Kamalesh Sainath

Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments.

We develop a general-purpose formulation, based on two-dimensional spectral integrals, for computing electromagnetic fields produced by arbitrarily oriented dipoles in planar-stratified environments, where each layer may exhibit arbitrary and independent anisotropy in both its (complex) permittivity and permeability tensors. Among the salient features of our formulation are (i) computation of eigenmodes (characteristic plane waves) supported in arbitrarily anisotropic media in a numerically robust fashion, (ii) implementation of an hp-adaptive refinement for the numerical integration to evaluate the radiation and weakly evanescent spectra contributions, and (iii) development of an adaptive extension of an integral convergence acceleration technique to compute the strongly evanescent spectrum contribution. While other semianalytic techniques exist to solve this problem, none have full applicability to media exhibiting arbitrary double anisotropies in each layer, where one must account for the whole range of possible phenomena (e.g., mode coupling at interfaces and nonreciprocal mode propagation). Brute-force numerical methods can tackle this problem but only at a much higher computational cost. The present formulation provides an efficient and robust technique for field computation in arbitrary planar-stratified environments. We demonstrate the formulation for a number of problems related to geophysical exploration.

Interference-nulling time-reversal beamforming for mm-Wave massive MIMO systems

We present a novel beamforming technique for multi-user frequency-selective indoor channels called interference-nulling time-reversal (INTR). The beamformer is implemented with a pre-filter designed to minimize the inter-user interference present in conventional time-reversal (TR). Moreover, our technique relies on a large number of antennas at the transmitter to mitigate inter-symbol interference, enabling low computational complexity receivers. We demonstrate that INTR outperforms previous TR techniques with respect to average bit error rate per user and achievable sum rate. Thus, INTR can be used for space division multiple access in no-line-of-sight mm-wave massive MIMO, providing remarkable diversity and multiplexing gains.

Perfectly reflectionless omnidirectional absorbers and electromagnetic horizons

We demonstrate the existence of metamaterial blueprints describing, and fundamental limitations concerning, perfectly reflectionless omnidirectional electromagnetic absorbers (PR-OEMAs). Previous attempts to define PR-OEMA blueprints have led to active (gain), rather than passive, media. We explain this fact and unveil new, distinct limitations of true PR-OEMA devices, including the appearance of an “electromagnetic horizon” on physical solutions. As practical alternatives we introduce alternative OEMA blueprints corresponding to media that, while not reflectionless, are nonetheless effective in absorbing incident waves in a manner robust to incident wave diversity.

Complex-plane generalization of scalar Levin transforms: A robust, rapidly convergent method to compute potentials and fields in multi-layered media

Abstract We propose the complex-plane generalization of a powerful algebraic sequence acceleration algorithm, the method of weighted averages (MWA), to guarantee exponential-cum-algebraic convergence of Fourier and Fourier–Hankel (F–H) integral transforms. This “complex-plane” MWA, effected via a linear-path detour in the complex plane, results in rapid, absolute convergence of field and potential solutions in multi-layered environments regardless of the source-observer geometry and anisotropy/loss of the media present. In this work, we first introduce a new integration path used to evaluate the field contribution arising from the radiation spectra. Subsequently, we (1) exhibit the foundational relations behind the complex-plane extension to a general Levin-type sequence convergence accelerator, (2) specialize this analysis to one member of the Levin transform family (the MWA), (3) address and circumvent restrictions, arising for two-dimensional integrals associated with wave dynamics problems, through minimal complex-plane detour restrictions and a novel partition of the integration domain, (4) develop and compare two formulations based on standard/real-axis MWA variants, and (5) present validation results and convergence characteristics for one of these two formulations.

Spectral-domain-based scattering analysis of fields radiated by distributed sources in planar-stratified environments with arbitrarily anisotropic layers.

We discuss the numerically stable, spectral-domain computation and extraction of the scattered electromagnetic field excited by distributed sources embedded in planar-layered environments, where each layer may exhibit arbitrary and independent electrical and magnetic anisotropic response and loss profiles. This stands in contrast to many standard spectral-domain algorithms that are restricted to computing the fields radiated by Hertzian dipole sources in planar-layered environments where the media possess azimuthal-symmetric material tensors (i.e., isotropic, and certain classes of uniaxial, media). Although computing the scattered field, particularly when due to distributed sources, appears (from the analytical perspective, at least) relatively straightforward, different procedures within the computation chain, if not treated carefully, are inherently susceptible to numerical instabilities and (or) accuracy limitations due to the potential manifestation of numerically overflown and (or) numerically unbalanced terms entering the chain. Therefore, primary emphasis herein is given to effecting these tasks in a numerically stable and robust manner for all ranges of physical parameters. After discussing the causes behind, and means to mitigate, these sources of numerical instability, we validate the algorithms performance against closed-form solutions. Finally, we validate and illustrate the applicability of the proposed algorithm in case studies concerning active remote sensing of marine hydrocarbon reserves embedded deep within lossy, planar-layered media.

InSAR coherence due to remote sensing of low-loss, guiding planar-layered geophysical media using H-polarized microwaves

We propose a planar-layered medium-based radar backscatter model to predict coherence trends, in Interferometric Synthetic Aperture Radar (InSAR) images, manifest when interrogating planar-layered dielectric geophysical subsurfaces. This InSAR coherence model improves upon past ones in two ways: Incorporation of “multi-bounce”, arising from the guidance behavior of minimally-attenuating and high-contrast dielectric slabs, as well as azimuthal deviation in antenna pointing. Including the former renders this model especially suitable for analyzing coherence modifications (decorrelation and phase bias) arising from remote sensing of low-attenuating targets (e.g., dry soil), which augments applicability to high-attenuating targets (e.g., wet, salty soils) readily analyzed with many traditional InSAR models. Representing the models key contributions, we discuss two predicted trends: Namely, in the limit of a perfectly guiding dielectric slab (i.e., zero attenuation and infinite dielectric contrast), the interferometric correlation is inversely proportional to the InSAR perpendicular baseline length and the phase bias linearly diverges.

Interface-Flattening Transform for EM Field Modeling in Tilted, Cylindrically Stratified Geophysical Media

We propose and investigate an “interface-flattening” transformation, hinging upon transformation optics (TO) techniques, to facilitate the rigorous analysis of electromagnetic (EM) fields radiated by sources embedded in tilted, cylindrically layered geophysical media. Our method addresses the major challenge in such problems of appropriately approximating the domain boundaries in the computational model while, in a full-wave manner, predicting the effects of tilting in the layers. When incorporated into standard pseudo-analytical algorithms, moreover, the proposed method is quite robust, as it is not limited by absorption, anisotropy, and/or eccentering profile of the cylindrical geophysical formations, nor is it limited by the radiation frequency. These attributes of the proposed method are in contrast to past analysis methods for tilted-layer media that often place limitations on the source and medium characteristics. Through analytical derivations as well as a preliminary numerical investigation, we analyze and discuss the methods strengths and limitations.

Spectral-Domain Computation of Fields Radiated by Sources in Non-Birefringent Anisotropic Media

We derive the key expressions to robustly address the eigenfunction expansion-based analysis of electromagnetic (EM) fields produced by current sources within planar non-birefringent anisotropic medium (NBAM) layers. In NBAM, the highly symmetric permeability and permittivity tensors can induce directionally dependent, but polarization-independent, propagation properties supporting “degenerate” characteristic polarizations, i.e., four linearly-independent eigenvectors associated with only two (rather than four) unique, nondefective eigenvalues. We first explain problems that can arise when the source(s) specifically reside within NBAM planar layers when using canonical field expressions. To remedy these problems, we exhibit alternative spectral-domain field expressions, immune to such problems, that form the foundation for a robust eigenfunction expansion-based analysis of time-harmonic EM radiation and scattering within such type of planar-layered media. Numerical results demonstrate the high accuracy and stability achievable using this algorithm.

Cross-pol InSAR coherence degradation due to wave penetration into layered, anisotropic media

We numerically study degradation in the cross-polarized, complex-valued Interferometric Synthetic Aperture Radar (InSAR) coherences magnitude (correlation) and phase due to electromagnetic (EM) wave penetration and guidance within planar-layered, (effectively) electrically anisotropic (i.e., electric field direction dependent) geophysical media. Specifically, we examine scenarios involving subsurface layers exhibiting electrical response given by deviated anisotropic tensors exhibiting low loss and high inter-layer dielectric contrast (i.e., strong subsurface wave guidance), as well as predominantly cross-pol specular interface scatter (XSIS)-based subsurface backscatter. We hypothesize that this scenario can occur within myriad layered geophysical structures containing media hosting a distribution of sub-wavelength, non-spherical inclusions with mean non-vertical orientation. Guidance-enhanced, XSIS-based backscatter we predict can dominate cross-pol InSAR observations (particularly at lower frequencies such as P-band) concerning these types of structures, leading (in the limit of stronger wave guidance) to rapid, inverse-quadratic degradation of correlation versus InSAR spatial baseline, as well as high and linearly divergent phase bias. Modeling the dominant cross-pol backscatter mechanisms adds another tool for Polarimetric InSAR (PolInSAR) data interpretation and inversion concerning sea ice and other complex layered geophysical structures which can contain media possessing effective anisotropic dielectric response.

Numerical study of co-polarized InSAR phase bias in remote sensing of layered media

We numerically explore, for a three-layered dielectric medium, Interferometric Synthetic Aperture Radar (InSAR) coherence phase bias arising from co-polarized interferometric observations of electromagnetic (EM) interrogation of, and scattering from, penetrable subsurface media which can be approximated (at least locally, at the SAR pixel level) as planar-layered. A recently-developed incoherent scattering model now allows prediction of InSAR phase bias arising from the radar wave undergoing an (if neglecting radar time-gating) unending succession of subsurface specular reflections (“multi-bounce”), which is crucial for more comprehensively understanding interferometric observations (both terrestrial and extraterrestrial) of many low-loss layered structures. Our papers results are as follows. First, for increasing subsurface wave attenuation the phase bias approaches zero (backscattering top interface) or the thickness of the subsurface slab (backscatter-free top interface). Second, increasing dielectric contrast between the central and outer two layers elevates (reduces) phase bias for a top interface weakly (strongly) backscattering power relative to the bottom interface. We conclude that subsurface scatter-enhanced phase bias should become significant primarily for geological structures characterized by a weakly-backscattering (i.e., very smooth) top interface and low-attenuating subsurface, which are attributes that may reasonably be used to describe the EM scattering properties of many manifestations of ice, snow, dry soil, and hyper-arid sand or regolith-mantled bedrock structures.