Frequency-dependent Reflection Research Articles

Spectroscopic Imaging of Metal-Enhanced Upconversion on Plasmonic Substrates

ABSTRACTWe use spectroscopic imaging to investigate the enhancement of infra-red to visible upconversion in rare-earth doped nano-particles (NaYF4:Yb:Er) supported on nano-fabricated plasmonic substrates consisting of square lattices of Au nano-pillars fabricated by electron beam lithography and designed to support a surface plasmon polariton at frequencies which are nearresonant with the rare-earth ion (Yb3+) absorption. We observe a systematic enhancement in the efficiency of upconversion associated with the interaction of the co-doped nano-particles with the plasmonic substrate. Spectrally-resolved imaging provides a massively parallel means of assessing the range of achievable enhancement and its relation to the specific configuration of the substrate / upconverting nano-particle system. Spectrally-resolved reflectivity of the plasmonic substrates confirms the role of the surface plasmon polariton in the upconversion enhancement. Experimental results are compared to Finite Difference Time Domain simulations of the frequency-dependent reflectivity of these metallic nanostructures.

First principles results on TbAl3(BO3)4: A promising magneto-optical material

The electronic and optical properties of TbAl3(BO3)4 are determined using density functional theory. The calculated total magnetic moment of 5.96 μB is close to the expected moment of Tb3+. The frequency dependent dielectric function, refractive index, extinction coefficient, absorption, optical reflectivity, and energy loss function are explained in terms of the transitions between the valence and conduction bands. We find very high Kerr angles for ultraviolet light and potential for extension, even into the visible range by band structure design.

Velocity and attenuation dispersion relations for the effective Biot model: total‐field formulation

ABSTRACTIn this paper, two approaches ‐ the host phase fields and the total fields, were respectively applied to formulate the effective Biot governing equations from the original double‐porosity dual‐permeability (DPDP) model. The host‐phase formulation given previously in the literature is made under the assumption that the macroscopic fluid flux of the included phase is zero, so that this term can be ignored in the conservation of the momentum equation. The total‐field formulation developed here has no such limiting assumption and gives rise to new and general governing equations that cover the host‐field approach as a special case. By computing the phase velocity and attenuation dispersion curves of sample rocks, we show that the two sets of governing equations are consistent at a very low frequency but for larger volume fractions of phase 2, there is a significantly increasing discrepancy in the slow P‐wave as the frequency increases. The slow P‐wave, whilst difficult to observe, does exist and must be considered when computing the frequency‐dependent reflection coefficients at an interface with a porous medium.

Frequency-dependent seismic reflection coefficient for discriminating gas reservoirs

The asymptotic equation of wave propagation in fluid-saturated porous media is available for calculating the normal reflection coefficient within a seismic frequency band. This frequency-dependent reflection coefficient is expressed in terms of a dimensionless parameter e, which is the product of the reservoir fluid mobility (i.e. inverse viscosity), fluid density and the frequency of the signal. In this paper, we apply this expression to the Xinchang gas field, China, where reservoirs are in super-tight sands with very low permeability. We demonstrate that the variation in the reflection coefficient at a gas–water contact as a transition zone within a sand formation is observable within the seismic frequency band. Then, we conduct seismic inversion to generate attributes which first indicate the existence of fluid (either gas or water), and then discriminate a gas reservoir from a water reservoir.

Non-invasive terahertz field imaging inside parallel plate waveguides

We present a non-invasive broadband air photonic method of imaging of the electric field of THz pulses propagating inside a tapered parallel plate waveguide. The method is based on field-enhanced second harmonic generation of the fundamental laser beam in an external electric field. We apply the technique to measure the frequency-dependent reflection coefficient at the end of the waveguide.

Characterisation of anomalies embedded in graphite fibre reinforced aluminium composite by chirplet parameters

To characterise anomalies embedded in graphite fibre reinforced aluminium matrix composite, chirplet parameters of ultrasonic signals were obtained by chirplet signal decomposition method. It was confirmed that the parameters of decomposed chirplets can represent the characteristic of ultrasonic signals in time and frequency domains compared with conventional time and frequency analysis method. Chirplet parameters were used to identify three types of anomalies embedded in graphite fibre reinforced aluminium matrix composite. The variations of centre frequency and phase of three anomalies were interpreted by frequency dependent attenuation coefficient of composite and frequency dependent reflection coefficient of thin anomalies embedded in composite.

Scanning acoustic microscopy investigation of frequency-dependent reflectance of acid- etched human dentin using homotopic measurements

Composite restorations in modern restorative dentistry rely on the bond formed in the adhesive-infiltrated acid-etched dentin. The physical characteristics of etched dentin are, therefore, of paramount interest. However, characterization of the acid-etched zone in its natural state is fraught with problems stemming from a variety of sources including its narrow size, the presence of water, heterogeneity, and spatial scale dependency. We have developed a novel homotopic (same location) measurement methodology utilizing scanning acoustic microscopy (SAM). Homotopic measurements with SAM overcome the problems encountered by other characterization/imaging methods. These measurements provide us with acoustic reflectance at the same location of both the pre- and post-etched dentin in its natural state. We have applied this methodology for in vitro measurements on dentin samples. Fourier spectra from acid-etched dentin showed amplitude reduction and shifts of the central frequency that were location dependent. Through calibration, the acoustic reflectance of acid-etched dentin was found to have complex and non-monotonic frequency dependence. These data suggest that acid-etching of dentin results in a near-surface graded layer of varying thickness and property gradations. The measurement methodology described in this paper can be applied to systematically characterize mechanical properties of heterogeneous soft layers and interfaces in biological materials.

Impact of fluid saturation on the reflection coefficient of a poroelastic layer

The impact of changes in saturation on the frequency-dependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the 1D White’s model for wave-induced fluid flow. White’s solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and/or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation.

Dispersion law in photonic crystals in sinusoidal and quasi-relativistic approximations

ω(k) dispersion curves are calculated for electromagnetic waves in a photonic crystal (at normal incidence). The calculations rely on a model of a one-dimensional periodic layered medium with two refractive indices. The ω(k) dispersion law thus derived is used to find the frequency-dependent reflectance of the photonic crystal. Approximations are proposed that allow the dispersion law ω(k) to be obtained in explicit form.

Performance of the x-ray free-electron laser oscillator with crystal cavity

Simulations of the x-ray free-electron laser (FEL) oscillator are presented that include the frequency-dependent Bragg crystal reflectivity and the transverse diffraction and focusing using the two-dimensional FEL code GINGER. A review of the physics of Bragg crystal reflectors and the x-ray FEL oscillator is made, followed by a discussion of its numerical implementation in GINGER. The simulation results for a two-crystal cavity and realistic FEL parameters indicate $\ensuremath{\sim}{10}^{9}$ photons in a nearly Fourier-limited, ps pulse. Compressing the electron beam to 100 A and 100 fs results in comparable x-ray characteristics for relaxed beam emittance, energy spread, and/or undulator parameters, albeit in a larger radiation bandwidth. Finally, preliminary simulation results indicate that the four-crystal FEL cavity can be tuned in energy over a range of a few percent.

Ab initio study of the bandgap engineering of Al1−xGaxN for optoelectronic applications

A theoretical study of Al1−xGaxN, based on the full-potential linearized augmented plane wave method, is used to investigate the variations in the bandgap, optical properties, and nonlinear behavior of the compound with the change in the Ga concentration. It is found that the bandgap decreases with the increase in Ga. A maximum value of 5.50 eV is determined for the bandgap of pure AlN, which reaches a minimum value of 3.0 eV when Al is completely replaced by Ga. The static index of refraction and dielectric constant decreases with the increase in the bandgap of the material, assigning a high index of refraction to pure GaN when compared to pure AlN. The refractive index drops below 1 for higher energy photons, larger than 14 eV. The group velocity of these photons is larger than the vacuum velocity of light. This astonishing result shows that at higher energies the optical properties of the material shifts from linear to nonlinear. Furthermore, frequency dependent reflectivity and absorption coefficients show that peak values of the absorption coefficient and reflectivity shift toward lower energy in the ultraviolet (UV) spectrum with the increase in Ga concentration. This comprehensive theoretical study of the optoelectronic properties predicts that the material can be effectively used in the optical devices working in the visible and UV spectrum.

Quasi-static finite element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media

[1] The finite element method is used to solve Biot's equations of consolidation in the displacement-pressure (u − p) formulation. We compute one-dimensional (1-D) and two-dimensional (2-D) numerical quasi-static creep tests with poroelastic media exhibiting mesoscopic-scale heterogeneities to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations. The P wave modulus is used to calculate the frequency-dependent attenuation (i.e., inverse of quality factor) and phase velocity of the medium. Attenuation and velocity dispersion are due to fluid flow induced by pressure differences between regions of different compressibilities, e.g., regions (or patches) saturated with different fluids (i.e., so-called patchy saturation). Comparison of our numerical results with analytical solutions demonstrates the accuracy and stability of the algorithm for a wide range of frequencies (six orders of magnitude). The algorithm employs variable time stepping and an unstructured mesh which make it efficient and accurate for 2-D simulations in media with heterogeneities of arbitrary geometries (e.g., curved shapes). We further numerically calculate the quality factor and phase velocity for 1-D layered patchy saturated porous media exhibiting random distributions of patch sizes. We show that the numerical results for the random distributions can be approximated using a volume average of White's analytical solution and the proposed averaging method is, therefore, suitable for a fast and transparent prediction of both quality factor and phase velocity. Application of our results to frequency-dependent reflection coefficients of hydrocarbon reservoirs indicates that attenuation due to wave-induced flow can increase the reflection coefficient at low frequencies, as is observed at some reservoirs.

Investigation of Photonic Band Gap in a Circular Photonic Crystal

Photonic band gap (PBG) in a circular photonic crystal (CPC) has been theoretically investigated in detail on the basis of transfer matrix method in the cylinder Bragg wave. Analytical results in the PBG have been made based on the reflectance spectrum in a quarter-wavelength stack. It is found that, at azimuthal number m = 0, both wavelength- and frequency-dependent reflection responses for the CPC bear strong resemblances to those of a one-dimensional planar PC (PPC). The reflection spectrum is further shown to be strongly dependent on the azimuthal number. In addition, the PBG is greatly enhanced as the azimuthal number increases. The PBG structure is periodically distributed at odd multiples of design frequency for m = 0, which is consistent with the PPC. This periodic feature, however, is no longer present for a larger m-number.

Analyzing seismic imagery in the time–amplitude and time–frequency domains to determine fluid nature and migration pathways: A case study from the Queen Charlotte Basin, offshore British Columbia

Abstract Combining time–amplitude and time–frequency information from seismic reflection data sets of different resolutions allows the analysis of anomalous reflections from very-shallow to great subsurface depths. Thus, it can enhance the imaging of subsurface features which have a frequency-dependent reflectivity such as gas. Analysing seismic data of different resolution in the time–amplitude and time–frequency domains is a powerful method to determine hydrocarbon migration pathways from deep reservoirs to the seafloor. This interpretation method has been applied to the formerly-glaciated offshore Queen Charlotte Basin hosting several seafloor pockmarks and mounds associated with the leakage of underlying hydrocarbon reservoirs. Low-frequency shadows observed in the time–frequency domain provide evidence of different resolutions that several anomalous reflection amplitudes may be attributed to the occurrence of gas. The seismic imagery shows that gas uses a fault to migrate from deep reservoirs included in Upper Mesozoic strata towards secondary reservoirs located along the fault plane into Neogene layers. Once gas reaches a porous cut-and-fill succession, migration changes from structurally- to stratigraphically-controlled before gas leaks through unconsolidated Quaternary sediments forming the shallow subsurface to eventually seep at the seafloor where pockmarks and carbonate mounds are formed.

An Improved Reflectometric Method for Soil Moisture Measurement Exploiting an Innovative Triple-Short Calibration

Time-domain reflectometry (TDR) techniques have become increasingly attractive for soil moisture evaluation thanks to their adaptability, low cost, and measurement accuracy. Many different TDR-based approaches are currently available for deriving moisture content: empirical calibration curve, empirical dielectric models, frequency-dependent dielectric mixing models, etc. Generally, TDR soil moisture measurements resort to multiple-rod probes, which provide good adhesion to the soil and ease of insertion. However, the typical configuration of such probes does not allow performing a short-open-load (SOL) calibration procedure, which is definitely necessary for retrieving accurate dielectric characterization from TDR waveforms. To overcome the impracticability of the traditional SOL calibration, in this paper, an innovative triple-short calibration (TSC) procedure for commercially available three-rod probes is proposed. First, the robustness of the TSC procedure is validated on well-referenced liquids, demonstrating that its application to TDR measurements leads to a substantial enhancement of the final accuracy in the evaluation of the frequency-dependent reflection coefficient. Successively, the TSC procedure is applied to TDR measurements performed on moistened sand samples. In particular, it is demonstrated that the proposed TSC method, applied to traditional TDR measurements in combination with a dielectric mixing model, leads to an accurate and effective moisture evaluation procedure. This goal is reached through an efficient optimization algorithm that minimizes the difference between experimental and theoretical reflection coefficients. Results show that the proposed strategy is a suitable candidate for low-cost, highly accurate, and easy-to-perform moisture content estimation of soils.

The Wolf ramp: Reflection characteristics of a transition layer

The modern use of spectral decomposition has shown that reflection events in practice are always frequency dependent, a phenomenon called reflectivity dispersion. Often, this can be attributed to strong interference effects from neighboring reflection coefficients of the classical type (i.e., parameter discontinuities or jumps). However, an intrinsic frequency dependence from a single layer is possible if the contact is not a jump discontinuity but a gradual transition. We have expanded the normal-incidence theory of a linear velocity transition zone (termed a Wolf ramp) and have shown how it leads to frequency-dependent reflectivity. The development of waveform forward modeling in turn has led to a ramp detection method that we have tested on migrated field data.

Electronic and optical properties of the orthorhombic compounds PdPX (X=S and Se)

Abstract We have investigated the structural, electronic and optical properties of the orthorhombic layered compounds PdPX (X = S and Se). The calculations are based on the total-energy calculations within the full-potential augmented plane-wave plus local orbitals (FP-LAPW + lo) method. We have used the local density approximation for the exchange and correlation potential. The structural properties are determined through the total energy minimization and inter atomic forces calculations. The obtained results agree well with the measured ones. Our calculations show that these compounds are indirect-gap semiconductors. The calculated anisotropic frequency dependent dielectric functions, reflectivity, refractive index and absorption spectra are obtained and discussed.

Conversion of Direct to Indirect Bandgap and Optical Response of B Substituted InN for Novel Optical Devices Applications

Optical properties of BxIn1 - xN are calculated as a function of the varying concentration of boron and indium. Indium is gradually replaced by boron and optical properties of the resulting materials are studied. The fractional concentration of boron is increased gradually from x = 0 to x = 1 in steps of 0.25. The bandgap increases with the increasing boron concentration, from 0.95 eV for pure InN to 5.6 eV for BN. A unique behavior of BN in zinc-blend phase is observed, that is, it shifts from indirect to direct bandgap semiconductor by the substitution of In on B sites. This behavior can be used to make novel and advanced optical devices. Frequency dependent reflectivity, absorption coefficient, and optical conductivity of BxIn1 - xN are calculated and found to be the constituent's concentration dependent. The region of reflectivity, absorption coefficient and optical conductivity shifts from lower frequency into the higher frequency as the material goes from pure InN to pure BN.

Bandgap investigations and the effect of the In and Al concentration on the optical properties of In_xAl_1−xN

Optical properties of InxAl1−xN are calculated as a function of the concentration of indium and aluminum. Aluminum is partially replaced by indium in an AlN sample, and optical properties of the resulting materials are studied. The fractional concentration of indium is increased gradually from x=0 to x=1 in steps of 0.25. The bandgap decreases with increasing indium concentration, ending up with a narrow gap of 0.9 eV for pure InN and a wide gap of 5.4 eV for pure AlN. Frequency-dependent reflectivity, absorption coefficient, and optical conductivity of InxAl1−x N are calculated and found to be the constituent's concentration dependent. The maximum value of reflectivity, absorption coefficient, and optical conductivity shifts from higher frequency into the lower frequency region as the material goes from pure AlN to pure InN.

Diffraction of spin waves from a submicrometer-size defect in a microwaveguide

We have experimentally studied the diffraction of spin waves propagating in a Permalloy-film microwaveguide from a submicrometer-sized circular defect. For microwave excitation above the cutoff frequency of the fundamental transverse mode, the defect leads to a frequency dependent reflection of the spin wave. The efficiency of the reflection appears to be dependent on the wavelength of the incident spin wave in a nonmonotonous way. The observed two-dimensional spin wave distribution pattern after the defect can be understood based on the interference of several copropagating modes, suggesting that the defect couples the fundamental mode with higher order modes.