Wigner-Smith time delay matrix for acoustic scattering: Theory and phenomenology.

The Wigner-Smith (WS) time delay matrix relates a lossless system's scattering matrix to its frequency derivative. First proposed in the realm of quantum mechanics to characterize time delays experienced by particles during a collision, this article extends the use of WS time delay techniques to acoustic scattering problems governed by the Helmholtz equation. Expression for the entries of the WS time delay matrix involving renormalized volume integrals of energy densities are derived, and shown to hold true, independent of the scatterer's geometry, boundary condition (sound-soft or sound-hard), and excitation. Numerical examples show that the eigenmodes of the WS time delay matrix describe distinct scattering phenomena characterized by well-defined time delays.

Comparison of Experimental and Modeled EMI Shielding Properties of Periodic Porous xGNP/PLA Composites.

Microwave absorbing materials, particularly ones that can achieve high electromagnetic interference (EMI) absorption while minimizing weight and thickness are in high demand for many applications. Herein we present an approach that relies on the introduction of periodically placed air-filled pores into polymer composites in order to reduce material requirements and maximize microwave absorption. In this study, graphene nano platelet (xGNP)/poly-lactic acid (PLA) composites with different aspect ratio fillers were characterized and their complex electromagnetic properties were extracted. Using these materials, we fabricated non-perfect electrical conductor (PEC) backed, porous composites and explored the effect of filler aspect ratio and pore geometry on EMI shielding properties. Furthermore, we developed and experimentally verified a computational model that allows for rigorous, high-throughput optimization of absorbers with periodic porous geometries. Finally, we extend the modeling approach to explore the effect of pore addition on PEC-backed composites. Our composite structures demonstrated decreased fractions of reflected power and increased fractions of absorbed power over the majority of the X Band due to the addition of periodically arranged cylindrical pores. Furthermore, we showed that for xGNP/PLA composite material, reflection loss can be increased by as much as 13 dB through the addition of spherical pores. The ability to adjust shielding properties through the fabrication of polymer composites with periodically arranged pores opens new strategies for the modeling and development of new microwave absorption materials.

An FMM-FFT Accelerated SIE Simulator for Analyzing EM Wave Propagation in Mine Environments Loaded With Conductors.

A fast and memory efficient three-dimensional full-wave simulator for analyzing electromagnetic (EM) wave propagation in electrically large and realistic mine tunnels/galleries loaded with conductors is proposed. The simulator relies on Muller and combined field surface integral equations (SIEs) to account for scattering from mine walls and conductors, respectively. During the iterative solution of the system of SIEs, the simulator uses a fast multipole method-fast Fourier transform (FMM-FFT) scheme to reduce CPU and memory requirements. The memory requirement is further reduced by compressing large data structures via singular value and Tucker decompositions. The efficiency, accuracy, and real-world applicability of the simulator are demonstrated through characterization of EM wave propagation in electrically large mine tunnels/galleries loaded with conducting cables and mine carts.

Mode control in a multimode fiber through acquiring its transmission matrix from a reference-less optical system.

A simple imaging system, together with complex semidefinite programming, is used to generate the transmission matrix (TM) of a multimode fiber. Once the TM is acquired, we can modulate the phase of the input signal to induce strong mode interference at the fiber output. The optical design does not contain a reference arm, no internal reference signal is used, and no interferometric measurements are required. We use a phase-only spatial light modulator to shape the profile of the propagating modes, and the output intensity patterns are collected. The semidefinite program uses a convex optimization algorithm to generate the TM of the optical system using intensity only measurements. This simple, yet powerful, method can be used to compensate for modal dispersion in multimode fiber communication systems. It also yields great promise for the next generation biomedical imaging, quantum communication, and cryptography.

The ICVSIE: A General Purpose Integral Equation Method for Bio-Electromagnetic Analysis.

OBJECTIVE: An internally combined volume surface integral equation (ICVSIE) for analyzing electromagnetic (EM) interactions with biological tissue and wide ranging diagnostic, therapeutic, and research applications, is proposed. METHOD: The ICVSIE is a system of integral equations in terms of volume and surface equivalent currents in biological tissue subject to fields produced by externally or internally positioned devices. The system is created by using equivalence principles and solved numerically; the resulting current values are used to evaluate scattered and total electric fields, specific absorption rates, and related quantities. RESULTS: The validity, applicability, and efficiency of the ICVSIE are demonstrated by EM analysis of transcranial magnetic stimulation, magnetic resonance imaging, and neuromuscular electrical stimulation. CONCLUSION: Unlike previous integral equations, the ICVSIE is stable regardless of the electric permittivities of the tissue or frequency of operation, providing an application-agnostic computational framework for EM-biomedical analysis. SIGNIFICANCE: Use of the general purpose and robust ICVSIE permits streamlining the development, deployment, and safety analysis of EM-biomedical technologies.

Controlling Light Transmission Through Highly Scattering Media Using Semi-Definite Programming as a Phase Retrieval Computation Method.

Complex Semi-Definite Programming (SDP) is introduced as a novel approach to phase retrieval enabled control of monochromatic light transmission through highly scattering media. In a simple optical setup, a spatial light modulator is used to generate a random sequence of phase-modulated wavefronts, and the resulting intensity speckle patterns in the transmitted light are acquired on a camera. The SDP algorithm allows computation of the complex transmission matrix of the system from this sequence of intensity-only measurements, without need for a reference beam. Once the transmission matrix is determined, optimal wavefronts are computed that focus the incident beam to any position or sequence of positions on the far side of the scattering medium, without the need for any subsequent measurements or wavefront shaping iterations. The number of measurements required and the degree of enhancement of the intensity at focus is determined by the number of pixels controlled by the spatial light modulator.

Uncertainty quantification in transcranial magnetic stimulation via high-dimensional model representation.

A computational framework for uncertainty quantification in transcranial magnetic stimulation (TMS) is presented. The framework leverages high-dimensional model representations (HDMRs), which approximate observables (i.e., quantities of interest such as electric (E) fields induced inside targeted cortical regions) via series of iteratively constructed component functions involving only the most significant random variables (i.e., parameters that characterize the uncertainty in a TMS setup such as the position and orientation of TMS coils, as well as the size, shape, and conductivity of the head tissue). The component functions of HDMR expansions are approximated via a multielement probabilistic collocation (ME-PC) method. While approximating each component function, a quasi-static finite-difference simulator is used to compute observables at integration/collocation points dictated by the ME-PC method. The proposed framework requires far fewer simulations than traditional Monte Carlo methods for providing highly accurate statistical information (e.g., the mean and standard deviation) about the observables. The efficiency and accuracy of the proposed framework are demonstrated via its application to the statistical characterization of E-fields generated by TMS inside cortical regions of an MRI-derived realistic head model. Numerical results show that while uncertainties in tissue conductivities have negligible effects on TMS operation, variations in coil position/orientation and brain size significantly affect the induced E-fields. Our numerical results have several implications for the use of TMS during depression therapy: 1) uncertainty in the coil position and orientation may reduce the response rates of patients; 2) practitioners should favor targets on the crest of a gyrus to obtain maximal stimulation; and 3) an increasing scalp-to-cortex distance reduces the magnitude of E-fields on the surface and inside the cortex.

Backscatter analysis based algorithms for increasing transmission through highly scattering random media using phase-only-modulated wavefronts.

Recent theoretical and experimental advances have shed light on the existence of so-called "perfectly transmitting" wavefronts with transmission coefficients close to 1 in strongly backscattering random media. These perfectly transmitting eigen-wavefronts can be synthesized by spatial amplitude and phase modulation. Here, we consider the problem of transmission enhancement using phase-only-modulated wavefronts. Motivated by biomedical applications, in which it is not possible to measure the transmitted fields, we develop physically realizable iterative and non-iterative algorithms for increasing the transmission through such random media using backscatter analysis. We theoretically show that, despite the phase-only modulation constraint, the non-iterative algorithms will achieve at least about 25π%≈78.5% transmission with very high probability, assuming that there is at least one perfectly transmitting eigen-wavefront and that the singular vectors of the transmission matrix obey the maximum entropy principle such that they are isotropically random. We numerically analyze the limits of phase-only-modulated transmission in 2D with fully spectrally accurate simulators and provide rigorous numerical evidence confirming our theoretical prediction in random media, with periodic boundary conditions, that is composed of hundreds of thousands of non-absorbing scatterers. We show via numerical simulations that the iterative algorithms we have developed converge rapidly, yielding highly transmitting wavefronts while using relatively few measurements of the backscatter field. Specifically, the best performing iterative algorithm yields ≈70% transmission using just 15-20 measurements in the regime, where the non-iterative algorithms yield ≈78.5% transmission, but require measuring the entire modal reflection matrix. Our theoretical analysis and rigorous numerical results validate our prediction that phase-only modulation with a given number of spatial modes will yield higher transmission than amplitude and phase modulation with half as many modes.

Iterative, backscatter-analysis algorithms for increasing transmission and focusing light through highly scattering random media.

Scattering hinders the passage of light through random media and consequently limits the usefulness of optical techniques for sensing and imaging. Thus, methods for increasing the transmission of light through such random media are of interest. Against this backdrop, recent theoretical and experimental advances have suggested the existence of a few highly transmitting eigen-wavefronts with transmission coefficients close to 1 in strongly backscattering random media. Here, we numerically analyze this phenomenon in 2D with fully spectrally accurate simulators and provide rigorous numerical evidence confirming the existence of these highly transmitting eigen-wavefronts in random media with periodic boundary conditions that are composed of hundreds of thousands of nonabsorbing scatterers. Motivated by bio-imaging applications in which it is not possible to measure the transmitted fields, we develop physically realizable algorithms for increasing the transmission through such random media using backscatter analysis. We show via numerical simulations that the algorithms converge rapidly, yielding a near-optimum wavefront in just a few iterations. We also develop an algorithm that combines the knowledge of these highly transmitting eigen-wavefronts obtained from backscatter analysis with intensity measurements at a point to produce a near-optimal focus with significantly fewer measurements than a method that does not utilize this information.

Numerical analysis and design of single-source multicoil TMS for deep and focused brain stimulation.

Transcranial magnetic stimulation (TMS) is a tool for noninvasive stimulation of neuronal tissue used for research in cognitive neuroscience and to treat neurological disorders. Many TMS applications call for large electric fields to be sharply focused on regions that often lie deep inside the brain. Unfortunately, the fields generated by present-day TMS coils diffuse and decay rapidly as they penetrate into the head. As a result, they tend to stimulate relatively large regions of tissue near the brain surface. Earlier studies suggested that a focused TMS excitation can be attained using multiple nonuniformly fed coils in a multichannel array. We propose a systematic, genetic algorithm-based technique for synthesizing multichannel arrays that minimize the volume of the excited region required to achieve a prescribed penetration depth and maintain realistic values for the input driving currents. Because multichannel arrays are costly to build, we also propose a method to convert the multichannel arrays into single-channel ones while minimally materially deteriorating performance. Numerical results show that the new multi- and single-channel arrays stimulate tissue 2.4 cm into the head while exciting 3.0 and 2.6 times less volume than conventional Figure-8 coils, respectively.

A numerically optimized active shield for improved transcranial magnetic stimulation targeting.

Transcranial magnetic stimulation (TMS) devices suffer of poor targeting and penetration depth. A new approach to designing TMS coils is introduced in order to improve the focus of the stimulation region through the use of actively shielded probes. Iterative optimization techniques were used to design different active shielding coils for TMS probes. The new approach aims to increase the amount of energy deposited in a thin cylindrical region below the probe relative to the energy deposited elsewhere in the region ("sharpness"), whereas, simultaneously increase the induced electric field deep in the target region relative to the surface ("penetration"). After convergence, the resulting designs showed that there is a clear tradeoff between sharpness and penetration that can be controlled by the choice of a tuning parameter. The resulting designs were tested on a realistic human head conductivity model, taking the contribution from surface charges into account. The design of choice reduced penetration depths by 16.7%. The activated surface area was reduced by 24.1% and the volume of the activation was reduced from 42.6% by the shield. Restoring the lost penetration could be achieved by increasing the total power to the coil by 16.3%, but in that case, the stimulated volume reduction was only 13.1% and there was a slight increase in the stimulated surface area (2.9%).

Optical wave properties of nano-particle chains coupled with a metal surface.

Optical phenomena supported by ordered and disordered chains of metal nano-particles on a metal surface are investigated by considering a particular example of gold nano-bumps on a gold surface. The TWs supported by these structures are analyzed by studying the frequency-wavenumber spectra of the fields excited by localized sources placed near the chain. Periodic nano-bump chains support traveling waves (TWs) that propagate without radiation loss along, and are confined to the region near, the chain. These TWs are slow waves with respect to both space fields and surface plasmon polaritons supported by the metal surface. For nearly resonant nano-bumps, the TWs are well confined and can be excited efficiently by a localized source placed near the chain but the TW propagation length is short. For non-resonant nano-bumps, the TWs have large propagation lengths but are not well confined and are excited less efficiently. The TWs supported by nano-bump chains were shown to have larger propagation lengths than free-standing chains of the same dimension/size and cross-sectional confinement. TWs also are supported by disordered chains and chains with sharp bends. Perturbations in nano-bump positions are shown to reduce the TW propagation length much less significantly than perturbations in their sizes. Transmission through sharp chain bends is much stronger for nearly resonant nano-bumps than for nonresonant ones. In addition to their ability to support TWs, nano-bump chains can be used to manipulate (excite/reflect/refract) SPPs on the metal surface.

Plane-wave-time-domain-enhanced marching-on-in-time scheme for analyzing scattering from homogeneous dielectric structures.

A novel and fast integral-equation-based scheme is presented for analyzing transient electromagnetic scattering from homogeneous, isotropic, and nondispersive bodies. The computational complexity of classical marching-on-in-time (MOT) methods for solving time-domain integral equations governing electromagnetic scattering phenomena involving homogeneous penetrable bodies scales as O(NtNs2). Here, Nt represents the number of time steps in the analysis, and Ns denotes the number of spatial degrees of freedom of the discretized electric and magnetic currents on the body's surface. In contrast, the computational complexity of the proposed plane-wave-time-domain-enhanced MOT solver scales as O(NtNs log2Ns). Numerical results that demonstrate the accuracy and the efficacy of the scheme are presented.