Aspects of the Scattering and Impedance Properties of Chaotic Microwave Cavities

Abstract

We consider the statistics of the impedance Z of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental Z data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized impedance whose probability density function is predicted to be universal in that it depends only on the loss (quality factor) of the cavity. We find that impedance fluctuations decrease with increasing loss. The results apply to scattering measurements on any wave chaotic system.

Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner’s reaction matrix for irregular graphs with absorption

“…In the case of time reversal systems (symmetry index β = 1) P (R) has been studied experimentally by Méndez-Sánchez et al [35]. The distributions P (v) and P (u) have been studied for chaotic microwave cavities in [26,36] and for microwave networks for moderate absorption strength γ ≤ 7.1 in [22,23]. For systems without time reversal symmetry (β = 2) and a single perfectly coupled channel P (R) was calculated by Beenakker and Brouwer [37] while the exact formulas for the distributions P (v) and P (u) were given by Fyodorov and Savin [25].…”

Experimental Determination of the Autocorrelation Function of Level Velocities for Microwave Networks Simulating Quantum Graphs

“…One may expect that removing of the bond between the output/input vertices should profoundly eliminate the direct processes [50] and the results should not be worse than for the fully connected network.…”

Experimental Investigation of Reflection Coefficient and Wigner's Reaction Matrix for Microwave Graphs

“…The distribution forγ = 7.64 is obtained by averaging over 53 realizations of microwave graphs having γ within a window of [6.60, 8.59]. We estimated the experimental values of the γ parameter by adjusting the theoretical mean reflection coefficient R th to the experimental one R = SS † , where .64 (open triangles), respectively, calculated using the impedance approach [26,27]. Each corresponding theoretical distribution P (R) evaluated from Eq.…”

“…The function K = −iZ and therefore the scattering matrix S = (1 − Z)/(1 + Z) are directly connected with the impedance Z, which has been recently measured in a microwave cavity experiment [26,27]. The S matrix can be parameterized as…”

“…It is convenient to find the distribution P (R) of the reflection coefficient R and the distributions of imaginary and real parts of Wigner's reaction matrix K using the impedance approach [26,27]. In this approach one can easily obtain the real and imaginary parts of the normalized impedance…”