A. Radowicz

2D Electro-Elastic Fields in a Piezoelectric Layer-Substrate Structure

In the previous two chapters we have studied elasticity of piezoelectric plates considering their interactions with surrounding media through boundary conditions. In this chapter a more realistic situation will be studied, namely, we shall extend our theory for a description of 2D fields in piezoelectric films on substrates, which present in a large variety of modern electronic devices being their important element. Before our works [29, 30] such solutions were known only for purely elastic (non-piezoelectric) anisotropic media of the considered type in two cases: for a homogeneous film on a homogeneous substrate [52] and for an inhomogeneous (stratified or graded) coating on a homogeneous substrate [54]. Below we shall derive the corresponding Green’s functions for arbitrary piezoelectric strips on substrates with line sources in the bulk or at the surface. The chapter is based on the publications [29, 30].

Electromagnetic waves in uniaxial crystals with metallized boundaries: Mode conversion, pure reflections, and bulk polaritons

A theory is constructed for the reflection of plane electromagnetic waves in uniaxial crystals with a positive definite permittivity tensor and an arbitrarily oriented metallized boundary. The problem is solved both for general-position orientations corresponding to three-partial reflection and for special conditions allowing two-partial reflections: mode conversions when the incident and reflected waves belong to different sheets of the refraction surface and “pure” reflections when both waves belong to the same sheet. The space of pure reflections is shown to be formed by two types of optical-axis orientations: arbitrary directions in the plane of the crystal surface and in the plane of incidence. The configurations of the conversion surface for optically positive and negative crystals are investigated. A subspace of pure reflections that transform into one-partial bulk polaritons with the energy flux parallel to the surface at grazing incidence has been found. The domain of existence of such bulk eigenmodes is bounded by two “lines” of solutions. These are any directions along the boundary containing the optical axis for ordinary polaritons and the direction along the projection of the optical axis onto the surface at an arbitrary orientation of the axis with respect to the boundary for extraordinary polaritons.

Quasi-Rayleigh waves in sandwich structures: Dispersion equation, eigenmodes, and resonance reflection

The dispersion equation for quasi-Rayleigh acoustic modes in transversely isotropic sandwich-type structures (an elastic layer between two substrates) has been obtained in the analytical form. The equation is analyzed for three types of structures—a layer between two soft substrates, a layer between a soft and a hard substrate, and a structure consisting of two contacting substrates with markedly different values of hardness. Eigenmodes are determined for all three structures. Depending on the combination of the material parameters in these structures, these eigenwaves are either Rayleigh-type waves localized at interfaces in the substrates and accompanying a Lamb wave in the interlayer (in the absence of an interlayer, forming a Stoneley wave) or the leaky modes characterized by a small imaginary addition to the phase velocity and the presence of bulk partial waves of leakage providing some energy removal from the interfaces. Without any calculations, simple criteria were established that allow one to predict the existence of a leaky mode in the given structure and the number of leakage fluxes it contains. The resonance reflection is analized for the case where the incidence angle of the wave in the substrate corresponding to the velocity v of the wave-front propagation along the interface is close to the value of the real part of the phase velocity of the leaky mode.

Topological Transformations in the Acoustic Spectrum of Anisotropic Plate under Asymmetric Perturbations

It is shown how small variations in the conditions for the propagation of waveguide acoustic modes in anisotropic plates lead to a topological transformation of the entire net of acoustic dispersion curves. When both the sagittal plane and midplane of a plate are simultaneously planes of symmetry, the acoustic dispersion curves of the plate form four independent sets with many intersection points. If the symmetry is violated as a result of perturbations, the intersection points disappear and the curves are “repulsed”; thus, the eigenmode spectrum of the plate radically changes its topology. Versions of such changes are revealed. The polarization of waves in the repulsion zones sharply changes at small segments of the corresponding dispersion branches. The field structure of the wave is analyzed for the case where the perturbation is elastic anisotropy or a piezoelectric effect. The features of transformations of the acoustic spectrum of anisotropic plates in all purely elastic and piezoelectric symmetry classes are analyzed.

Properties of nonlinear elastic waves propagating along acoustic axes

Amplitudes and polarization of nonlinear elastic harmonics exited along an arbitrary acoustic axis of the conic type have been studied as functions of the rotation angle of the polarization vector of the degenerate reference wave. When the reference polarization is rotated by an angle of π, the resulting rotation angle for the polarization vector of the second harmonic turns out to be equal to either zero or 2π or −2π. The actual type of the behavior of the second harmonic propagating along the given acoustic axis is determined by an algebraical criterion for elastic moduli of the second and the third order for the medium. For polarization of the reference wave, we determined the orientations corresponding to the maximum and minimum for the amplitude of the second harmonic. Similar results were obtained for different cases of collinear interactions between degenerate waves, in particular, for the excitation of longitudinal harmonics. The possible control of nonlinear interactions with the use of degenerate-wave polarization in optics and acoustooptics is also discussed.

1D electro-elastic fields in piezoelectrics excited by intrinsic strains

The electro-elastic fields induced by the transversely 1D distribution of intrinsic strains in an arbitrary infinite piezoelectric plate with metallized surfaces are determined. The results obtained generalize the well-known theory of internal stresses in anisotropic purely elastic plates developed by Indenbom, Sil’vestrova, and Sirotin [1]. The coupled fields found in the piezoelectric are expressed in terms of the 4D formalism and the corresponding generalized planar tensor of electro-elastic moduli. It is shown that the limiting transitions from a piezoelectric plate to an unbounded medium and half-space lead to identical formulas.

Specific characteristics of the configurations of optical axes in absorptive crystals

AbstractThe spherical coordinates of four optical axes in absorptive orthorhombic crystals have been determined in terms of the components of the tensor of inverse permittivity constant

Interaction between non-parallel dislocations in piezoelectrics

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