Expressions For Reflection Coefficients Research Articles

Reflection of plane waves from the impedance boundary of a magneto-thermo-microstretch solid with diffusion in a fractional order theory of thermoelasticity

In this research article, the effect of the impedance boundary on the reflection problem in a magnetized thermo-microstretch diffusion solid half-space is analyzed. The governing equations in generalized Sherief’s Model of fractional-order magneto-thermo-microstretch elasticity with diffusion in specialized x-y plane are derived and are solved for a plane-wave solution. The plane-wave solution indicates the existence of four coupled longitudinal waves namely CLD-1, CLD-2, CLD-3, CLD-4 waves and two coupled transverse waves namely CTD and CTM waves propagating with distinct speeds in the half-space. The thermally insulated/isothermal plane surface of a half-space is subjected to impedance boundary conditions. The expressions for reflection coefficient and energy ratios for the reflected waves are obtained and the numerical results are illustrated graphically to observe the effect of the magnetic field, fractional-order and diffusion parameters against the angle of incidence on the reflection coefficient and energy ratios of reflected waves.

Reflection of plane waves from the boundary of a thermo-magneto-electroelastic solid half space

The theory of generalized thermo-magneto-electroelasticity is employed to obtain the plane wave solutions in an unbounded, homogeneous and transversely isotropic medium. Reflection phenomena of plane waves is considered at a stress free and thermally insulated surface. For incidence of a plane wave, the expressions of reflection coefficients and energy ratios for reflected waves are derived. To explore the characteristics of reflection coefficients and energy ratios, a quantitative example is set up. The half-space of the thermo-magneto-electroelastic medium is assumed to be made out of lithium niobate. The dependence of reflection coefficients and energy ratios on the angle of incidence is illustrated graphically for different values of electric, magnetic and thermal parameters.

On the characteristics of reflected waves in Rotating Functionally graded Initially stressed piezoelectric-orthotropic half-space

ABSTRACT As a result of technological escalation in sensing applications, piezopolymers like Polyvinylidene fluoride (PVDF), very flexible in nature, are preferred over most of the piezoceramics which are stiff and brittle. PVDF, which is a Piezoelectric-Orthotropic material with a higher anisotropy, is frequently used in sensing devices for structural health monitoring and repairing. In the present analysis reflection phenomenon of plane wave incident at the boundary surface of the Rotating Functionally graded Initially stressed Piezoelectric-Orthotropic (RFIPO) half-space has been analyzed. The influence of Horizontal Normal Compressive Initial-stress (HNCIS); Tensile Shear Stress (TSS), and Vertical Normal Compressive Initial-stress (VNCIS) has been examined on Reflection Coefficients (RCs) of reflected qP, qSV, and EA-waves. Furthermore, the impacts of rotation and functional-gradient are analyzed extensively. Moreover, this phenomenon in the undertaken model has been compared with the model where half-space comprised of Rotating Functionally graded Initially stressed Transversely-isotropic Piezoelectric (RFITP) material. The deduced closed-form expression of RCs of reflected waves has been validated in view of law of conservation of energy and condition of grazing incidence of qP-wave. The comparative analysis of various cases concerned with RFIPO half-space and RFITP half-space serves as the key feature.

Reflection of plane waves on the stress-free and rigid boundary surfaces of pre-stressed piezoelectric-orthotropic substrate: A comparative approach

This study delves with the reflection phenomenon of plane-waves due to incidence of quasi-longitudinal (QL) wave at a semi-infinite structure comprising of pre-stressed piezoelectric-orthotropic substrate (POS) with stress-free (Case I) and rigid (Case II) bounding surfaces. The compact-form expressions of reflection-coefficients (RCs) of reflected QL wave, quasi-transverse (QT) wave and evanescent-electroacoustic (EA) wave for different cases of pre-stressed POS are deduced. To unravel effects of higher anisotropy in substrate, comparative analysis in pre-stressed transversely isotopic piezoelectric substrate (TIPS) medium with stress-free (Case III) and rigid (Case IV) boundaries is carried out. PVDF and ALN materials are considered for numerical computations. For validation, energy-partition and conditions of grazing incidence for all the undertaken cases are analyzed.

Plane wave propagation in a fiber-reinforced diffusive magneto-thermoelastic half space with two-temperature

This paper is devoted to study the characteristics of various reflected waves in a homogeneous anisotropic fiber-reinforced magneto-thermoelastic diffusive solid under dual-phase lag theory of generalized thermoelasticity with two-temperature. The problem is solved analytically and it is found that there exist four coupled quasi waves: qP (quasi-P), qMD (quasi mass diffusion), qT (quasi thermal) and qSV (quasi-SV) waves propagating with different speeds in a two-dimensional model of the solid. The speeds of all the existing waves are found to be complex valued. The stress free surface of the half space is considered thermally insulated and expressions of reflection coefficients and energy ratios are derived in closed form. With the help of MATLAB programming, different characteristics of waves like the phase velocity, reflection coefficient and energy ratio are computed numerically and plotted graphically against angle of incidence to evince the significance of two-temperature, magnetic field, diffusion and reinforcement. The conservation of the energy at the surface is also verified.

2D Low-frequency Penetration of Elastic Waves Through a Double Periodic Array of Cracks

The paper is devoted to derivation of analytic expressions for coefficients of reflection and transmission when a plane wave interacts with a system of three identical twodimensional gratings, each of which consists of a periodic array of rectangular cracks of the elastic isotropic medium in 2-D. In a one-mode range approximation the problem is reduced to the system of hypersingular integral equations, solution of which gives the coefficients of reflection and propagation, and an explicit representation of the wave field inside the structure.

Semi-Infinite Reflection Coefficients of Bi-Anisotropic Metamaterial Slabs Including Boundary Effects

We analyzed semi-infinite reflection coefficients at an interface formed by a bi-anisotropic metamaterial (MM) slab and an air region by considering boundary effects. Corresponding expressions for reflection coefficients are derived using the ray-tracing technique. Derivations are validated by simulated S-parameters of a bi-anisotropic MM slab composed of circular split-ring-resonators. It is noted that while reflection coefficients at left and right interfaces of the analyzed bi-anisotropic MM slab are closely linked to one another aside from the resonance, they are different from one another especially around resonance.

Soliton reflection in a magnetized inhomogeneous warm plasma: effect of ionization

The reflection of nonlinear solitary waves is studied in a plasma under the effect of an external magnetic field and constant ionization along with finite ion temper- ature. To investigate the reflection of solitary waves, rele- vant modified Korteweg-deVries equations for the right and left going waves are derived, and coupled at the point of reflection for obtaining the expression of reflection coefficient. The solitary waves are found to shift after their reflection. Variation of reflection coefficient and shift are studied for different plasma parameters like ion tempera- ture, ionization rate and wave propagation angle or the obliqueness of magnetic field.

Formation of nonlinear magnetization oscillations by spin waves transmission through the boundary of two uniaxial ferromagnets

In this paper, the possibility of nonlinear spin wave formation at transmission of a bulk spin wave through the boundary of two ferromagnets with uniaxial magnetic anisotropy in the external magnetic field was shown at the certain conditions. The bulk spin waves with different values of precession angles of magnetizations can propagate in the second ferromagnet so both linear and nonlinear states can be excited. Also, expressions for coefficients of reflection and transmission of spin waves were obtained depending on value of a precession angle of magnetization in the second ferromagnet.

Reflection of homogeneous elastic waves from free surface of nematic elastomer half-space

An application of the linear viscoelastic theory of nematic elastomers in the low-frequency (hydrodynamic) limit is considered. The boundary conditions at a free surface of a nematic elastomer half-space are satisfied to obtain the reflection of acoustic waves (qP or qSV). The expressions for reflection coefficients are obtained for each incident wave. The reflection coefficients are found to depend on various elastic constants, angle of incidence, frequency of incident wave, relaxation times and angle α between a wavevector and a nematic director. The reflection coefficients are plotted against the angle of incidence for suitable values of angle α, frequency and relaxation times. These coefficients are also plotted against non-dimensional frequency.

Refraction of bulk spin waves on a boundary of two homogeneous easy-axis antiferromagnetic media

Spin-wave refraction index is defined on the boundary of two bulk homogeneous antiferromagnetic media having different parameters of exchange coupling and anisotropy. The effect of spin-wave birefringence is revealed in such structure. The expression for reflection coefficient is obtained on the boundary. The dependencies of the reflection coefficient on frequency and value of the external homogeneous permanent magnetic field are obtained for both branches of spin wave spectrum.

Diffuse reflectance spectroscopy of particulate systems: a comparative study of discrete models

A comparative study of statistical particle model theory of diffuse reflectance has been made. Theories have been applied to six particulate samples having different optical characteristics and average particle sizes that vary from 42 to 106 mum. We made an overall assessment of each theoretical model by determining the CIELAB color difference using experimentally measured and theoretically predicted diffuse reflectance spectra in the visible spectral range. We discuss the performance ratings of the models of other researchers and discovered numerous typographical errors in Fresnel reflection coefficient expressions. We provide the correct versions for these expressions.

Enhanced back-scattering with surface and guided modes coupled to a phase conjugate mirror

The optical properties of a multilayered medium (with or without losses) near a phase conjugate mirror are studied. Expressions for reflection coefficients in both specular and back scattering directions are obtained in terms of simple 2 × 2 matrices. Numerical results are obtained for systems supporting the guided and the surface modes. it is shown that the excitation of the surface and guided modes leads to enhanced back scattering which is quite sensitive to the distance of the guiding layer from the phase conjugate mirror. An instability in the linear regime is predicted for sufficiently short distances.

Analytical expressions for reflection coefficients of artificially soft and hard surfaces: dielectric slab loaded with a periodic array of strips over a ground plane

Simple and closed form expressions for plane wave reflection coefficients of a dielectric slab loaded with a periodic array of strips over a ground plane are presented for use in antenna applications. In the analysis, a set of integral equations for the fields between the strips and dielectric slab are derived from the three-dimensional boundary value problem. Using the low frequency approximation, closed form expressions were obtained for the reflection coefficients. Numerical comparison with the point matching method shows that the accuracy is excellent in practical uses. The frequency bandwidth of the surfaces at the artificially soft and hard boundaries is discussed.

Optical properties of non-ideal interface boundaries

Optical properties of an interface boundary containing thin inhomogeneous transitional layers have been investigated within the framework of the classical Maxwell electrodynamics with the use of generalized functions. As a particular case, expressions for reflection coefficients have been obtained for S- and P-polarized light.

VLF ionospheric reflection coefficients-Derivation from impedance concepts and values for some model ionospheres

A convenient general method is presented for computing the reflected wave excited by an arbitrarily polarized, plane, VLF electromagnetic wave incident at an arbitrary direction upon a sharply bounded, absorptive ionosphere in the geomagnetic field. The relative simplicity of the method results from the use of impedance concepts coupled with Booker's treatment of the propagation vector. Expressions for reflection coefficients are given that are exact (for the model assumed) in the case of propagation perpendicular to magnetic meridians and indicate clearly lack of east-west and west-east reciprocity. The results of calculations for eight model ionospheres are given in the form of graphs of reflection coefficient amplitude and phase versus angle of incidence for both east-west and west-east propagation at 16 kc/sec. The model ionospheres are characterized by values of electron density and collision frequency. A brief relation is made between the computations and some experimental results.

Calculations of Grating Efficiency in the Soft X-Ray Region*

Modified expressions for reflection coefficients are derived for the purpose of predicting the energy distribution among spectral orders produced by a grating at near grazing incidence. Predictions carried out under reasonable simplifying assumptions are compared with experimental data obtained by the use of a grating with 30 000 lines/in. set at a grazing angle of 4.64°. Experimental evidence indicates that in the particular arrangement first-order spectra begin to have appreciable intensity at about 60 A, while second and third orders become observable at 100 A and 150 A, respectively. At 110 A, the fraction of the incident energy present in the first- and second-order spectra is 5.4% and 1.5%, respectively. The calculations are in good general agreement with the observed response of the grating.