Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Coordinated analysis of delayed sprites with high-speed images and remote electromagnetic fields

Simultaneous measurements of high-altitude optical emissions and magnetic fields produced by sprite-associated lightning discharges enable a close examination of the link between low-altitude lightning processes and high-altitude sprite processes. We report results of the coordinated analysis of high-speed sprite video and wideband magnetic field measurements recorded simultaneously at Yucca Ridge Field Station and Duke University. From June to August 2005, sprites were detected following 67 lightning strokes, all of which had positive polarity. Our data showed that 46% of the 83 discrete sprite events in these sequences initiated more than 10 ms after the lightning return stroke, and we focus on these delayed sprites in this work. All delayed sprites were preceded by continuing current moments that averaged at least 11 kA km between the return stroke and sprites. The total lightning charge moment change at sprite initiation varied from 600 to 18,600 C km, and the minimum value to initiate long-delayed sprites ranged from 600 for 15 ms delay to 2000 C km for more than 120 ms delay. We numerically simulated electric fields at altitudes above these lightning discharges and found that the maximum normalized electric fields are essentially the same as fields that produce short-delayed sprites. Both estimated and simulation-predicted sprite initiation altitudes indicate that long-delayed sprites generally initiate around 5 km lower than short-delayed sprites. The simulation results also reveal that slow (5-20 ms) intensifications in continuing current can play a major role in initiating delayed sprites. Copyright 2008 by the American Geophysical Union.

Probing polarization and dielectric function of molecules with higher order harmonics in scattering-near-field scanning optical microscopy

The idealized system of an atomically flat metallic surface [highly oriented pyrolytic graphite (HOPG)] and an organic monolayer (porphyrin) was used to determine whether the dielectric function and associated properties of thin films can be accessed with scanning-near-field scanning optical microscopy (s-NSOM). Here, we demonstrate the use of harmonics up to fourth order and the polarization dependence of incident light to probe dielectric properties on idealized samples of monolayers of organic molecules on atomically smooth substrates. An analytical treatment of light/sample interaction using the s-NSOM tip was developed in order to quantify the dielectric properties. The theoretical analysis and numerical modeling, as well as experimental data, demonstrate that higher order harmonic scattering can be used to extract the dielectric properties of materials with tens of nanometer spatial resolution. To date, the third harmonic provides the best lateral resolution (∼50 nm) and dielectric constant contrast for a porphyrin film on HOPG. © 2009 American Institute of Physics.

Plasmonic Nanoparticles and Nanowires: Design, Fabrication and Application in Sensing.

This study involves two aspects of our investigations of plasmonics-active systems: (i) theoretical and simulation studies and (ii) experimental fabrication of plasmonics-active nanostructures. Two types of nanostructures are selected as the model systems for their unique plasmonics properties: (1) nanoparticles and (2) nanowires on substrate. Special focus is devoted to regions where the electromagnetic field is strongly concentrated by the metallic nanostructures or between nanostructures. The theoretical investigations deal with dimers of nanoparticles and nanoshells using a semi-analytical method based on a multipole expansion (ME) and the finite-element method (FEM) in order to determine the electromagnetic enhancement, especially at the interface areas of two adjacent nanoparticles. The experimental study involves the design of plasmonics-active nanowire arrays on substrates that can provide efficient electromagnetic enhancement in regions around and between the nanostructures. Fabrication of these nanowire structures over large chip-scale areas (from a few millimeters to a few centimeters) as well as FDTD simulations to estimate the EM fields between the nanowires are described. The application of these nanowire chips using surface-enhanced Raman scattering (SERS) for detection of chemicals and labeled DNA molecules is described to illustrate the potential of the plasmonics chips for sensing.

Gold nanoparticles on polarizable surfaces as Raman scattering antennas.

Surface plasmons supported by metal nanoparticles are perturbed by coupling to a surface that is polarizable. Coupling results in enhancement of near fields and may increase the scattering efficiency of radiative modes. In this study, we investigate the Rayleigh and Raman scattering properties of gold nanoparticles functionalized with cyanine deposited on silicon and quartz wafers and on gold thin films. Dark-field scattering images display red shifting of the gold nanoparticle plasmon resonance and doughnut-shaped scattering patterns when particles are deposited on silicon or on a gold film. The imaged radiation patterns and individual particle spectra reveal that the polarizable substrates control both the orientation and brightness of the radiative modes. Comparison with simulation indicates that, in a particle-surface system with a fixed junction width, plasmon band shifts are controlled quantitatively by the permittivity of the wafer or the film. Surface-enhanced resonance Raman scattering (SERRS) spectra and images are collected from cyanine on particles on gold films. SERRS images of the particles on gold films are doughnut-shaped as are their Rayleigh images, indicating that the SERRS is controlled by the polarization of plasmons in the antenna nanostructures. Near-field enhancement and radiative efficiency of the antenna are sufficient to enable Raman scattering cyanines to function as gap field probes. Through collective interpretation of individual particle Rayleigh spectra and spectral simulations, the geometric basis for small observed variations in the wavelength and intensity of plasmon resonant scattering from individual antenna on the three surfaces is explained.

Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry.

We present an analytical method that yields the real and imaginary parts of the refractive index (RI) from low-coherence interferometry measurements, leading to the separation of the scattering and absorption coefficients of turbid samples. The imaginary RI is measured using time-frequency analysis, with the real part obtained by analyzing the nonlinear phase induced by a sample. A derivation relating the real part of the RI to the nonlinear phase term of the signal is presented, along with measurements from scattering and nonscattering samples that exhibit absorption due to hemoglobin.

Measuring morphological features using light-scattering spectroscopy and Fourier-domain low-coherence interferometry.

We present measurements of morphological features in a thick turbid sample using light-scattering spectroscopy (LSS) and Fourier-domain low-coherence interferometry (fLCI) by processing with the dual-window (DW) method. A parallel frequency domain optical coherence tomography (OCT) system with a white-light source is used to image a two-layer phantom containing polystyrene beads of diameters 4.00 and 6.98 mum on the top and bottom layers, respectively. The DW method decomposes each OCT A-scan into a time-frequency distribution with simultaneously high spectral and spatial resolution. The spectral information from localized regions in the sample is used to determine scatterer structure. The results show that the two scatterer populations can be differentiated using LSS and fLCI.

Fiber-optic interferometric two-dimensional scattering-measurement system.

We present a fiber-optic interferometric system for measuring depth-resolved scattering in two angular dimensions using Fourier-domain low-coherence interferometry. The system is a unique hybrid of the Michelson and Sagnac interferometer topologies. The collection arm of the interferometer is scanned in two dimensions to detect angular scattering from the sample, which can then be analyzed to determine the structure of the scatterers. A key feature of the system is the full control of polarization of both the illumination and the collection fields, allowing for polarization-sensitive detection, which is essential for two-dimensional angular measurements. System performance is demonstrated using a double-layer microsphere phantom. Experimental data from samples with different sizes and acquired with different polarizations show excellent agreement with Mie theory, producing structural measurements with subwavelength accuracy.

Measurements of nonlinear refractive index in scattering media.

We have recently developed a spectral re-shaping technique to simultaneously measure nonlinear refractive index and nonlinear absorption. In this technique, the information about the nonlinearities is encoded in the frequency domain, rather than in the spatial domain as in the conventional Z-scan method. Here we show that frequency encoding is much more robust with respect to scattering. We compare spectral re-shaping and Z-scan measurements in a highly scattering environment and show that reliable spectral re-shaping measurements can be performed even in a regime that precludes standard Z-scans.

Information-theoretic analysis of a stimulated-Brillouin-scattering-based slow-light system.

We use an information-theoretic method developed by Neifeld and Lee [J. Opt. Soc. Am. A 25, C31 (2008)] to analyze the performance of a slow-light system. Slow-light is realized in this system via stimulated Brillouin scattering in a 2 km-long, room-temperature, highly nonlinear fiber pumped by a laser whose spectrum is tailored and broadened to 5 GHz. We compute the information throughput (IT), which quantifies the fraction of information transferred from the source to the receiver and the information delay (ID), which quantifies the delay of a data stream at which the information transfer is largest, for a range of experimental parameters. We also measure the eye-opening (EO) and signal-to-noise ratio (SNR) of the transmitted data stream and find that they scale in a similar fashion to the information-theoretic method. Our experimental findings are compared to a model of the slow-light system that accounts for all pertinent noise sources in the system as well as data-pulse distortion due to the filtering effect of the SBS process. The agreement between our observations and the predictions of our model is very good. Furthermore, we compare measurements of the IT for an optimal flattop gain profile and for a Gaussian-shaped gain profile. For a given pump-beam power, we find that the optimal profile gives a 36% larger ID and somewhat higher IT compared to the Gaussian profile. Specifically, the optimal (Gaussian) profile produces a fractional slow-light ID of 0.94 (0.69) and an IT of 0.86 (0.86) at a pump-beam power of 450 mW and a data rate of 2.5 Gbps. Thus, the optimal profile better utilizes the available pump-beam power, which is often a valuable resource in a system design.

High-fidelity, broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation.

We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noisemodulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. In comparison with a previous slow-modulation method, eye-diagram and signal-to-noise ratio (SNR) analysis show that this broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR in the comparison.

Beam-target double-spin asymmetry A{LT} in charged pion production from deep inelastic scattering on a transversely polarized {3}He target at 1.4

We report the first measurement of the double-spin asymmetry A{LT} for charged pion electroproduction in semi-inclusive deep-inelastic electron scattering on a transversely polarized {3}He target. The kinematics focused on the valence quark region, 0.16

Resonant transmission near nonrobust periodic slab modes.

We present a precise theoretical explanation and prediction of certain resonant peaks and dips in the electromagnetic transmission coefficient of periodically structured slabs in the presence of nonrobust guided slab modes. We also derive the leading asymptotic behavior of the related phenomenon of resonant enhancement near the guided mode. The theory applies to structures in which losses are negligible and to very general geometries of the unit cell. It is based on boundary-integral representations of the electromagnetic fields. These depend on the frequency and on the Bloch wave vector and provide a complex-analytic connection in these parameters between generalized scattering states and guided slab modes. The perturbation of three coincident zeros-those of the dispersion relation for slab modes, the reflection constant, and the transmission constant-is central to calculating transmission anomalies both for lossless dielectric materials and for perfect metals.

Construction of invisibility cloaks of arbitrary shape and size using planar layers of metamaterials

Transformation optics (TO) is a powerful tool for the design of electromagnetic and optical devices with novel functionality derived from the unusual properties of the transformation media. In general, the fabrication of TO media is challenging, requiring spatially varying material properties with both anisotropic electric and magnetic responses. Though metamaterials have been proposed as a path for achieving such complex media, the required properties arising from the most general transformations remain elusive, and cannot implemented by state-of-the-art fabrication techniques. Here, we propose faceted approximations of TO media of arbitrary shape in which the volume of the TO device is divided into flat metamaterial layers. These layers can be readily implemented by standard fabrication and stacking techniques. We illustrate our approximation approach for the specific example of a two-dimensional, omnidirectional "invisibility cloak", and quantify its performance using the total scattering cross section as a practical figure of merit. © 2012 American Institute of Physics.

Broadband electromagnetic cloaking with smart metamaterials.

The ability to render objects invisible with a cloak that fits all objects and sizes is a long-standing goal for optical devices. Invisibility devices demonstrated so far typically comprise a rigid structure wrapped around an object to which it is fitted. Here we demonstrate smart metamaterial cloaking, wherein the metamaterial device not only transforms electromagnetic fields to make an object invisible, but also acquires its properties automatically from its own elastic deformation. The demonstrated device is a ground-plane microwave cloak composed of an elastic metamaterial with a broad operational band (10-12 GHz) and nearly lossless electromagnetic properties. The metamaterial is uniform, or perfectly periodic, in its undeformed state and acquires the necessary gradient-index profile, mimicking a quasi-conformal transformation, naturally from a boundary load. This easy-to-fabricate hybrid elasto-electromagnetic metamaterial opens the door to implementations of a variety of transformation optics devices based on quasi-conformal maps.