Revealing underlying universal wave fluctuations in a scaled ray-chaotic cavity with remote injection

The Random Coupling Model (RCM) predicts the statistical properties of waves inside a ray-chaotic enclosure in the semiclassical regime by using Random Matrix Theory, combined with system-specific information. Experiments on single cavities are in general agreement with the predictions of the RCM. It is now desired to test the RCM on more complex structures, such as a cascade or network of coupled cavities, that represent realistic situations but that are difficult to test due to the large size of the structures of interest. This paper presents an experimental setup that replaces a cubic-meter-scale microwave cavity with a miniaturized cavity, scaled down by a factor of 20 in each dimension, operated at a frequency scaled up by a factor of 20 and having wall conductivity appropriately scaled up by a factor of 20. We demonstrate experimentally that the miniaturized cavity maintains the statistical wave properties of the larger cavity. This scaled setup opens the opportunity to study wave properties in large structures such as the floor of an office building, a ship, or an aircraft, in a controlled laboratory setting.

Figure 1

(a) Schematic diagram and (b) picture of the experimental setup. High-frequency waves propagate in free space from the frequency extender to the cavity and from the cavity to the receiving frequency extender. The horn antenna launches the electromagnetic waves into space and the Teflon lens collimates the waves into a parallel beam. The signal then goes through a focusing lens and enters the cavity through a receiving horn antenna. The outgoing waves follow a similar path to reach the second frequency extender.

Figure 2

(a) Magnetically coupled mode stirrer powered by a cryogenic stepper motor. The magnetic strip outside the cavity (lower yellow bar) is coupled by its static magnetic field to the magnetic strip inside the cavity (upper yellow bar), eliminating the need for any opening on the wall or direct mechanical contact. The mode stirrer panel is a copper foil of irregular shape. (b) Two consecutive measurements of $|S_{21}|$ of the miniature enclosure between 90 and 90.5 GHz, where the stepper motor rotates once to perturb the cavity modes.

Figure 3

The inverse Fourier transform of the measured S-parameters give the value of $\tau$ from each fit in log-scale versus time (a) for the case of transmission and (b) for the case of reflection of the $s=20$ scaled enclosure measured through remote injection. Data from nine realizations at room temperature are plotted with different colors. The purple line is the average, and the green line is the linear fit for the energy decay portion of the average. The slope of the fitted line is $-1/2\tau$, where $\tau$ is the energy decay time of the cavity. The time domain response inside the blue dashed box in (b), labeled “Prompt response,” arises from the impedance mismatch between the external transmission channel and the cavity. This information is captured in $Z_{avg}$ (see Sec. 5b).

Figure 4

Cycling of the scaled cavity experiment from room temperature to 15 K and back again, a comparison between resultant $\alpha$ values calculated from different methods. Blue solid line: ${\alpha }_Q$ calculated from time domain energy decay time method; red dotted line: ${\alpha }_{fit}$ calculated from the best fit of ${\eta }_{11}$ and ${\eta }_{22}$ to the RCM prediction at room temperature.

Figure 5

Comparison between the normalized impedance PDF for a two-port system from an RCM Monte Carlo simulation with $\alpha =5.6$, in solid lines, and that from a normalization process of experimental data with ${\eta }_{11}=0.14$ and ${\eta }_{22}=0.19$, in dotted lines.

Figure 6

The tunable range of $\alpha$ values of the $s=20$ scaled cavity using different wall material and varying temperature. The least lossy case is with polished copper walls and has a range of $2.6\le \alpha \le 4.2$. The overall range is $2.6\le \alpha \le 6.4$.

Figure 7

Comparison of the probability density function for the imaginary part of the normalized impedance ${\xi }_{21}$ for the full-scale cavity (blue diamond dots based on data), the miniature cavity (red cross dots based on data), and the RCM Monte Carlo simulation with $\alpha =3.0$ (yellow solid line) for the entire frequency range of either 3.75–5.5 GHz or 75–110 GHz.

Figure 8

(a) Comparison of the loss parameter $\alpha$ at room temperature and at base temperature (15 K in this experiment) in the corresponding 10 frequency bands and (b) radiation efficiency $\eta$ calculated for 10 frequency bands.

Figure 9

Comparison of the PDF for the imaginary part of the normalized impedance ${\xi }_{12}$ and ${\xi }_{21}$ between the full-scale cavity (solid line based on data) and the miniature cavity (dotted line based on data) for three different frequency bands (of the full-scale cavity) at different temperatures (of the scaled cavity). Top row shows the PDFs in linear scale while the bottom row shows the same PDFs in log scale. (a) $\alpha =2.83$ within [4.45, 4.625] GHz at 130 K, (b) $\alpha =4.19$ within [4.975, 5.15] GHz at 217 K, and (c) $\alpha =5.82$ within [5.325, 5.5] GHz at 297 K. Notice that in each plot, all four curves collapse into one because they match each other very well.