arXiv : Wide-band full-wave electromagnetic modal analysis of the coupling between dark-matter axions and photons in microwave resonators

The electromagnetic coupling axion-photon in a microwave cavity is revisited with the BI-RME (Boundary Integral - Resonant Mode Expansion) 3D technique. Such full-wave modal technique has been applied for the rigorous analysis of the excitation of a microwave cavity with an axion field. In this scenario, the electromagnetic field generated by the axion-photon coupling can be assumed to be driven by equivalent electrical charge and current densities. These densities have been inserted in the general BI-RME 3D equation, which expresses the RF electromagnetic field existing within a cavity as an integral involving the Dyadic Green functions of the cavity (under Coulomb gauge) as well as such densities. Next, we have obtained a simple network driven by the axion current source, which represents the coupling between the axion field and the resonant modes of the cavity. Using the classical Kirchhoff's Laws we demonstrate that the energy injected in the cavity by the axion field is split in two terms: the energy lost in the cavity (Ohmic losses), and the energy transmitted to the waveguide port (which is connected to the electronic system readout). Thus, we have been able to calculate the extracted and dissipated RF power as a function of frequency along a broad band and without Cauchy-Lorentz approximations, obtaining the spectrum of the electromagnetic field generated in the cavity, and dealing with modes relatively close to the axion resonant mode. Moreover, with this technique we have a complete knowledge of the signal extracted from the cavity, not only in magnitude but also in phase. This can be an interesting issue for future analysis where the axion phase is an important parameter. In order to validate the present formulation, these calculations have been compared with data available in the technical literature, obtaining good results.