scispace - formally typeset
Search or ask a question

Showing papers on "Reflection (physics) published in 2008"


Journal ArticleDOI
TL;DR: In this paper, an exact solution for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals.
Abstract: An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally thin, local, and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green’s functions represented as Sommerfeld integrals. The solution of plane wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity σ=σ′+jσ″, a proper transverse-electric surface wave exists if and only if σ″>0 (associated with interband conductivity), and a proper transverse-magnetic surface wave exists for σ″<0 (associated with intraband conductivity). By tuning the chemical potential at infrared frequencies, the sign of σ″ can be varied, allowing for some control over surface wave properties.

2,304 citations


Journal ArticleDOI
TL;DR: In this article, the authors present the experimental realization and theoretical understanding of a membrane-type acoustic metamaterial with very simple construct, capable of breaking the mass density law of sound attenuation in the 100-1000 Hz regime by a significant margin.
Abstract: We present the experimental realization and theoretical understanding of a membrane-type acoustic metamaterial with very simple construct, capable of breaking the mass density law of sound attenuation in the 100--1000 Hz regime by a significant margin ($\ensuremath{\sim}200$ times). Owing to the membrane's weak elastic moduli, there can be low-frequency oscillation patterns even in a small elastic film with fixed boundaries defined by a rigid grid. The vibrational eigenfrequencies can be tuned by placing a small mass at the center of the membrane sample. Near-total reflection is achieved at a frequency between two eigenmodes where the in-plane average of normal displacement is zero. By using finite element simulations, negative dynamic mass is explicitly demonstrated at frequencies around the total reflection frequency. Excellent agreement between theory and experiment is obtained.

810 citations


Journal ArticleDOI
TL;DR: It is shown theoretically that a directional dipole wave can be perfectly reflected by a single pointlike oscillating dipole, and found that, in the case of a strongly focused plane wave, up to 85% of the incident light can be reflected by the dipole.
Abstract: We show theoretically that a directional dipole wave can be perfectly reflected by a single pointlike oscillating dipole Furthermore, we find that, in the case of a strongly focused plane wave, up to 85% of the incident light can be reflected by the dipole Our results hold for the full spectrum of the electromagnetic interactions and have immediate implications for achieving strong coupling between a single propagating photon and a single quantum emitter

198 citations


Patent
25 Jul 2008
TL;DR: In this paper, an integrated proximity and light sensor includes an indicating light-emitting device (ILD), a projecting light emitting device (PLD), and a light sensing integrated circuit (LSIC) configured as a single package.
Abstract: An integrated proximity and light sensor includes an indicating light-emitting device (“ILD”), a projecting light-emitting device (“PLD”), and a light sensing integrated circuit (“LSIC”) configured as a single package. The LSIC controls each of the ILD and the PLD to emit light therefrom and the LSIC is configured to detect an ambient light level and also to detect a reflection of the light projected by the PLD from a surface for proximity detection.

166 citations


Journal ArticleDOI
TL;DR: In this paper, the interaction of Lamb wave modes at varying frequencies with a through-thickness crack of different lengths in aluminium plates was analyzed in terms of finite element method and experimental study.
Abstract: The interaction of Lamb wave modes at varying frequencies with a through-thickness crack of different lengths in aluminium plates was analysed in terms of finite element method and experimental study. For oblique-wave incidence, both numerical and experimental results showed that the wave scattering from a crack leads to complicated transmission, reflection and diffraction accompanied by possible wave-mode conversion. A dual-PZT actuation scheme was therefore applied to generate the fundamental symmetrical mode (S0) with enhanced energy to facilitate the identification of crack-scattered wave components. The relationship between crack length and the reflection/transmission coefficient obtained with the aid of the Hilbert transform was established, through which the crack length was quantitatively evaluated. The effects of wavelength of Lamb waves and wave diffraction on the properties of the reflection and transmission coefficients were analysed.

163 citations


Journal ArticleDOI
TL;DR: In this paper, the authors experimentally demonstrated blackbody-like behavior in a thin nanostructured metallic layer shaped in the form of a composite deep diffraction grating for a wide optical wavelength range (240-550 nm).
Abstract: We have experimentally demonstrated blackbodylike behavior in a thin nanostructured metallic layer shaped in the form of a composite deep diffraction grating. This behavior is recorded over a wide optical wavelength range (240--550 nm) and for a broad range of angles of light incidence $(0--75\ifmmode^\circ\else\textdegree\fi{})$ for samples with metal thickness of just 90 nm. The strong absorption at a level of 97--99% is observed for one light polarization and is attributed to excitation of localized plasmons coupled to incident light waves. We show that the studied structures exhibit anomalies which consist in disappearance of reflection for both $p$- and $s$-polarized light at corresponding ``Brewster'' angles. An effective-medium approach provides a satisfactory qualitative description of the reflection and transmission spectra in our samples and confirms their blackbody behavior.

158 citations


Patent
12 Sep 2008
TL;DR: In this article, a satellite signal reception apparatus and a method using the satellite signals reflected by the main reflection plate is provided for improving signal reception efficiency by adjusting the position of an auxiliary reflection plate adaptively to the size and paraboloid of a main reflector.
Abstract: A satellite signal reception apparatus and satellite signal reception antenna and method using the satellite signal reception apparatus is provided for improving satellite signal reception efficiency by adjusting the position of an auxiliary reflection plate adaptively to the size and paraboloid of a main reflection plate. The satellite signal reception apparatus of the present invention is installed on a main reflection plate of an antenna system for collecting satellite signals reflected by the main reflection plate and includes a wave guide tube mounted at a center of the main reflection plate, an auxiliary reflection plate positioned above an inlet of the wave guide tube for re- reflecting the satellite signals reflected by the main reflection plate into the wave guide tube, and a position adjustment unit mounted on the wave guide tube for adjusting distance between the main and auxiliary reflection plates. The satellite signal reception antenna of the present invention enables an auxiliary reflection plate facing a main reflection plate to concentrate the satellite signals reflected by the main reflection plate into a wave guide tube, thereby improving signal reception efficiency without increasing size of the antenna. The satellite signal reception apparatus of the present invention allows adjusting the height of the wave guide and the position of the auxiliary reflection plate relative to the main reflection plate so as to be adapted to various sizes of parabolic main reflection plates.

152 citations


Journal ArticleDOI
TL;DR: In this article, a Monte Carlo simulation is used to study the complex spectra of Compton-thick AGNs and to figure out the relation between their nuclear structures and X-ray spectra.
Abstract: Monte Carlo simulation is one of the best tools to study the complex spectra of Compton-thick AGNs and to figure out the relation between their nuclear structures and X-ray spectra. We have simulated X-ray spectra of Compton-thick AGNs obscured by an accretion torus whose structure is characterized by a half-opening angle, an inclination angle of the torus relative to the observer, and a column density along the equatorial plane. We divided the simulated spectra into three components: one direct component, an absorbed reflection component and an unabsorbed reflection component. We then deduced the dependencies of these components on the parameters describing the structure of the torus. Our simulation results were applied to fit the wide-band spectrum of the Seyfert 2 galaxy Mrk 3 obtained by $Suzaku$. The spectral analysis indicates that we observe the nucleus along a line of sight intercepting the torus near its edge, and the column density along the equatorial plane was estimated to be ~10^24 cm^-2. Using this model, we can estimate the luminosities of both the direct emission and the emission irradiating the surrounding matter. This is useful to find the time variability and time lag between the direct and reflected light.

144 citations


Journal ArticleDOI
TL;DR: A Fabry-P erot model was formulated that successfully predicts both the peak position and spectral shape of metallic nano-strip antennas and provides simple design rules for engineering resonant properties of such plasmonic resonator antennas.
Abstract: A theoretical study of the optical properties of metallic nano-strip antennas is presented. Such strips exhibit retardation-based resonances resulting from the constructive interference of counter propagating short-range surface plasmon-polaritons (SR-SPPs) that reflect from the antenna terminations. A Fabry-P erot model was formulated that successfully predicts both the peak position and spectral shape of their optical resonances. This model requires knowledge of the SR-SPP reflection amplitude and phase pickup upon reflection from the structure terminations. These quantities were first estimated using an intuitive Fresnel reflection model and then calculated exactly using full-field simulations based on the finite-difference frequency-domain (FDFD) method. With only three dimensionless scaling parameters, the Fabry-P erot model provides simple design rules for engineering resonant properties of such plasmonic resonator antennas.

140 citations


Journal ArticleDOI
TL;DR: To define the location of a reflection site is elusive and that PWV cannot be calculated from time of return of the reflected wave, which is an important indicator of cardiovascular risk.
Abstract: Aortic pulse wave velocity (PWV), a measure of aortic stiffness, is an important indicator of cardiovascular risk. Derivation of PWV from uncalibrated proximal aortic or carotid pressure alone has practical advantages. However, when the time of return of the reflected wave, (Delta)t, is used to calculate PWV, inaccurate data are obtained. With aging PWV increases but (Delta)t hardly decreases, suggesting that the reflection site moves toward the periphery. We hypothesized that the forward and reflected waves in the distal aorta are not in phase, leading to an undefined reflection site. We derived forward and backward waves, at the entrance and distal end of a uniform tube, with length "L." With the tube closed at the end, forward and reflected waves are there in phase, and PWV=2L/(Delta)t. When the tube is ended with the input impedance of the lower body, forward and backward waves at its end are not in phase, and (Delta)t is increased, suggesting that the reflection site is further away (tube seems longer), and PWV calculated from 2L/(Delta)t is underestimated. Using an anatomically accurate model of the human arterial system, we show that the forward and backward waves in the distal aorta are not in phase. When aortic PWV increases, (Delta)t changes only little, and the reflection site appears to move to the periphery, similar to what is observed in humans. We conclude that to define the location of a reflection site is elusive and that PWV cannot be calculated from time of return of the reflected wave.

131 citations


Patent
Toni Järvenpää1, Levola Tapani1
14 Feb 2008
TL;DR: In this paper, a diffractive beam expander is used to provide two substantially collimated illuminating light beams (B11, B12) appearing in the image of the eye, and the gaze direction is calculated from the positions of the reflection spots (G1, G2) with respect to the pupil (P) of an eye.
Abstract: An eye tracker device (200) comprises a diffractive beam expander (207) to provide two substantially collimated illuminating light beams (B11, B12). The collimated light beams (B11, B12) provide two reflection spots (G1, G2) appearing in the image of the eye. The gaze direction (GZD) is calculated from the positions of the reflection spots (G1, G2) with respect to the pupil (P) of the eye (E1). The two illuminating beams (B11, B12) are provided by splitting an infrared laser beam (B4) into two in-coupled beams (B5, B6), which propagate in different directions in the substrate (7) of the beams expander. The in-coupled beams (B5, B6) are expanded and their light is subsequently coupled out of the substrate (7) by an out-coupling grating (230) to illuminate the eye (E1). The same substrate (7) may also be used to implement a virtual display device (100) for displaying virtual images to said eye (E1).

Journal ArticleDOI
TL;DR: The extremal transmission of the acoustic wave near the Dirac point in two-dimensional (2D) sonic crystals, being inversely proportional to the thickness of sample, has been demonstrated experimentally for the first time.
Abstract: The extremal transmission of the acoustic wave near the Dirac point in two-dimensional (2D) sonic crystals, being inversely proportional to the thickness of sample, has been demonstrated experimentally for the first time. Some unusual beating effects have been observed experimentally, when the acoustic pulse transports through the 2D sonic crystal slabs. Such phenomena are completely different from the oscillations of the wave in a slab or cavity originating from the interface reflection or the Fabry-Perot effect. They can be regarded as an acoustic analogue effect to Zitterbewegung of the relativistic electron. The physical origination for the phenomenon has been analyzed.

Journal ArticleDOI
TL;DR: In this article, a matching transfer matrix simulation of the frequency dependent reflection coefficient of multi-layer building materials in the frequency range from 100 to 500 GHz for a set of angles, both in TE- and TM-polarization, is presented.
Abstract: In order to derive reliable propagation models for future terahertz indoor pico-cellular communication systems, accurate reflectivity data of building materials is necessary. Here we present reflection terahertz time domain spectroscopy (THz-TDS) measurements and matching transfer matrix simulations of the frequency dependent reflection coefficient of multi layer building materials in the frequency range from 100 to 500 GHz for a set of angles, both in TE- and TM-polarization. Two prominent stratified structures, a double pane window and white paint on plaster are investigated as they usually account for large areas in indoor environments. Communication systems located above 100 GHz are expected to be strongly affected by the variations of the reflectivity over the frequency and incident angle of such stratified materials as they will rely both on line of sight (LOS) and non line of sight (NLOS) propagation. We discuss this impact on the power distribution in a sample scenario employing the ray-tracing method.

Journal ArticleDOI
TL;DR: In this article, the authors apply the Hilbert transform to the physics of internal waves in two-dimensional fluids and use this demodulation technique to discriminate internal waves propagating in different directions.
Abstract: We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: This is very helpful in answering several fundamental questions in the context of internal waves. We focus more precisely in this paper on phenomena associated with dissipation, diffraction, and reflection of internal waves.

Journal ArticleDOI
TL;DR: In this article, the angular distribution of optical light reflectance from surfaces is modeled by an array of silicon photodiodes, which are movable to cover 2π of solid angle.
Abstract: When simulating light collection in scintillators, modeling the angular distribution of optical light reflectance from surfaces is very important. Since light reflectance is poorly understood, either purely specular or purely diffuse reflectance is generally assumed. In this paper we measure the optical reflectance distribution for eleven commonly used reflectors. A 440 nm, output power stabilized, un-polarized laser is shone onto a reflector at a fixed angle of incidence. The reflected light's angular distribution is measured by an array of silicon photodiodes. The photodiodes are movable to cover 2pi of solid angle. The light-induced current is, through a multiplexer, read out with a digital multimeter. A LabVIEW program controls the motion of the laser and the photodiode array, the multiplexer, and the data collection. The laser can be positioned at any angle with a position accuracy of 10 arc minutes. Each photodiode subtends 6.3deg, and the photodiode array can be positioned at any angle with up to 10 arc minute angular resolution. The dynamic range for the current measurements is 10 5:1. The measured light reflectance distribution was measured to be specular for several ESR films as well as for aluminum foil, mostly diffuse for polytetrafluoroethylene (PTFE) tape and titanium dioxide paint, and neither specular nor diffuse for Lumirrorreg, Melinexreg and Tyvekreg. Instead, a more complicated light distribution was measured for these three materials.

Journal ArticleDOI
TL;DR: In this paper, a new simple formula has been developed that relates the reflection coefficient to the breaker parameter and seems to fit all kinds of revetment materials by changing two coefficients.

Journal ArticleDOI
J. Rahola1
TL;DR: New physical reasoning of power waves is given starting from the principle of conjugate matching and a new formula for the reference impedances for a two-port system is given such that the system is simultaneously conjugates matched for both ports.
Abstract: The concept of power waves gives more natural relations between incident and reflected power in a microwave network than the typically used traveling waves. The reflection coefficient for power waves directly describes the reflection of power whereas the reflection coefficient of traveling waves describes the reflection of the waves themselves. In this brief, new physical reasoning of power waves is given starting from the principle of conjugate matching. In addition, a new formula for the reference impedances for a two-port system is given such that the system is simultaneously conjugate matched for both ports.

Journal ArticleDOI
TL;DR: In this paper, a simulation model for type III bursts that originate in the solar corona and are observed at Earth is developed, which incorporates the three-dimensional structure of the source region, dynamics in the source of electron beam, Langmuir waves, ion-sound waves, electromagnetic emissions at the fundamental (fp) and second harmonic (2fp) of the plasma frequency, and propagation of electromagnetic radiation from the corona to interplanetary space, and it predicts the radiation dynamic spectrum measured by a remote observer.
Abstract: [1] A simulation model is developed for type III bursts that originate in the solar corona and are observed at Earth. The model incorporates the three-dimensional structure of the source region, dynamics in the source of electron beam, Langmuir waves, ion-sound waves, electromagnetic emissions at the fundamental (fp) and second harmonic (2fp) of the plasma frequency, and propagation of electromagnetic radiation from the corona to interplanetary space, and it predicts the radiation dynamic spectrum measured by a remote observer. During the propagation of the radiation, the effects of refraction and reflection on large-scale density variations, scattering off small-scale density fluctuations, and free-free absorption are taken into account. The scattering of fp emission is modeled numerically on the basis of an analytic approach developed previously. The numerical results confirm approximations made in the approach and generalize it to more realistic solar plasma conditions.

Journal ArticleDOI
TL;DR: In this paper, the model of generalized magneto-thermoelasticity with two relaxation times in an isotropic elastic medium under the effect of reference temperature on the modulus of elasticity is established.

Patent
05 Feb 2008
TL;DR: An interference type optical head and an optical disk device that can easily adjust an optical path length difference of a couple of lights, ensure higher signal amplification effect, and are suitable for reduction in size are provided in this paper.
Abstract: An interference type optical head and an optical disk device that can easily adjust an optical path length difference of a couple of lights, ensure higher signal amplification effect, and are suitable for reduction in size are provided in order to improve a regeneration signal quality with amplification of signal in the case where reflectivity of each layer must be lowered and relative noise for the signal increases because read speed is high in a multilayer optical disk. In view of essentially improving an S/N ratio of the regeneration signal in high-speed rotation of a multilayer disk, a plurality of interference phases are generated and an optical system for differential calculation has been reduced in size with an angular selective polarization conversion element in the optical disk device for amplifying the signal with interference of the light not radiated to the disk with the reflected light from the disk. Moreover, adjustment of reflection mirror angle of the reference light is no longer required by using a corner cube prism as the reference light reflection mirror and highly accurate signal detection can also be realized with a simplified structure.

Journal ArticleDOI
TL;DR: In this paper, a true-amplitude prestack elastic depth-migration algorithm includes compensation for transmission and anelastic attenuation losses in an isotropic medium by extrapolating up-and downgoing waves using a full two-way wave equation.
Abstract: A new true-amplitude prestack elastic depth-migration algorithm includes compensation for transmission and anelastic attenuation losses in an isotropic medium. Geometric spreading and its compensation are incorporated by extrapolating up- and downgoing waves using a full two-way wave equation. Intrinsic attenuation is simulated and compensated for using composite memory variables derived from standard linear solid relaxation mechanisms. Zoeppritz equations and their approximations are used to compute and analyze the angle-dependent reflection/transmission coefficients; converted energy is included at each interface. Transmission losses for compressional waves are compensated, based on estimation of angle-dependent elastic reflectivity using a two-pass recursive procedure. The image condition is the ratio of the compressional receiver/source wavefield amplitudes. Application to synthetic data from a dipping-layer model and a salt model accurately extracts P-velocity, S-velocity, density, and P-wave impedance beneath the target reflector, even under a salt overhang. Factors not explicitly considered include building of the smooth background velocity and attenuation models, estimates of the source time function, directivity and coupling, multipathing arrivals, and effects of attenuation and anisotropy on the reflection/transmission coefficients.

Journal ArticleDOI
Sun-Goo Lee1, Jin-sun Choi1, Jae-Eun Kim1, Hae Yong Park1, Chul-Sik Kee1 
TL;DR: It is shown that the optimal antireflection structure significantly improves the performance of the device and can be obtained from the one-dimensional antireFlection coating theory and the finite-difference time-domain simulations.
Abstract: We propose a method to design antireflection structures to minimize the reflection of light beams at the interfaces between a two-dimensional photonic crystal and a homogeneous dielectric. The design parameters of the optimal structure to give zero reflection can be obtained from the one-dimensional antireflection coating theory and the finite-difference time-domain simulations. We examine the performance of a Mach-Zehnder interferometer utilizing the self-collimated beams in two-dimensional photonic crystals with and without the optimal antireflection structure introduced. It is shown that the optimal antireflection structure significantly improves the performance of the device.

Journal ArticleDOI
TL;DR: This two-part paper proposes an alternative approach for calculating surface-leaving IR radiance that treats both emissivity and atmospheric reflection in a systematic yet practical manner.
Abstract: Although published sea surface infrared (IR) emissivity models have gained widespread acceptance for remote sensing applications, discrepancies have been identified against field observations obtained from IR Fourier transform spectrometers at view angles ≳40°. We therefore propose, in this two-part paper, an alternative approach for calculating surface-leaving IR radiance that treats both emissivity and atmospheric reflection in a systematic yet practical manner. This first part presents the theoretical basis, development, and computations of the proposed model.

Journal ArticleDOI
TL;DR: In this article, a theoretical and experimental analy- sis of the application of photonic band stop filters on top of photovoltaic fluorescent concentrators in order to increase the photon collection efficiency is presented.
Abstract: In this study we present a theoretical and experimental analy- sis of the application of photonic band stop filters on top of photovoltaic fluorescent concentrators in order to increase the photon collection efficiency. The light guiding effect of the fluorescent concentrator relies on total internal reflection. The escape cone of total internal reflection is their major loss mechanism. Our ray tracing simulation allows to calculate the beneficial effect of photonic band stop reflection filters, which reduce these losses, and to simulate the angular distribu- tion of the light trapped in the concentrator. We present simula- tions of the optical properties of 1D and 3D photonic structures and how 3D structures are realized with colloidal opals. We also show that the application of a 1D photonic structure in- creases the efficiency of a real system by 20% relative.

Journal ArticleDOI
TL;DR: In this paper, the reflection and refraction of a plane wave incidence obliquely at the interface between piezoelectric and piezomagnetic media is analyzed, and the authors show that the most amount of the incident energy goes with the waves that are the same type as the incident wave, while the energy arising from wave mode conversion occupies a less part of the energy.

Journal ArticleDOI
Baljeet Singh1
TL;DR: Reflection from insulated and isothermal stress-free surface of a thermoelastic solid half-space under hydrostatic initial stress is studied and the reflection coefficients as well as energy ratios of reflected waves are obtained.

Journal ArticleDOI
TL;DR: The Fresnel paraxial propagator in a birefringent plate having topological charge q at its center, named "q-plate" is calculated and it is found that if small losses due to reflection, absorption, and scattering are neglected, the plate can convert the photon spin into orbital angular momentum with up to 100% efficiency provided the thickness of the plate is less than the Rayleigh range of the incident beam.
Abstract: We calculated the Fresnel paraxial propagator in a birefringent plate having topological charge $q$ at its center, named "$q$-plate". We studied the change of the beam transverse profile when it traverses the plate. An analytical closed form of the beam profile propagating in the "$q$-plate" can be found for many important specific input beam profiles. We paid particular attention to the plate having a topological unit charge and we found that if small losses due to reflection, absorption and scattering are neglected, the plate can convert the photon spin into orbital angular momentum with up to 100% efficiency, provided the thickness of the plate is less than the Rayleigh range of the incident beam.

Journal ArticleDOI
TL;DR: In this paper, the power reflection and transmission coefficients for a symmetrical notch were computed using finite element and the well-known average power flow equation, with the help of a finite element finite element model.
Abstract: The aim of this work is to predict the propagation of the fundamental Lamb modes in an isotropic structure containing discontinuities in a simple and a fast way. The key point is to decompose the symmetrical notch into two elementary abrupt changes in the plate section. The power reflection and transmission coefficients are computed, using two techniques, with the help of the finite element and the well-known average power flow equation. In the first technique, the through-thickness displacements and stresses are used while in the second technique only the normal or tangential displacement at a given location on the plate surface is used. An equality relation between the direct and the inverse abrupt changes of the plate section is given, which allows computing the power reflection and transmission coefficients for a symmetrical notch from those obtained from one elementary damage. Finally, aluminum plates with different notches depths are tested. Experimental and numerical results are in good agreement.

Journal ArticleDOI
TL;DR: In this article, the dispersion relation of Bloch modes in a fishnet metamaterial in the optical frequency domain is derived and the dependence of the longitudinal wave vector component on the transverse one and the frequency, which governs diffraction and dispersive spreading of localized light excitations, respectively, is analyzed.
Abstract: We derive the dispersion relation of Bloch modes in a fishnet metamaterial in the optical frequency domain. The dependence of the longitudinal wave vector component on the transverse one and the frequency, which governs diffraction and dispersive spreading of localized light excitations, respectively, are analyzed. We show that this type of metamaterial exhibits an involved anisotropic behavior with diffraction changing the sign in passing even a zero diffraction point. For completeness we derive furthermore a formal angle-dependent effective refractive index which exhibits discontinuities. Thus we conclude that an effective refractive index tends to get meaningless and that only the dispersion relation predicts reliably light propagation in metamaterials. The results are double checked with those obtained from a retrieval algorithm based on angular resolved reflection/transmission data of a finite slab. Excellent agreement is observed.

Journal ArticleDOI
TL;DR: In this article, the authors show that the Biot theory also contains a fast S-wave reflection at the interface of a planar air-water interface in a porous medium, and that this reflection degenerates to a viscous process governed by a diffusion equation with a damping term.
Abstract: It is accepted widely that the Biot theory predicts only one shear wave representing the in-phase/unison shear motions of the solid and fluid constituent phases (fast S-wave). The Biot theory also contains a shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow S-wave). From the outset of the development of the Biot framework, the existence of this mode has remained unnoticed because of an oversight in decoupling its system of two coupled equations governing shear processes. Moreover, in the absence of the fluid strain-rate term in the Biot constitutive relation, the velocity of this mode is zero. Once the Biot constitutive relation is corrected for the missing fluid strain-rate term (i.e., fluid viscosity), this mode turns out to be, in the inertial regime, a diffusive process akin to a viscous wave in a Newtonian fluid. In the viscous regime, it degenerates to a process governed by a diffusion equation with a damping term. Although this mode is damped so heavily that it dies off rapidly near its source, overlooking its existence ignores a mechanism to draw energy from seismic waves (fast P- and S-waves) via mode conversion at interfaces and at other material discontinuities and inhomogeneities. To illustrate the consequence of generating this mode at an interface, I examine the case of a horizontally polarized fast S-wave normal incident upon a planar air-water interface in a porous medium. Contrary to the classical Biot framework, which suggests that the incident wave should be transmitted practically unchanged through such an interface, the viscosity-corrected Biot framework predicts a strong, fast S-wave reflection because of the slow S-wave generated at the interface.