arXiv subjects

Isaac Harris

Publications and source records attributed to Isaac Harris.

At least 37 records · Page 2Linked to original sources

arXiv2024

Designed spin-texture-lattice to control anisotropic magnon transport in antiferromagnets

Spin waves in magnetic materials are promising information carriers for future computing technologies due to their ultra-low energy dissipation and long coherence length. Antiferromagnets are strong candidate materials due, in part, to their stability to external fields and larger group velocities. Multiferroic aniferromagnets, such as BiFeO$_3$ (BFO), have an additional degree of freedom stemming from magnetoelectric coupling, allowing for control of the magnetic structure, and thus spin waves, with electric field. Unfortunately, spin-wave propagation in BFO is not well understood due to the complexity of the magnetic structure. In this work, we explore long-range spin transport within an epitaxially engineered, electrically tunable, one-dimensional (1D) magnonic crystal. We discover a striking anisotropy in the spin transport parallel and perpendicular to the 1D crystal axis. Multiscale theory and simulation suggests that this preferential magnon conduction emerges from a combination of a population imbalance in its dispersion, as well as anisotropic structural scattering. This work provides a pathway to electrically-reconfigurable magnonic crystals in antiferromagnets.

cond-mat.mtrl-sci↗

arXiv2024

Inverse parameter and shape problem for an isotropic scatterer with two conductivity coefficients

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident direction for multiple frequencies. Then, we address the inverse shape problem for recovering the scatterer for the measured far-field data at a fixed frequency. Furthermore, we examine the direct sampling method for recovering the scatterer by studying the factorization for the far-field operator. The direct sampling method is stable with respect to noisy data and valid in two dimensions for partial aperture data. The theoretical results are verified with numerical examples to analyze the performance by the direct sampling method.

math-ph↗

arXiv2023

Heterogeneous integration of spin-photon interfaces with a scalable CMOS platform

Color centers in diamonds have emerged as a leading solid-state platform for advancing quantum technologies, satisfying the DiVincenzo criteria and recently achieving a quantum advantage in secret key distribution. Recent theoretical works estimate that general-purpose quantum computing using local quantum communication networks will require millions of physical qubits to encode thousands of logical qubits, which presents a substantial challenge to the hardware architecture at this scale. To address the unanswered scaling problem, in this work, we first introduce a scalable hardware modular architecture "Quantum System-on-Chip" (QSoC) that features compact two-dimensional arrays "quantum microchiplets" (QMCs) containing tin-vacancy (SnV-) spin qubits integrated on a cryogenic application-specific integrated circuit (ASIC). We demonstrate crucial architectural subcomponents, including (1) QSoC fabrication via a lock-and-release method for large-scale heterogeneous integration; (2) a high-throughput calibration of the QSoC for spin qubit spectral inhomogenous registration; (3) spin qubit spectral tuning functionality for inhomogenous compensation; (4) efficient spin-state preparation and measurement for improved spin and optical properties. QSoC architecture supports full connectivity for quantum memory arrays in a set of different resonant frequencies and offers the possibility for further scaling the number of solid-state physical qubits via larger and denser QMC arrays and optical frequency multiplexing networking.

quant-ph↗

arXiv2023

Metal-Optic Nanophotonic Modulators in Standard CMOS Technology

Integrating nanophotonics with electronics promises revolutionary applications, from LiDAR to holographic displays. Although silicon photonics is maturing, realizing active nanophotonics in the ubiquitous bulk CMOS processes remains challenging. We introduce a fabless approach to embed active nanophotonics in bulk CMOS by co-designing the back-end-of-line metal layers for optical functionality. Using a 65nm CMOS process, we create plasmonic liquid crystal modulators with switching speeds 100x faster than commercial technologies. This zero-change nanophotonics method could equip mass-produced chips with optical communications, sensing and imaging. Embedding nanophotonics in the dominant electronics platform democratizes nanofabrication, spawning technologies from chip-scale LiDAR to holographic light-field displays.

physics.optics↗

arXiv2023

Reconstruction of extended regions in EIT with a generalized Robin transmission condition

We consider an inverse shape problem coming from electrical impedance tomography with a generalized Robin transmission condition. We will derive an algorithm in order to detect whether two materials that should be in contact are separated or delaminated. More precisely, we assume that the undamaged material or background state is known and shares an interface or boundary with the damaged subregion. The Robin transmission condition on this boundary asymptotically models delamination. We assume that the DtN operator is given from measuring the current on the surface of the material from an imposed voltage. We show that this mapping uniquely recovers the boundary parameters. Furthermore, using this electrostatic Cauchy data as physical measurements, we can determine if all of the coefficients from the Robin transmission condition are real-valued or complex-valued. We study these two cases separately and show that the regularized factorization method can be used to detect whether delamination has occurred and recover the damaged subregion. Numerical examples will be presented for both cases in two dimensions in the unit circle.

math.AP↗

arXiv2023

The anisotropic interior transmission eigenvalue problem with a conductive boundary

In this paper, we study the transmission eigenvalue problem for an anisotropic material with a conductive boundary. We prove that the transmission eigenvalues for this problem exist and are at most a discrete set. We also study the dependence of the transmission eigenvalues on the physical parameters and prove that the first transmission eigenvalue is monotonic. We then consider the limiting behavior of the transmission eigenvalues as the conductive boundary parameter $η$ vanishes or goes to infinity in magnitude. Finally, we provide some numerical examples on three different domains to demonstrate our theoretical results.

math.AP↗

arXiv2023

Reconstruction of small and extended scatterers with a conductive boundary using far-field data

In this paper, we consider the inverse shape problem of recovering small and extended isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. We will provide qualitative reconstruction methods for recovering either small or extended scatterers. For the case of small scatterers, we model this by a region(possibly with multiple components) with small volume. We derive an asymptotic expansion for the far-field pattern which will allow us to study the MUSIC algorithm for solving the problem. In the case of an extended scatterer, we derive a new factorization of the far-field operator. This is then used to provide the resolution analysis for a direct sampling method. The theoretical results are verified with some numerical experiments in 2--dimensions.

math.AP↗

arXiv2023

Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary

In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we study a new direct sampling indicator based on the Landweber iteration and the factorization method. Therefore, we prove the connection between these reconstruction methods. The method studied here falls under the category of qualitative reconstruction methods where an imaging function is used to recover the absorbing scatterer. We prove stability of our new imaging function as well as derive a discrepancy principle for recovering the regularization parameter. The theoretical results are verified with numerical examples to show how the reconstruction performs by the new Landweber direct sampling method.

math.AP↗

arXiv2023

On reconstruction of small sources from Cauchy data at a fixed frequency

This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way. Furthermore, the method can also compute the intensity of point sources provided that the sources are well separated. A simple justification of the method is done using the Green representation formula and an asymptotic expansion of the radiated field for small volume sources. The implementation of the method is non-iterative, computationally cheap, fast, and very simple. Numerical examples are presented to illustrate the performance of the method.

math.NA↗

arXiv2023

Regularized Factorization Method for a perturbed positive compact operator applied to inverse scattering

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are advantageous to use due to the fact that they are computationally simple and require little a priori knowledge of the object one wishes to reconstruct. The main focus of this paper is to prove that the regularization strategy presented here produces stable reconstructions. We will show this is the case analytically and numerically for the inverse shape problem of recovering an isotropic scatterer with a conductive boundary condition. We also provide a strategy for picking the regularization parameter with respect to the noise level. Numerical examples are given for a scatterer in 2 dimensions.

math.AP↗

arXiv2023

Reciprocity gap functional methods for potentials/sources with small volume support for two elliptic equations

In this paper, we consider inverse shape problems coming from diffuse optical tomography and inverse scattering. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an object. In order to achieve this, we will derive an asymptotic expansion of the reciprocity gap functional associated with each problem. The reciprocity gap functional takes in the measured Cauchy data on the exterior surface of the object. In diffuse optical tomography, we prove that a MUSIC-type algorithm can be used to recover the unknown subregions. This gives an analytically rigorous and computationally simple method for recovering the small volume regions. For the problem coming from inverse scattering, we recover the subregions of interest via a direct sampling method. The direct sampling method presented here allows us to accurately recover the small volume region from one pair of Cauchy data. We also prove that the direct sampling method is stable with respect to noisy data. Numerical examples will be presented for both cases in two dimensions where the measurement surface is the unit circle.

math.AP↗

arXiv2023

Functional-Input Gaussian Processes with Applications to Inverse Scattering Problems

Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are scarce. Motivated by an inverse scattering problem in which functional inputs representing the support and material properties of the scatterer are involved in the partial differential equations, a new class of kernel functions for functional inputs is introduced for GPs. Based on the proposed GP models, the asymptotic convergence properties of the resulting mean squared prediction errors are derived and the finite sample performance is demonstrated by numerical examples. In the application to inverse scattering, a surrogate model is constructed with functional inputs, which is crucial to recover the reflective index of an inhomogeneous isotropic scattering region of interest for a given far-field pattern.

stat.ME↗

arXiv2022

Analysis of the transmission eigenvalue problem with two conductivity parameters

In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We will prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.

math.AP↗

arXiv2022

Regularization of the Factorization Method with Applications to Inverse Scattering

Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In general, qualitative methods seek to reconstruct the shape of an unknown object using little to no a priori information. The regularized factorization method presented here seeks to avoid numerical instabilities in the inversion algorithm. This allows one to recover unknown structures in a computationally simple and analytically rigorous way. We will discuss the theory and application of the regularized factorization method to examples coming from acoustic inverse scattering. Numerical examples will also be presented using synthetic data to show the applicability of the method.

math.AP↗

arXiv2022

Reconstruction of small and extended regions in EIT with a Robin transmission condition

We consider an inverse shape problem coming from electrical impedance tomography with a Robin transmission condition. In general, a boundary condition of Robin type models corrosion. In this paper, we study two methods for recovering an interior corroded region from electrostatic data. We consider the case where we have small volume and extended regions. For the case where the region has small volume, we will derive an asymptotic expansion of the current gap operator and prove that a MUSIC-type algorithm can be used to recover the region. In the case where one has an extended region, we will show that the regularized factorization method can be used to recover said region. Numerical examples will be presented for both cases in two dimensions in the unit circle.

math.AP↗

arXiv2021

Direct sampling for recovering sound soft scatterers from point source measurements

In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here we will propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data which will allow us to derive explicit bounds in the resolution analysis for the direct sampling method's imaging functional. Two direct sampling methods will be studied using the far-field transformation. For these imaging functionals, we will use the Funk-Hecke identities to study the resolution analysis. We will also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer in 2D.

math.AP↗

arXiv2021

Regularization of the Factorization Method applied to diffuse optical tomography

In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to image an unknown region. In most applications, the data operator is compact which gives that the singular values can tend to zero rapidly which can cause numerical instabilities. The regularization of the Factorization Method presented here seeks to avoid the numerical instabilities in applying Picard's Criteria. This method allows one to image the interior structure of an object with little a priori information in a computationally simple and analytically rigorous way. Here we will focus on an application of this method to diffuse optical tomography where will prove that this method can be used to recover an unknown subregion from the Dirichlet-to-Neumann mapping. Numerical examples will be presented in two dimensions.

math.AP↗

arXiv2021

Direct sampling methods for isotropic and anisotropic scatterers with point source measurements

In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the inverse problem. The first one employs a far-field transform to the data which we then use to derive and provide an explicit decay rate for the imaging functional. In order to analyze the behavior of this imaging functional we use the factorization of the near field operator as well as the Funk-Hecke integral identity. For the second imaging functional the Cauchy data is used to define the functional and its behavior is analyzed using the Green's identities. Numerical experiments are given in two dimensions for both isotropic and anisotropic scatterers.

math.AP↗