Resonance compression of an acoustic beam in a crystal

Resonance Compression of Acoustic Beams in Crystals

“…They are determined by the special extremal relations between the angles φ and δα. In framework of our approximate theory [8] (see Section 6), these trajectories coincide and are described by the relation of the type δα = Cφ 4 . And along the ridges, one obtains…”

“…In Figure 3 and in further considerations, we illustrate the performed analysis by numerical calculations for the series of crystals of various symmetry systems. The parameters of the resonance are calculated by exact formulas (5) and (8). We also vary the angle χ and do not limit ourselves to small angles φ and ψ.…”

“…Given the found relations for reflectances (40) and (41), we can obtain the gain (K 2 ) and loss (K 1 ) coefficients (8) where one can put…”

“…This motivates us to a short consideration of the simplified approach to the reflection resonance with unchanged crystal surface orientation. As was shown in [8], the description becomes especially compact if to choose the crystal boundary parallel to the plane of crystal symmetry. By the way, such planes exist in all crystals, except triclinic [14,15].…”

“…In [5,8], we considered perturbed geometries, where the surface of the crystal remained unchanged and the plane of reflection (sagittal plane) was rotated by a small angle φ about the normal n to the surface (Figure 1a). In this case, an increase in the intensity of excited beam was controlled by the angle φ, whereas the energy loss to the parasitic beam was completely determined by the relation between the moduli of elasticity and could be reduced only by an appropriate choice of the crystal.…”