The search for axion dark matter runs into the scaling problem of closed microwave resonators: as frequency rises, their dimensions must shrink, and the conversion volume falls. Nearby in the archive are papers on kilohertz gravitational-wave detectors, on levitating dust grains, and on laser dark-matter detectors, but all of them either use different physical principles or fail to solve the volume problem at high frequencies. DALI offers a different route: a phased array of dielectric layers in a magnetic field, coupled to a half-open Fabry-Perot resonator. This approach relies on mature components, including superconducting solenoids from medical technology, and promises to preserve sensitivity where conventional resonators lose ground.
The authors build an analytical model of a resonator made of N dielectric layers with permittivity ε_r and thickness d_e, separated by vacuum gaps d_v, with a conducting mirror at one end and a coupling port at the other. A static magnetic field B_0 is directed parallel to the layer surfaces. The axion field induces an electric field E_0 = g_{aγγ} B_0 a_0, which generates radiation at every interface between media. The power at the receiver is derived as the product of four factors: the reference mirror power P_0, the transverse projection η, the loaded quality factor Q_L, and the extraction coefficient β/(1+β). The model is tested against full-wave simulations of a four-layer assembly at frequencies of 6.832 GHz and 24.508 GHz and against laboratory measurements of the quality factor up to 20 layers.
The key result is the closed-form formula P_out = P_0 × η × Q_L × β/(1+β), where P_0 = (E_0^2/2Z_0) A_phys. The axion-to-photon conversion is shown to be a surface effect: the power grows with the mirror area, not with the magnetized volume, because contributions from deep elements interfere destructively. Resonant enhancement is described by the quality factor Q_L, which does not depend on the longitudinal phase structure of the mode, since it is determined by quadratic functionals of the field. The transverse projection η is the only coherent factor sensitive to the phase of the transverse lobes. The simulation demonstrates two limiting configurations of the same assembly: at λ/8 the surface coherence is C_B = 0.050, while at λ/2 it is C_B = 0.810, whereas the photon lifetime τ_p changes by only 16%, confirming that the mechanisms are independent.
The work differs from neighboring approaches in that it explicitly separates coherent addition of surface radiation and resonant field accumulation as independent factors. Unlike closed resonators, where the volume is limited by diffraction, a half-open Fabry-Perot resonator allows the number of layers to be increased without losing coherence. This is the first formulation to show that calibration with an external source carries over completely to axion excitation, because the eigenmode does not depend on the source. This conclusion removes the need to model a distributed axion source in order to determine the quality factor and the coupling coefficient.
Further development could proceed by increasing the number of layers and optimizing their thicknesses to achieve maximum coherence while preserving resonant accumulation. Adaptation to other frequency ranges, including the sub-terahertz band, where open resonators have an advantage, is also possible. Studying configurations with variable permittivity to control the effective coherence length is another promising direction. Experimental verification on a prototype with a larger number of layers and stronger magnets will be the next step toward a practical axion search.
The results will influence the design of future axion haloscopes, especially in the 10-100 GHz range, where traditional cavity detectors lose sensitivity. The method of separating power factors can be used in other resonator experiments searching for weak signals.
The immediate steps include experimental confirmation of the predicted independence of the quality factor from coherence on assemblies with a larger number of layers. It is also necessary to measure the transverse projection η in a real prototype and compare it with simulations.
In particle physics and astrophysics, the nature of dark matter remains an open problem. This work links the axion search to the engineering constraints of resonators, offering a way to overcome the volume problem at high frequencies. The exact axion mass and its coupling to the photon remain open questions, and they determine the required detector sensitivity.
The DALI prototype uses ceramic plates of yttrium-stabilized zirconium oxide only 1 mm thick, and the quality factor grows linearly with the number of layers up to 20, regardless of whether that number is even or odd.