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

Abstract

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.

Wave scattering properties of multiple weakly coupled complex systems

“…The cavities contain mode stirrers of irregular shape to create many realizations of ray chaos in their interior. With the scaled-down dimension and scaled-up operating frequency, identical statistical electrical properties are achieved in the two configurations [50].…”

“…The amount of loss in a cavity is controlled by varying the temperature of the copper walls in the scaled cavities [50], and by placing RF absorber cones in the full scale set-ups. The single cavity 'lossyness' is described by the RCM loss parameter α, which is defined as the ratio of the 3-dB bandwidth of a typical resonance mode to the mean frequency spacing between the modes [43,50]. The loss parameter can be explicitly expressed as α = k 2 /(Q ∆k 2 n ), where k is the wavevector, and Q and ∆k 2 n are the quality factor and averaged mode spacing for modes near k. At room temperature the loss parameter of a scaled and a full scale cavity can both be made equal at a value of α ∼ 9.…”

“…The loss parameter can be explicitly expressed as α = k 2 /(Q ∆k 2 n ), where k is the wavevector, and Q and ∆k 2 n are the quality factor and averaged mode spacing for modes near k. At room temperature the loss parameter of a scaled and a full scale cavity can both be made equal at a value of α ∼ 9. By matching the single cavity loss and the scaling in Maxwell equations, equivalent EM wave statistical properties are expected between the two experimental set-ups [50].…”

“…As shown schematically in Fig. 1, our approach first adopts RCM to describe each individual chaotic enclosure [43,50]. The system-specific details are identified in yellow in Fig.…”

“…In contrast to the other above mentioned methods, the RCM generates both mean-field and statistical predictions, treats interference and utilizes a minimum of information, namely, the system coupling details and the enclosure loss parameter [45][46][47][48][49]. It was recently demonstrated that two single RCM enclosures with a specific scaling relationship with regard to size, frequency and wall conductivity share the same normalized impedance statistics [50]. This work paves the way for experimentally testing the wave properties of an extensive variety of networks of large coupled complex systems experimentally in a typical lab environment by studying their scaled-down-in-size counterparts [51,52].…”