Tunable photonic crystal haloscope for high-mass axion searches

In the search for axion dark matter, the cavity-based haloscope offers the most sensitive approach to the theoretically interesting models in the microwave region. However, experimental searches have been limited to relatively low masses up to a few tens of $\mathrm{\mu }\mathrm{eV}$, benefiting from large detection volumes and high-quality factors for a given experimental setup. We propose a new cavity design suitable for axion searches in higher mass regions with enhanced performance. The design features a periodic arrangement of dielectric material in a conventional conducting cavity where the resonant frequency is determined by the interspace. This photonic crystal haloscope can make full use of a given volume even at high frequencies while substantially improving the cavity quality factor. An auxetic structure is considered to deploy the array for two-dimensional frequency tuning. We present the characteristics of this haloscope design and demonstrate its feasibility for high-mass axion searches.

Figure 1

Electric field distributions of a TM mode for a square unit cell with a conducting wire (left) and a dielectric rod (right) positioned in the middle. The dimensions of the unit cells are determined to have the same resonant frequency. A 2D lattice structure (either wire metamaterial or photonic crystal) can be simulated as a repeating pattern of the unit cell with periodic boundary conditions imposed.

Figure 2

Two-dimensional geometries of dielectric metamaterial unit cell. A square shape (left) can be approximated to a circular one (right) for analytical calculation.

Figure 3

Resonant frequency $\omega$ of our TM mode obtained from the analytical approach [Eq. (8)] for the circular geometry (top left) and from a numerical calculation for the square geometry (top right). The lattice size of $s=1\mathrm{cm}$ is assumed. The bottom plot shows the difference between the two approaches normalized to the latter.

Figure 4

Resonant frequency of $n\times n$ 2D dielectric array models for different array length $n$. Each array consists of the unit cells, depicted in the text, bounded by a square conducting boundary. The red dashed line corresponds to the resonant frequency of an ideal photonic crystal (infinite structure).

Figure 5

Performance comparison between wire (dashed lines) and dielectric (solid lines) arrays as a function of resonant frequency. The area below the solid lines, ${\int }_{\mathrm{\Delta }f}(C^{2}Q)df$, corresponds to our FOM.

Figure 6

Auxetic behavior of rotating rigid squares. With the vertices connected together, the relative rotation of the unit cells forms more open or closed structures.

Figure 7

Two-dimensional design of a photonic crystal haloscope with a $3\times 3$ square array (black square lines) in a conducting cylindrical cavity. A dielectric rod is placed in the center of each square. The array structure deforms in the same pattern shown in Fig. 6 and the corresponding $e$-field distributions are displayed using the same color scale shown in Fig. 1. Eight metal poles (white circles) are deployed to prevent field localization.

Figure 8

Photo of the photonic crystal cavity and frequency tuning system for demonstration.

Figure 9

Mode map of the prototype cavity depicted in the text. The resonant frequencies of the first three TM modes are in good agreement with the simulation represented by colored dots. Our desired mode corresponds to the lowest curve (with overlapping red dots) that spans the frequency from 10.9 to 9.6 GHz.

Figure 10

Measured quality factors of the demonstration cavity, compared to simulation results obtained from modeling in different dimensions assuming $\tan \delta =5\times {10}^{-6}$. The values for an infinitely periodic array labeled “Simulation (inf)” are taken from Fig. 5. The simulated values of form factor are also overlapped.