Wave Amplitude Research Articles

Multi-scale fracture characterization method for transitional shale reservoir based on post-stack multi-attribute ant-tracking fusion and pre-stack wide-azimuth gathers AVAZ analysis

Transitional shale gas represents a significant domain for exploration in the oil and gas sector. The distribution area is extensive, and the resource potential is significant, representing approximately 25% of China's total shale gas resources. Approaches for predicting reservoir fractures using seismic attributes has been well-established. Seismic attributes are frequently constrained by elements including the frequency and resolution of seismic data. The characteristics of transitional shale reservoirs, including complex lithological combinations, frequent changes in lithology, low resolution and variable frequency of seismic data, as well as the presence of strong reflection shielding in coal seams, significantly influence fracture prediction. The use of a single seismic attribute technique presents challenges in delivering a thorough and precise prediction of fractures within transitional reservoirs. This study extracts discontinuity information of large fractures, fine fractures, and fractures obscured by strong reflections from coal seams using variance attributes, amplitude contrast attributes, and the amplitude of diffracted waves, respectively. The discontinuity features obtained from the three methods are monitored through an ant-tracking technique and integrated. Fractures in the work area are methodically described. The near-offset Rüger formula method is utilized to analyze the pre-stack wide-azimuth gathers. Anisotropic gradients and anisotropic directions have been derived. The results of the fracture prediction are analyzed and validated. A novel and reliable methodology, designed specifically for the challenges of transitional shale reservoirs, has been developed for combined pre-stack and post-stack seismic multi-scale fracture prediction. The robust reflection shielding effect of the coal seam has been effectively eliminated. The characterization of fractures in transitional shale reservoirs has been enhanced.

Amplitude and Phase Imaging of CW-THz Waves Using a Photomixing System with Coherent Detection

Continuous-Wave Terahertz (CW-THz) phase and amplitude imaging provides valuable insights into the interaction between THz waves and matter, particularly in low-absorption materials. This information is also essential for enhancing CW-THz beam profiling, a critical aspect in the design of free-space THz devices. Hereby, we introduce a single-pixel THz amplitude and phase imaging technique based on frequency scanning and fringe analysis, incorporated into a straightforward experimental setup. We validate the usefulness of the proposed approach by demonstrating two representative case studies. The first is a 3-D measurement of the amplitude and phase profile of a THz wave that is transmitted through a 3-D printed metalens. The second is beam profiling of a THz beam emitted from a photomixer antenna. In both cases, our results are in excellent agreement with previous predictions and validate the usefulness of this imaging technique. As such, we believe that the demonstrated approach will provide an important tool in the quest for establishing THz as an important method for a myriad of applications, including imaging, range finding and metrology.

Importance sampling of seismic tsunami sources with near-field emphasis for inundation PTHA: benchmarking with complete ensembles

Summary Site-specific Probabilistic Tsunami Hazard Assessment (PTHA) is a powerful tool for coastal planning against tsunami risk. However, its typically high computational demands led to the introduction of a Monte Carlo Stratified Importance Sampling (SIS) approach, which selects a representative subset of scenarios for numerical inundation simulations. We here empirically validate this sampling approach, for the first time to our knowledge, using an existing extensive dataset of numerical inundation simulations for two coastal sites in the Mediterranean Sea (Catania and Siracusa, both located in Sicily, Italy). Moreover, we propose a modified importance sampling function to prioritise seismic tsunami scenarios based on their arrival time at an offshore point near the target site, in addition to their wave amplitude and occurrence rate as leveraged in the previous work. This sampling function is applied separately in each earthquake magnitude bin, and allows denser sampling of near-field earthquakes to whose variations tsunamis are very sensitive. We compare the confidence intervals of the offshore PTHA estimates obtained with the new and the original importance sampling functions. Then, we benchmark our onshore PTHA estimates obtained with both functions against the inundation PTHA calculated using the full set of scenarios. We also test the assumption that onshore random errors follow a normal distribution, as found previously for the offshore case. As a result of the benchmarks, we find that the SIS approach works satisfactorily. Introducing the arrival time as an additional sampling factor enhances the precision of the estimates of both the mean and the percentiles for the two coastal sites considered. With this modification it is possible to deal efficiently with heterogeneous near-field earthquake sources involving coastal deformation at Catania and Siracusa, in addition to regional crustal and subduction sources. By comparing the sampling errors with the model (epistemic) uncertainty, an optimal trade-off between the number of simulations employed and the uncertainty of the PTHA model can be found, even for such a complex situation. A relatively small number of scenarios, on the order of a few thousand, is sufficient to perform site-specific PTHA for practical applications. These numbers correspond to 4–8% of the already reduced ensembles used in previous assessments at the same sites.

Carbon Black Absorption Enhanced Fiber-Optic Photoacoustic Gas Sensing System with Ultrahigh Sensitivity.

A highly sensitive trace gas sensing system based on carbon black absorption enhanced photoacoustic (PA) spectroscopy (PAS) is reported. A carbon black sheet and a fiber-optic cantilever microphone (FOCM) are integrated to form a fiber-optic cantilever spectrophone (FOCS). The gas concentration is obtained by measuring the acoustic wave amplitude generated by the carbon black sheet, which absorbs the laser passing through the interest gas. Due to the higher laser absorption rate of carbon black than that of flake graphite, the excited solid-state PA pressure wave is enhanced. The ability of the FOCS to detect weak sound waves is related to the laser power and the absorption length. Therefore, an Erbium-doped optical fiber amplifier and a multipass cell are also used to increase laser absorption by the tested gas, which combines with the FOCM to achieve multimechanism enhancement of the system performance. Different from traditional PAS gas detection systems, this system is a noncontact measurement solution, which not only effectively avoids gas flow noise but also makes the sensing element immune to the damage of corrosive gases. The experimental results show that the sensitivity of the system is about four times higher than that of the system using flake graphite as the light-absorbing element. When the average time is 100 s, the minimum detection limit of acetylene is 0.31 ppb. The normalized noise equivalent absorption coefficient of the designed PA system is achieved to be 7.1 × 10-10 cm-1·W·Hz-1/2.

Experimental study and field application of hydraulic flushing technology in soft coal seam

To enhance the safety of coal mining operations and improve the efficiency of gas extraction, hydraulic flushing technology has been widely used in low permeability coal seams. This study aims to investigate the mechanism of hydraulic flushing by conducting experiments focusing on four aspects: sample strength, punching pressure, punching position and vibration direction. The results show that an increase in hydraulic flushing pressure leads to a deeper impact groove, whereas higher sample strength results in a shallower groove. Additionally, the amplitude of stress wave is positively correlated with the density of the sample, with low-strength samples exhibiting extensive stress wave propagation and minimal attenuation. The stress wave vibration is multi-directional, which can maximize the instability and destruction of the internal structure of the coal body. To validate the practical efficacy of hydraulic flushing, a field test was conducted at the Yuwu Coal Mine in Changzhi City, Shanxi Province. The field trial shows that the effective influence radius of hydraulic flushing can reach 4 m, with a significantly lower gas flow attenuation coefficient compared to ordinary borehole. Notably, the permeability of coal seam in hydraulic flushing area is close to twice that of ordinary drilling area.

Crack characterisation in a thin plate with unknown acoustic properties based on phase difference of Lamb wave propagation

ABSTRACT A method is presented to characterise a crack in a thin plate with unknown acoustic properties when the position of the acoustic source is approximately known. Due to the unknown source generation waveform, a method based on the phase difference of Lamb wave propagation is proposed to determine the propagation distance difference between two different direct Lamb waves and extract the propagation distances of crack-scattered Lamb waves. The acoustic properties are inverted by establishing their relationship with the dispersion degree of intersections between any two hyperbolas formed by direct Lamb waves, and these intersections determine the source position. The difference in amplitude of crack-scattered Lamb waves is used to distinguish reflections from diffractions, and both edge points and endpoints of the crack are identified using the ellipse method to estimate the crack location, size, and shape. Linear, arc-shaped, and kinked cracks in aluminium plates are experimentally verified using a line-scanning laser vibrometer to collect Lamb wave signals from an acoustic source that is generated by a PZT transducer installed on the plate. The results show that the obtained cracks agree well with the actual cracks in terms of location, size, and shape, with mean relative errors of less than 1.59%.

Detection of ceramic stress intensity factor based on digital holography

This study investigates the application of digital holography in investigating fracture problems of the ceramic material magnesium oxide under three-point bending fracture experiments. A digital holographic optical path system was constructed for this purpose. Three-point bending experiments were performed on magnesium oxide samples using the system, with holograms of the specimens recorded both before and after the application of loads. By utilizing the angular spectrum diffraction reconstruction algorithm, we obtained the complex amplitude of the object wave under varying load conditions and computed the phase changes of the object wave corresponding to different loads. Subsequently, we derived interference fringes from these phase changes, enabling the measurement of the stress intensity factor of magnesium oxide through holographic interferometry and plane stress theory. A comparison of the experimental measurements with theoretical values demonstrates that digital holographic technology is a viable method for measuring the stress intensity factor of ceramic magnesium oxide.

Geometrical Optics Stability Analysis of Rotating Visco-Diffusive Flows

Geometrical optics stability analysis has proven effective in deriving analytical instability criteria for 3D flows in ideal hydrodynamics and magnetohydrodynamics, encompassing both compressible and incompressible fluids. The method models perturbations as high-frequency wavelets, evolving along fluid trajectories. Detecting local instabilities reduces to solving ODEs for the wave vector and amplitude of the wavelet envelope along streamlines, with coefficients derived from the background flow. While viscosity and diffusivity were traditionally regarded as stabilizing factors, recent extensions of the geometrical optics framework have revealed their destabilizing potential in visco-diffusive and multi-diffusive flows. This review highlights these advancements, with a focus on their application to the azimuthal magnetorotational instability in magnetohydrodynamics and the McIntyre instability in lenticular vortices and swirling differentially heated flows. It introduces new analytical instability criteria, applicable across a wide range of Prandtl, Schmidt, and magnetic Prandtl numbers, which still remains beyond the reach of numerical methods in many important physical and industrial applications.

Effect of different clay additions to concrete on its ultrasonic acoustic parameters and compressive strength

Due to various factors, the concrete may contain mud, a condition that can lead to a decrease in strength and changes in the ultrasonic acoustic parameters of the concrete. In order to study the effect of concrete mud content () on ultrasonic acoustic parameters and compressive strength, this paper firstly derived the relationship equations between concrete mud content and acoustic parameters and compressive strength. Subsequently, the acoustic parameters and compressive strength were tested for concrete specimens with different mud contents cast on site. Finally, the effects of concrete mud content on wave velocity, sound time, amplitude, frequency and strength were analyzed according to the measured acoustic parameters, and the relational equations of mud content on acoustic parameters were verified, which provided a reference for evaluating the defective degree of concrete mud content. The main conclusions are: According to sound field theory, the higher the mud content of concrete, the lower its strength, the higher the sound time value, the lower the sound velocity value, and the smaller the amplitude value. The measured data shows that as the age of concrete containing mud increases, its sound velocity value increases, the sound duration value decreases, the amplitude changes are dispersed, and the frequency value increases. Specifically, with the increase of concrete age and when is between 0 and 10%, the changes in concrete sound velocity and sound time are minimal; With the increase of concrete age and when exceeds 20%, the frequency value significantly increases; The changes in amplitude values are similar during the age of concrete from 7 to 28 days. The measured parameters indicate that an increase in the mud content of concrete will lead to a decrease in its compressive strength, a decrease in sound velocity, an increase in sound duration, a decrease in amplitude, and a decrease in frequency. This law is highly consistent with theoretical deductions. Specifically, as increases, there is a non-linear relationship between compressive strength and (R²=0.97); When is greater than 10%, the sound velocity and sound time values change significantly, and both show linear and nonlinear relationships with the mud content; As increases, the amplitude also exhibits a nonlinear relationship with (R²=0.91);When is greater than 20%, the frequency value changes significantly and shows a linear relationship with (R²=0.95).In addition, concrete with higher mud content has a longer first wave period, larger waveform spacing, and faster signal attenuation.

Single-cell bilayer design of a terahertz six-channel metasurface for simultaneous holographic and grayscale images

Metasurfaces have exhibited excellent capabilities in controlling main characteristics of electromagnetic fields. Thus, a lot of significant achievements have been attained in many areas especially in the fields of hologram and near-field imaging. However, some of these designs are implemented in a manner of interleaved subarrays that complicates the design and makes them difficult to achieve integration. Here, an innovative stacking technique of metasurface is combined with vanadium dioxide (VO2) to achieve independent imaging of six channels in terahertz band. Our research combines intensity modulation controlled by the Malus’s law and phase modulation of geometry and propagation to merge amplitude, phase, and polarization manipulation of electromagnetic wave. A “six-in-one” meta-device is constructed by combining phase change properties of VO2 to realize simultaneous near-field grayscale imaging and far-field holography. This design has advantages of wide bandwidth and low crosstalk. Based on the advantage of low crosstalk, single-cell bilayer design allows the number of independent channels to be doubled within an acceptable error range. The proposed metasurface introduces a fresh viewpoint for the design of multi-purpose meta-devices, and has broad application prospects in information encryption and multi-channel image display.

Terahertz programmable metasurface based on solid-state plasma.

Terahertz modulation technology based on programmable metasurfaces can respond in real time to external signals or environmental changes, enabling flexible and adaptive control of terahertz waves. This technology demonstrates significant potential and importance across various fields, including communication, imaging, scientific research, security monitoring, and industrial applications. This paper proposes a terahertz programmable metasurface based on solid-state plasma, utilizing solid-state plasma devices to achieve dynamic control of properties such as the amplitude and phase of terahertz waves. Compared to traditional silicon-based devices, GaAs/AlGaAs heterostructures enhance both the forward current and solid-state plasma concentration of the metasurface devices by two orders of magnitude, with carrier concentrations exceeding 1019 cm-3. Additionally, we designed a solid-state plasma metasurface containing 12×12 supercells, achieving dynamic modulation of terahertz waves in the elevation direction through different coding schemes. Furthermore, this paper explores the stealth control mechanism of solid-state plasma metasurfaces, achieving effective cloaking of detection targets through specific phase compensation.

Based on an all-dielectric metamaterial sensing strategy to reveal the effect of acoustic AO effect on optical fiber transmission performance

Abstract Acousto-optic (AO) effect is an important factor affecting the transmission performance of optical fiber. Here, a metamaterial-based sensing scheme is proposed and applied to measure the AO effect resonance behaviors inside optical fibers due to sound wave transmission. This sensor scheme can obtain the effect of the amplitude and frequency of the sound wave on the optical fiber at the same time, which is different from the traditional photoelectric measurement scheme. The physical mechanism of the AO effect is revealed by measuring the amplitude and frequency of sound waves. The AO effect in the fiber is enhanced with the drive voltage of the sound wave generator increasing, which leads to the transmission performance of the fiber be suppressed. On the contrary, the attenuation coefficient and the group velocity of the fiber are basically stable. At the same time, the time for sound waves to enter and leave the AO effect zone is extended. Moreover, the AO effect is enhanced as the sound frequency gradually approached the resonant frequency. These measurements reveal the physical mechanism of the AO effect of optical fibers and validate the feasibility of this proposed metamaterial sensing scheme.

A new thermoelectric ECG model: Influence of bundle branch block and variations in body temperature

Abstract The present work proposes a novel 2D thermoelectric model to investigate the behavior of specific pathological situation, such as bundle branch block. This model incorporates the heart, lungs, torso, and blood cavities. The dynamics of this system are governed by the Fitzhugh-Nagumo equations that simulate the electrical activity of cardiac myocytes coupled with temperature equations. Then, the parameters of the bundle branch block are considered to analyze their impact on the electrocardiogram. As results, we establish that the presence of bundle branch block significantly affects electrocardiogram morphology, leading to changes in wave amplitude and interval durations. Moreover, our results reveal that variations in body temperature deteriorate this pathological state, leading to further distortions of the electrocardiogram. These results clearly show that our thermoelectric model provides valuable insights into the behavior of bundle branch block under temperature variations. This knowledge could contribute to the development of new treatment and management strategies using thermal control to improve outcomes for patients with similar symptoms.

Attenuation of progressive surface gravity waves by floating spheres

Laboratory experiments were performed to investigate the attenuation of progressive deep-water waves by a mono-layer of loose- and close-packed floating spheres. We measured the decay distance of waves having different incident wave frequency and steepness. The attenuation of waves was strong if the surface concentration of particles was close-packed, with the decay distance being shorter for incident waves with higher frequency and steepness. The amplitude of the highest-frequency (2.0 Hz) and largest amplitude incident waves (with steepness 0.25) decayed by half over a distance of approximately 3 wavelengths. Theoretical models used previously in the study of surface wave damping by sea ice do not capture correctly the physics of wave attenuation by floating spheres. We developed a new theory that estimates the influence upon wave attenuation of turbulent dissipation resulting from oscillatory flow under a close-packing of spheres. This theory predicts that the wave amplitude decays as a power law, and gives a correct order-of-magnitude estimate of the observed decay distance. We explore the potential implications of these findings for the attenuation of progressive waves by (pancake) sea ice and for the indirect detection of marine plastic pollution from space.

Wind‐Wave Momentum Flux in Steep, Strongly Forced, Surface Gravity Wave Conditions

AbstractThe airflow separation from the water surface strongly impacts the coupling between wind and waves. To visualize the airflow and quantify the potential airflow separation's effect on the momentum transfer from wind to the wave, we conducted colocated sampling of air pressure, airflow, and water elevation under a range of wind and wave conditions in the laboratory. The experiments were conducted in the SUrge‐STructure‐Atmosphere INteraction (SUSTAIN) facility at the University of Miami. Three background wave conditions were subjected to wind forcing ( 5–16 m ) to investigate the effects of wave amplitude, frequency, and wind forcing on the airflow regime and momentum transfer. We found the wind forcing shifts the phase of the wave‐induced pressure fluctuations, enhancing the momentum transfer. An increase in wave amplitude or frequency also enhances the aerodynamic sheltering and the momentum transfer. The airflow‐derived pressure based on the nonseparated sheltering (NSS) hypothesis accounts for more than 90% of the momentum transfer until potential airflow separation. We found that the potential airflow separation over the waves' leeward face, which is not accounted for by the NSS hypothesis, leads to an underestimate in momentum transport of more than 30% than the actual value of momentum transport obtained from pressure measurements. Our wave growth rate is consistent with the revisited Miles theory that incorporates the wave‐induced Reynolds stress. The results of this work help explain the wave growth mechanism and inform the development of wind input functions for numerical wave models that account for airflow separation.

Electrokinetic flow instabilities in shear thinning fluids with conductivity gradients.

Instabilities in the form of periodic or irregular waves at the fluid interface have been demonstrated in microchannel electrokinetic flows with conductivity gradients when the applied electric field is above a threshold value. Most prior studies on electrokinetic instabilities (EKI) are restricted to Newtonian fluids though many of the chemical and biological samples in microfluidic applications exhibit non-Newtonian characteristics. We present in this work an experimental study of the effects of fluid shear thinning on the development of EKI waves through the addition of a small amount of xanthan gum (XG) polymer to both the high- and low-concentration Newtonian buffer solutions. The threshold electric field for the onset of EKI in the XG solution is significantly lower than in the Newtonian solution. However, the propagation speed, amplitude and frequency of EKI waves in the former are all smaller. Increasing the polymer concentration reduces the threshold electric field and as well the critical electric Rayleigh number that considers the fluid property variations in XG solutions. This decreasing trend indicates the enhancing effect of fluid shear thinning on EKI, which is qualitatively consistent with a recent numerical prediction. However, the measured wave properties all follow a non-monotonic trend with XG concentration, different from the continuously decreasing electroosmotic velocity.

A method of enhanced shear wave elastography based on Chirp coded excitation.

Shear Wave Elastography (SWE) is an imaging technique that detects shear waves generated by tissue excited by Acoustic Radiation Force (ARF), and characterizes the mechanical properties of soft tissue by analyzing the propagation velocity of shear wave. ARF induces a change in energy density through the nonlinear propagation of ultrasound waves, which drives the tissue to generate shear waves. However, the amplitude of shear waves generated by ARF is weak, and the shear waves are strongly attenuated in vivo. Furthermore, the shear waves are usually drowned out by noise at deep locations, which presents a challenge in the detection of shear waves and low signal-to-noise ratios. In this paper, we investigate the feasibility of applying the Chirp coded signal for shear wave excitation (Chirp-SWE) in ARF-based shear wave elastography. The use of Chirp coded excitation of push waveforms was employed to enhance the action of ARF, thereby effectively exciting shear waves. Comparative experiments were carried out with conventional sine long pulses (SWE) and the Barker coded signal (Barker-SWE). The analysis of theoretical and simulation results revealed that Chirp-SWE could increase the excitation energy by approximately 10% compared to conventional SWE and Barker-SWE. The results of the elastic phantom experiments demonstrated that the average peak axial particle velocity obtained by Chirp-SWE was approximately 30%-50% higher, which facilitated the formation of a more stable shear wave. Additionally, it exhibited a higher signal-to-noise ratio during elasticity measurements. The in vitro liver experiments further validated the feasibility of implementing Chirp-SWE in tissues. The results demonstrated the feasibility and advantages of Chirp coded excitation of push waveforms in improving shear wave elastography results. It is expected that this will enhance the accuracy and robustness of soft tissue elastography.

Innovative solutions to the 2D nonlinear Schrödinger model in mathematical physics

We utilize a cohesive methodology to obtain some new solitary wave solutions for the (2 + 1)-dimensional nonlinear Schrödinger equation (2D-NLSE). The solutions provided herein are significant for elucidating physical phenomena in various domains, including optical fibers, plasma media, and ocean waves. Furthermore, scientific computing would be used to illustrate the physical interpretation of nonlinear waves. Our study examines how 2D-NLSE wave solutions affect physical model characteristics such as group velocity dispersion, nonlinearity, and linear coefficients. These variables functioned to control the amplitude and wave phase of the optical solitary waves during transmission. Finally, the strategy provided here is applicable to many nonlinear systems and new energy trends in natural science.

Neurophysiological and Cognitive Changes Induced by the Acute Head-Down Tilt.

In space, under weightlessness conditions, human brain activity is changed due to the shifting of body fluid and blood toward the cephalic region. This shifting leads to changes in cerebral hemodynamics and, consequently, neurophysiological function, which impacts mental functions like cognition and decision-making capabilities of space travelers. The present study reports the effect of acute exposure to simulated microgravity on cognitive functions and event-related potentials. There were 18 healthy human subjects who participated in a 1-h 6° head-down tilt (HDT) bed rest to simulate physiological conditions during microgravity. Subjects were instructed to perform event-related potential tasks and cognitive tasks with a simulator sickness questionnaire to evaluate their performance, attention, and alertness during weightlessness, at baseline, after microgravity exposure, and after a recovery of 30 min. A significant change was found in the latency of P300 as compared to the baseline. The amplitude of the P300 wave was changed during HDT. The mean reaction time of contingent negative variation increased significantly as compared to the baseline. A significant increase in choice reaction time was observed during HDT vs. baseline. The values recovered partially after 30 min of exposure. It was concluded that simulated microgravity impacts mental functions as evidenced by alterations in choice reaction time and event-related potential latencies and reaction time. The study has applied value for understanding neurophysiological responses and optimization of cognitive performance in space conditions. Sharma M, Gaur S, Pawar H, Yadav N, Thondala B, Kumar S, Kishore K, Ray K, Panjwani U. Neurophysiological and cognitive changes induced by the acute head-down tilt. Aerosp Med Hum Perform. 2025; 96(1):45-52.

Linear and nonlinear resonant properties of electron gas in n-InSb and graphene layers in terahertz range in bias magnetic fields

Abstract The nonlinear conductivity of 2D electron gas in graphene and 3D electron gas in the narrow-gap n-InSb semiconductor has been simulated in terahertz (THz) range by various methods including the direct quantum approach, the quasi-classical kinetics, and the quasi-relativistic hydrodynamics. These methods yield the same results under the electron temperatures ≤100 K when the kinetic electron effective mass used in the nonlinear hydrodynamics is equal to the effective mass in n-InSb and it is equal to some nonzero mass that depends on 2D electron concentration in the graphene. The linear resonant dependencies of the complex electron conductivity are simulated both from the kinetic theory and from the hydrodynamic one. The kinetic dependencies of the resonant conductivity on frequency coincide with ones obtained from the hydrodynamic theory under realistic electron concentrations and collision frequencies. Thus, the nonlinear hydrodynamic equations are valid to describe the nonlinear dynamics of the electron gas in graphene and in n-InSb. The nonlinear hydrodynamics has been applied for simulations of nonlinear propagation of THz electromagnetic waves through the multilayer structures dielectric - graphene or n-InSb - dielectric placed in a bias magnetic field. The simplest three-layer structures demonstrate the sharp nonlinear switching of the transparency of THz waves and the bistability under relatively low values of amplitudes of the incident electromagnetic wave.