This project will enhance the precision and sensitivity of radio detectors used for the study of ultrahigh-energy cosmic particles through the development of Eisvogel, a novel open-source electromagnetic simulation code that enables for the first time the detailed study of radio propagation in complex media. The simplistic geometric optics modeling currently used by the radio detection community is not valid in the complicated environments inhabited by real detectors, leading to substantial uncertainty in signal identification and sensitivity predictions. Eisvogel uses a novel reciprocity formulation to make tractable the correct modeling of radio propagation in these complex environments. Under this award, Eisvogel will emerge from its current prototype status into a turnkey asset for the community. Integrating it with other community software, Eisvogel will be used to study important problems, to inform data interpretation for current experiments and the design of future experiments. This research incorporates undergraduate researchers and will develop new compelling visualizations for education and outreach.<br/><br/>Eisvogel provides a general framework for computing the Green's function of an antenna in an arbitrary environment, storing it to disk, and then loading on demand the relevant portion of the Green's function for an appropriate numerical convolution against the emitting shower current. Eisvogel will interface to the popular open-source finite-difference time-domain package MEEP, and to the community particle cascade simulation tool CORSIKA 8. This enables simulation of shower development and radio propagation in fully general media. This award will also apply Eisvogel to conditions that cannot currently be simulated, including cosmic ray showers that do not terminate before reaching polar plateaus and the coupling of near-surface antennas to both in-air showers and deep particle cascades. Eisvogel will provide improved modeling of beam test experiments, and estimate the thermal noise seen by antennas in complex media.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.