authors emphasize that the tool is designed for seamless integration into existing NuRadio-based analyses, requiring only a switch in the medium definition, and relies solely on established Python libraries. This advancement supports the ongoing development of reconstruction algorithms and the analysis of data from current and future radio-based neutrino and cosmic-ray experiments.

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