arXiv subjects

Jared Erb

Publications and source records attributed to Jared Erb.

5 recordsLinked to original sources

arXiv2026

Measurement and Optimal Targeting of a Hidden Scatterer in a Complex Environment Utilizing Fisher Information

A complex, non-Hermitian scattering system with a high degree of multiple scattering and interference is often treated as a black box, described simply by the relationship between a set of incoming and outgoing waves of a given frequency or energy. The scattering matrix S that describes the system is a non-unique, generally sub-unitary matrix that reveals very little about the microscopic processes that are responsible for the observed scattering. We form the Fisher information operator $F_x$, a Hermitian matrix, utilizing a derivative of S with respect to the value of some varying parameter x of the system, associated with a localized perturbation, and experimentally demonstrate that the principal eigenvector of Fx can be used to quantitatively measure changes in the value of parameter x using only information from the scattering matrix. We propose a "discrete feedback loop" protocol enabled by the knowledge we gain from the Fisher information operator, that repeatedly determines the counter perturbation necessary to return a varying parameter to some fixed benchmark value. A further application of the Fisher information operator for energy focusing that utilizes the principal eigenvector excitation is demonstrated through compelling indirect evidence of targeting within a complex system. These methods are experimentally demonstrated to work even in the presence of time-reversal symmetry breaking due to absorption and/or loss of scattering reciprocity.

physics.optics↗

arXiv2025

Universal Frequency Correlations and Recurrence Statistics of Complex Impedance Matrices

Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved, the impedance matrix becomes a complicated function of the details of the system, in which case a statistical model, such as the Random Coupling Model (RCM) becomes useful. The statistics of the elements of the RCM impedance matrix depend on the excitation frequency, the spectral density of the modes of the enclosed system volume, the average loss factor (Q^{-1}) of the system, and the properties of the coupling ports as given by their radiation impedances. In this paper, properties of the elements of impedance matrices are explored numerically and experimentally. These include the two point frequency correlation functions for the complex impedance of elements and the expected difference in frequencies between which impedance values are approximately repeated. Universal scaling arguments are then given for these quantities, hence these results are generic for all sufficiently complicated scattering systems, including acoustic and optical systems. The experimental data presented in this paper come from microwave graphs, billiards, and three-dimensional cavities with embedded tunable perturbers such as metasurfaces. The data is found to be in generally good agreement with the predictions for the two point frequency correlations and the frequency interval for successive repetitions of impedance matrix elements values.

nlin.CD↗

arXiv2025

Robust Wave Splitters Based on Scattering Singularities in Complex non-Hermitian Systems

We have discovered specific conditions for generic scattering systems to act as wave splitters that are robust to any change in relative amplitude or phase of an arbitrary injected waveform. Specifically for complex systems with tunable parameters, these conditions for robust splitting (RS) are abundant, and by using multiple tunable parameters the relative amplitude and phase of the output signals can also be tuned. The splitting property of the systems works for all possible input phase differences and amplitude ratios and does not require a particular coherent input signal. We show experimentally that the fixed splitting ratios and output phases at RS conditions are robust to 100 dB of relative power and 2$\pi$ phase changes of the input waves to a complex non-Hermitian two-port system. We also demonstrate that the splitting power ratio can be tuned by multiple orders of magnitude and the RS conditions can be tuned to any desired frequency with suitable tunable perturbations embedded in the system. Although this phenomenon is realized in two-port systems and involves some degree of attenuation, tunable robust splitting can be achieved between any two ports of multiport systems. These results are general to all wave scattering phenomena (electromagnetic, acoustic, etc.) and hold in generic complex scattering systems.

cond-mat.mes-hall↗

arXiv2024

Novel Topology and Manipulation of Scattering Singularities in Complex non-Hermitian Systems

The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks, wavefront shaping protocols, active metasurface development, and more. At their core, these achievements rely on our ability to engineer the resonant spectrum of the underlying physical structures which is conventionally accomplished by carefully imposing geometrical and/or dynamical symmetries. In contrast, by taking active control over the boundary conditions in complex scattering environments which lack artificially-imposed geometric symmetries, we demonstrate via microwave experiments the ability to manipulate the spectrum of the scattering operator. This active control empowers the creation, destruction and repositioning of exceptional point degeneracies (EPD's) in a two-dimensional (2D) parameter space. The presence of EPD's signifies a coalescence of the scattering eigenmodes, which dramatically affects transport. The scattering EPD's are partitioned in domains characterized by a binary charge, as well as an integer winding number, are topologically stable in the two-dimensional parameter space, and obey winding number-conservation laws upon interactions with each other, even in cases where Lorentz reciprocity is violated; in this case the topological domains are destroyed. Ramifications of this understanding is the proposition for a unique input-magnitude and phase-insensitive 50:50 in-phase/quadrature (I/Q) power splitter. Our study establishes an important step towards complete control of scattering processes in complex non-Hermitian settings.

cond-mat.mes-hall↗

arXiv2023

Control of the Scattering Properties of Complex Systems By Means of Tunable Metasurfaces

We demonstrate the ability to control the scattering properties of a two-dimensional wave-chaotic microwave billiard through the use of tunable metasurfaces located on the interior walls of the billiard. The complex reflection coefficient of the metasurfaces can be varied by applying a DC voltage bias to varactor diodes on mushroom-shaped resonant patches, and this proves to be very effective at perturbing the eigenmodes of the cavity. Placing multiple metasurfaces inside the cavity allows us to engineer desired scattering conditions, such as coherent perfect absorption (CPA), by actively manipulating the poles and zeros of the scattering matrix through the application of multiple voltage biases. We demonstrate the ability to create on-demand CPA conditions at a specific frequency, and document the near-null of output power as a function of four independent parameters tuned through the CPA point. A remarkably low output-to-input power ratio of $\frac{P_{out}}{P_{in}} = 3.71 \times 10^{-8}$ is achieved near the CPA point at 8.54 GHz.

cond-mat.mes-hall↗