Fig. 1.

Schematic representation of a grAl stripline resonator with open-boundary conditions. a The length of the stripline, $\ell$, is in the range of mm, its width, b, is in the range of a few μm, and the thickness, d, is between 20 and 30 nm. Al grains (sketched in bordeaux color in the inset) have a diameter a = 3 ± 1 nm⁴. They are separated by aluminum oxide barriers (shown in gray), forming a 3D network of superconducting islands connected by Josephson contacts. b For the lowest-frequency standing-current modes along the stripline, the resonator can be modeled as a 1D array of effective Josephson junctions with critical current I_c and junction capacitance C_J, corresponding to the summed critical currents and capacitances of the grains in a stripline section of length a. c The resulting circuit diagram consists of identical cells, each containing an effective JJ and the self capacitance C₀ of the superconducting island. d Typical dispersion relation of a 1D JJ array, following Eq. (3). The spectrum saturates at the effective plasma frequency ${\omega }_{\mathrm{p}}=\sqrt{2e{I}_{\mathrm{c}}\mathrm{∕}\hslash C_{\mathrm{J}}}$. The slope in the linear part of the dispersion relation is defined by the ratio $\frac{a\pi }{\ell }\sqrt{C_{\mathrm{J}}\mathrm{∕}{C}_0}$