Experimental examination of the effect of short ray trajectories in two-port wave-chaotic scattering systems

Superuniversal Statistics of Complex Time Delays in Non-Hermitian Scattering Systems

The Wigner-Smith time delay of flux conserving systems is a real quantity that measures how long an excitation resides in an interaction region. The complex generalization of time delay to non-Hermitian systems is still under development, in particular, its statistical properties in the short-wavelength limit of complex chaotic scattering systems has not been investigated. From the experimentally measured multiport scattering (S) matrices of one-dimensional graphs, a two-dimensional billiard, and a three-dimensional cavity, we calculate the complex Wigner-Smith (τ_{WS}), as well as each individual reflection (τ_{xx}) and transmission (τ_{xy}) time delay. The complex reflection time-delay differences (τ_{δR}) between each port are calculated, and the transmission time-delay differences (τ_{δT}) are introduced for systems exhibiting nonreciprocal scattering. Large time delays are associated with scattering singularities such as coherent perfect absorption, reflectionless scattering, slow light, and unidirectional invisibility. We demonstrate that the large-delay tails of the distributions of the real and imaginary parts of each time-delay quantity are superuniversal, independent of experimental parameters: wave propagation dimension D, number of scattering channels M, Dyson symmetry class β, and uniform attenuation η. The tails determine the abundance of the singularities in generic scattering systems, and the superuniversality is in direct contrast with the well-established time-delay statistics of unitary scattering systems, where the tail of the τ_{WS} distribution depends explicitly on the values of M and β. We relate the distribution statistics to the topological properties of the corresponding singularities. Although the results presented here are based on classical microwave experiments, they are applicable to any non-Hermitian wave-chaotic scattering system in the short-wavelength limit, such as optical or acoustic resonators.

Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

The statistical properties of wave chaotic systems of varying dimensionalities and realizations have been studied extensively. These systems are commonly characterized by the statistics of the eigenmode spacings and the statistics of the eigenfunctions. Here, we propose photonic crystal (PC) defect waveguide graphs as a physical setting for chaotic graph studies. Photonic crystal waveguides possess a dispersion relation for the propagating modes, which is engineerable. Graphs constructed by joining these waveguides possess junctions and bends with distinct scattering properties. We present numerically determined statistical properties of an ensemble of such PC graphs including both eigenfunction amplitude and eigenmode-spacing studies. Our proposed system is compatible with silicon nanophotonic technology and opens chaotic graph studies to a new community of researchers.

Diffuse field cross-correlations: Scattering theory and electromagnetic experiments

The passive estimation of impulse responses from ambient noise correlations arouses increasing interest in seismology, acoustics, optics, and electromagnetism. Assuming the equipartition of the noise field, the cross-correlation function measured with noninvasive receiving probes converges towards the difference of the causal and anticausal Green's functions. Here, we consider the case when the receiving field probes are antennas which are well coupled to a complex medium-a scenario of practical relevance in electromagnetism. We propose a general approach based on the scattering matrix formalism to explore the convergence of the cross-correlation function. The analytically derived theoretical results for chaotic systems are confirmed in microwave measurements within a mode-stirred reverberation chamber. This study provides fundamental insight into the Green's function retrieval technique and paves the way for a new technique to characterize electromagnetic antennas.

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.

Wave scattering properties of multiple weakly coupled complex systems

The statistics of the scattering of waves inside single ray-chaotic enclosures have been successfully described by the random coupling model (RCM). We expand the RCM to systems consisting of multiple complex ray-chaotic enclosures with various coupling scenarios. The statistical properties of the model-generated quantities are tested against measured data of electrically large multicavity systems of various designs. The statistics of model-generated transimpedance and induced voltages on a load impedance agree well with the experimental results. The RCM coupled chaotic enclosure model is general and can be applied to other physical systems, including coupled quantum dots, disordered nanowires, and short-wavelength electromagnetic and acoustic propagation through rooms in buildings, aircraft, and ships.

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.

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.

Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices

In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation functions with respect to energy. The analytical results are tested in several models by numerical simulations. Some applications are discussed for a relation between transition probabilities and for expectation values of some local observables.

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.

Focusing waves at arbitrary locations in a ray-chaotic enclosure using time-reversed synthetic sonas

Time-reversal methods are widely used to achieve wave focusing in acoustics and electromagnetics. Past time-reversal experiments typically require that a transmitter be initially present at the target focusing point, which limits the application of this technique. In this paper, we propose a method to focus waves at an arbitrary location inside a complex enclosure using a numerically calculated wave excitation signal. We use a semiclassical ray algorithm to calculate the signal that would be received at a transceiver port resulting from the injection of a short pulse at the desired target location. The time-reversed version of this signal is then injected into the transceiver port, and an approximate reconstruction of the short pulse is created at the target. The quality of the pulse reconstruction is quantified in three different ways, and the values of these metrics are shown to be predicted by the statistics of the scattering parameter |S_{21}|^{2} between the transceiver and target points in the enclosure over the bandwidth of the pulse. We demonstrate the method experimentally using a flat microwave billiard, and we quantify the reconstruction quality as a function of enclosure loss, port coupling, and other considerations.

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.

Impedance and power fluctuations in linear chains of coupled wave chaotic cavities

The flow of electromagnetic wave energy through a chain of coupled cavities is considered. The cavities are assumed to be of sufficiently irregular shape that their eigenmodes are described by random matrix theory. The cavities are coupled by electrically short single mode transmission lines. Approximate expressions for the power coupled into successive cavities are derived, and the predictions are compared with Monte Carlo simulations. The analytic formulas separate into a product of factors. Consequently, the distribution of power in the last cavity of a very long chain approaches lognormal. For lossless cavities, signatures of Anderson localization, similar to those of the conductances of quantum wires, are observed.

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

Fading is the time-dependent variation in transmitted signal strength through a complex medium due to interference or temporally evolving multipath scattering. In this paper we use random matrix theory (RMT) to establish a first-principles model for fading, including both universal and nonuniversal effects. This model provides a more general understanding of the most common statistical models (Rayleigh fading and Rice fading) and provides a detailed physical basis for their parameters. We also report experimental tests on two ray-chaotic microwave cavities. The results show that our RMT model agrees with the Rayleigh and Rice models in the high-loss regime, but there are strong deviations in low-loss systems where the RMT approach describes the data well.