First-principles model of time-dependent variations in transmission through a fluctuating scattering environment

Multipath Signal-Selective Metasurface: Passive Time-Varying Interlocking Mechanism to Vary Spatial Impedance for Signals with the Same Frequency

Electromagnetic (EM) multipath interference is difficult to address with passive approaches due to two physical restrictions-the shared frequency of the initial and interfering signals and their variable incident angles. Thus, to address multipath interference, the spatial impedance, i.e., the impedance structured in three-dimensional space, must be adjusted in response to the incident angles of multiple signals with the same frequency, which is impossible with classic linear time-invariant (LTI) systems. We present a design concept for metasurface-based spatial filters to overcome LTI behavior and suppress multipath interference signals using a time-varying interlocking mechanism without any active biasing systems. The proposed filters are comprised of metasurface panels and internally coupled circuit elements including MOSFETs, which permit accepting only the first incoming wave, while adjusting the spatial impedance to reject time-delayed waves from different angles. The proposed concept is numerically and experimentally validated to have a shielding effectiveness of more than 10 dB. This Letter opens a new avenue for passive yet time-varying selective EM metasystems, enabling the adjustment of spatially complicated EM waves and fields even at the same frequency.

Implementing nonuniversal features with a random matrix theory approach: Application to space-to-configuration multiplexing

We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is studied to quantify the channel diversity and to assess a specific system's performance. System-specific features such as unstirred field components give rise to nontrivial interchannel correlations and need to be properly accounted for in modeling based on random matrix theory. To address this challenge, we propose a two-step hybrid approach. Based on an ensemble of experimentally measured scattering matrices for different random metasurface configurations, we first learn a system-specific pair of coupling matrix and unstirred contribution to the Hamiltonian, and then add an appropriately weighted stirred contribution. We verify that our method is capable of reproducing the experimentally found distribution of the effective rank with good accuracy. The approach can also be applied to other wave phenomena in complex media.

Scattering statistics in nonlinear wave chaotic systems

The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings, including both microwave and acoustic systems. It is of great interest to extend its use in nonlinear systems. This paper studies the impact of a nonlinear port on the measured statistical electromagnetic properties of a ray-chaotic complex enclosure in the short wavelength limit. A Vector Network Analyzer is upgraded with a high power option, which enables calibrated scattering (S) parameter measurements up to +43dBm. By attaching a diode to the excitation antenna, amplitude-dependent S-parameters and Wigner reaction matrix (impedance) statistics are observed. We have systematically studied how the key components in the RCM are affected by this nonlinear port, including the radiation impedance, short ray orbit corrections, and statistical properties. By applying the newly developed radiation efficiency extension to the RCM, we find that the diode admittance increases with the excitation amplitude. This reduces the amount of power entering the cavity through the port so that the diode effectively acts as a protection element. As a result, we have developed a quantitative understanding of the statistical scattering properties of a semi-classical wave chaotic system with a nonlinear coupling channel.

Envelope and phase distribution of a resonance transmission through a complex environment

A transmission amplitude is considered for quantum or wave transport mediated by a single resonance coupled to the background of many chaotic states. Such a model provides a useful approach to quantify fluctuations in an established signal induced by a complex environment. Applying random matrix theory to the problem, we derive an exact result for the joint distribution of the transmission intensity (envelope) and the transmission phase at arbitrary coupling to the background with finite absorption. The intensity and phase are distributed within a certain region, revealing essential correlations even at strong absorption. In the latter limit, we obtain a simple asymptotic expression that provides a uniformly good approximation of the exact distribution within its whole support, thus going beyond the Rician distribution often used for such purposes. Exact results are also derived for the marginal distribution of the phase, including its limiting forms at weak and strong absorption.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Nonlinear wave chaos: statistics of second harmonic fields

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

Distribution of scattering matrix elements in quantum chaotic scattering

Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory, the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic scattering systems. To model the universal properties, stochasticity is introduced to the scattering matrix on the level of the Hamiltonian by using random matrices. A long-standing problem was the computation of the distribution of the off-diagonal scattering-matrix elements. We report here an exact solution to this problem and present analytical results for systems with preserved and with violated time-reversal invariance. Our derivation is based on a new variant of the supersymmetry method. We also validate our results with scattering data obtained from experiments with microwave billiards.

In situ broadband cryogenic calibration for two-port superconducting microwave resonators

We introduce an improved microwave calibration method for use in a cryogenic environment, based on a traditional three-standard calibration, the Thru-Reflect-Line (TRL) calibration. The modified calibration method takes advantage of additional information from multiple measurements of an ensemble of realizations of a superconducting resonator, as a new pseudo-Open standard, to correct errors in the TRL calibration. We also demonstrate an experimental realization of this in situ broadband cryogenic calibration system utilizing cryogenic switches. All calibration measurements are done in the same thermal cycle as the measurement of the resonator (requiring only an additional 20 min), thus avoiding 4 additional thermal cycles for traditional TRL calibration (which would require an additional 12 days). The experimental measurements on a wave-chaotic microwave billiard verify that the new method significantly improves the measured scattering matrix of a high-quality-factor superconducting resonator.