Elastic wave surfaces for the (111) plane of cubic crystals

The nature of inverse velocity surfaces as well as energy surfaces for elastic wave propagation in the (111) plane have been studied for a number of cubic crystals. The sections of inverse velocity surfaces by the (111) plane exhibit six-fold symmetry in all cases. Cuspidal edges are exhibited with a six-fold symmetry by both the slow transverse and fast transverse shear modes in the (111) plane, unlike the case of the (100) and (110) planes for which only the slow transverse shear mode exhibits cuspidal edges. The slow transverse mode energy surface exhibits cuspidal edges along direction or an equivalent symmetry direction. The inverse velocity surfaces of the A-15 compounds exhibit unusually large inflexions for the slow transverse mode, whereas their energy surfaces have large cuspidal edges which intersect each other resulting in common regions of cusps.     

Shear-horizontal surface waves on the (001) face of cubic crystals

A connection is made between (1) the result of elasticity theory that shear-horizontal (SH) surface waves cannot exist on a cubic (001) surface and (2) the result of a number of lattice studies of surface modes in thin films to the effect that SH surface waves do appear to exist along [110] for large, but finite wavelength λ. The SH surface wave frequency departs from the bulk band edge as λ^-3 and the localization depth is proportional to λ².     

Diffraction distortion of surface acoustic waves in crystals

A method for the numerical modeling and visualization of the diffraction of surface acoustic waves propagating in anisotropic crystals is described. Examples of two-dimensional wave energy distributions are presented for some crystal orientations widely used in acoustoelectronics.     

Linear and nonlinear vibrations and waves in optical or acoustic superlattices (photonic or phonon crystals)

A model of a dielectric or an elastic superlattice is proposed which describes quite simply the frequency spectrum of electromagnetic or acoustic waves. The frequency band spectrum of a one-dimensional lattice consists of minibands, which narrow down with increasing frequency (so that the forbidden bands in the spectrum broaden with increasing frequency). An elementary analysis of the spectrum of a one-dimensional lattice reveals the presence of many forbidden frequency bands in this case as well. It is shown that dynamic equations for superlattices can be generalized to the nonlinear case, leading to equations of the type of the nonlinear Schrödinger equation for the lattice. Soliton excitations are described and the particle-like dynamics of solitons is demonstrated. Local vibrations near point defects of different complexity in superlattices are studied and graphically illustrated. The existence of Bloch oscillations of a wave packet in a superlattice in a homogeneous external field is discussed.     

Photorefractive optical properties of volume phase gratings induced in sillenite crystals, when the grating vector lies on the (111) plane

We study the diffraction efficiency of volume phase gratings in Bi₁₂GeO₂₀, when the grating vector, lying on a (111) plane, is at an angle with respect to the crystallographic direction. An external bias field parallel to the direction is applied during recording, thus, the recording conditions depend on the grating vector orientation. The basic parameters determining the diffraction efficiency are the grating vector orientation, the rotatory power and the field-induced linear birefringence (primary and secondary). Analytic expressions for the diffraction efficiency have been obtained by taking into account all the above-mentioned parameters, provided that linearly polarized light is incident on the crystal. In this configuration, the influence of the secondary electro-optic effect (inverse piezoelectric and photoelastic effects) to the diffraction efficiency is actually stronger than the influence of the primary effect. Experimental results are given. Received: 3 January 2000 / Revised version: 6 June 2000 / Published online: 13 September 2000     

LiNbO3晶体界面非线性表面波的研究

理论和实验研究了扩散和光伏机理下LiNbO₃晶体界面非线性表面波的传播. 改变传播常数可以得到不同振荡周期的表面波模, 光波的能量随传播常数的递增而单调地递增.本文的实验结果与理论分析能很好地符合. 实验结果还表明, 增加入射光功率可缩短表面波的产生, 增大入射光束与晶体正c轴的夹角(小于90°)可提高表面波的激发效率.     

Migration of vacancies and impurities on the (111) surface of a face-centered cubic lattice

The paper presents an analytic study of impurity atom movements over the (111) surface of a face-centered cubic lattice initiated by the diffusion of vacancies. If multiple collisions of a single impurity with vacancies are taken into account, impurity movement acquires the character of Brownian movement. At long times, the time dependence of the mean-square displacement of the impurity insignificantly differs from linear, and its spatial distribution is close to normal, which allows us to introduce a diffusion coefficient. An analytic equation obtained for this diffusion coefficient differs from the product of the diffusion coefficient of vacancies by their relative concentration by a numerical factor only.     

Acousto-optic interaction with leaky surface acoustic waves in Y-cut LiTaO3 crystals

The acousto-optic interaction with leaky surface acoustic wave radiation into the bulk of YX-cut LiTaO₃ crystals has been investigated. The light incidence and diffraction angles corresponding to the strongest acousto-optic interaction were calculated and measured as functions of the acoustic wave frequency. The dependencies of the diffracted light intensity on the amplitude of radio-frequency voltage applied to the interdigital transducer (IDT) were studied. Our acousto-optic measurements revealed generation, by the IDTs, of slow shear bulk acoustic waves propagating at different angles depending on their frequency. A secondary acousto-optic interaction from the bulk waves radiated by the receiving IDT has been studied.     

The explicit secular equation for surface acoustic waves in monoclinic elastic crystals

The secular equation for surface acoustic waves propagating on a monoclinic elastic half-space is derived in a direct manner, using the method of first integrals. Although the motion is at first assumed to correspond to generalized plane strain, the analysis shows that only two components of the mechanical displacement and of the tractions on planes parallel to the free surface are nonzero. Using the Stroh formalism, a system of two second order differential equations is found for the remaining tractions. The secular equation is then obtained as a quartic for the squared wave speed. This explicit equation is consistent with that found in the orthorhombic case. The speed of subsonic surface waves is then computed for 12 specific monoclinic crystals.     

Temperature-stable orientations in LGS and LGN piezoelectric crystals for surface acoustic waves

The temperature characteristics of surface acoustic waves (SAW) propagating in LGS and LGN crystals are numerically analyzed. The optimal orientations that correspond to the zero value of the first-order temperature coefficient of delay (TCD) for SAW propagating in these crystals are considered. The second-order TCD for SAW is calculated for a wide range of operating temperatures. It is shown that the temperature dependences of the material constants of LGS and LGN crystals are strongly nonlinear. The characteristics of SAW propagating in a structure that consists of an isotropic layer overlying an LGS or LGN piezoelectric crystal are numerically calculated. It is shown that, in the presence of a thin aluminum layer of a certain thickness on the crystal surface, in some cases it is possible to extend the operating temperature range within which the TCD for SAW is equal to zero.     

Resonant generation of surface acoustic waves between moving and stationary piezoelectric crystals

The propagation of surface acoustic waves in a system composed of two piezoelectric crystals moving with respect to each other and separated by a vacuum gap is considered. The waves are localized on different sides of the gap and coupled only through the electrostatic interaction. It is shown that when the velocity of the relative motion of crystals is close to some value, there occurs a wave instability resulting in a resonant generation of these surface waves. The rate of growth of Bleustein-Gulyaev waves in piezoelectric crystals of 6mm symmetry class is determined analytically.     

Surface reconstructions and phase transitions on the GaAs(111)B surface

The (111)B surface of GaAs has been investigated using scanning tunneling microscopy (STM) and a number of different reconstructions have been found at different surface stoichiometries. In accordance with electron diffraction studies, we find the series (2 × 2), (1 × 1)_LT, ( ) and (1 × 1)_HT with increasing annealing temperature, corresponding to decreasing surface As concentration. The (1 × 1)_LT is of particular interest, since it only occurs in a narrow temperature window between the two more established reconstructions, the (2 × 2) and the ( ). We find the (1 × 1)_LT to take the form of a mixture of the local structures of both the (2 × 2) and ( ) phases, rather than having a distinct structure. This is behaviour consistent with a kinetically limited system, dominated by the supply of As adatoms to the surface, and may be an example of a continuous phase transition. Above the (1 × 1)_LT transition, atomic resolution images of the ( ) surface reveal only a three-fold symmetry of the hexagonal structural units, brought about by inequivalent surface bonding due to the 23.4° rotation of the surface unit cell relative to the substrate. This is responsible for the disorder found in the ( ) reconstruction, since the structure may form in one of two domains. At lower surface As concentration, the (1 × 1)_HT surface adopts a structure combining small domains of a 19.1° structure and random disorder. There is no apparent similarity between the (1 × 1)_LT and (1 × 1)_HT structures, which may be due to our measurements being conducted at room temperature and without an As flux to control the surface As concentration.     

Sn/Ge(111) surface charge-density-wave phase transition

Angle-resolved photoemission has been utilized to study the surface electronic structure of 1 / 3 monolayer of Sn on Ge(111) in both the room-temperature (sqrt[3]xsqrt[3] )R30 degrees phase and the low-temperature ( 3x3) charge-density-wave phase. The results reveal a gap opening around the ( 3x3) Brillouin zone boundary, suggesting a Peierls-like transition despite the well-documented lack of Fermi nesting. A highly sensitive electronic response to doping by intrinsic surface defects is the cause for this unusual behavior, and a detailed calculation illustrates the origin of the ( 3x3) symmetry.     

Disordered flat phase separation of the Lennard-Jones fcc(111) surface

Recent lattice model calculations have suggested that a full-layered crystal surface may undergo, under canonical (particle-conserving) conditions, a preroughening-driven two-dimensional phase separation into two disordered flat regions, of opposite order parameter. We have carried out extensive classical molecular dynamics (MD) simulations of the Lennard-Jones fcc(111) surface, to check whether these predictions are relevant or not for a realistic continuous system. Very long simulation times, a grid of temperatures from to T_m, and unusually large system sizes are employed to ensure full equilibrium and good statistics. By examining layer-by-layer occupancies, height fluctuations, sublattice order parameter and X-ray structure factors, we find a clear anomaly at 0.83T_m. The anomaly is distinct from roughening (whose incipiency is also detected at 0.94T_m), and is seen to be consistent with the preroughening plus phase separation scenario.     

New nonlinear magnetostatic surface waves in a ferromagnetic (YIG)

The general propagation characteristics of magnetostatic surface waves guided by a single interface of a semi-infinite nonlinear dielectric cover and a ferromagnetic substrate (YIG) have been derived. The nonlinear dielectric cover has intensity dependent refractive indices. The magnetostatic approximation is considered and retardation is ignored in describing the electromagnetic fields in the structure. The used magnetostatic approximation is leading to new waves and might be called nonlinear magnetostatic surface waves. The propagation of these waves is non-reciprocal in contrast to the linear magnetostaic surface waves, which had been only found in the negative direction of propagation.     

Magnetostatic spin waves in (111)-oriented thin garnet films with combined cubic and uniaxial anisotropies

The magnetostatic spin wave theory in (111)-oriented ferromagnetic films characterized by cubic and uniaxial anisotropies (CUA) is developed. The theory is discussed for two cases when the magnetization vector is perpendicular or parallel to the sample plane. In CUA films, instead of the usually discussed magnetostatic surface waves known for the isotropic case, a new type of surface waves was found with the complex wavevector component normal to the surface.It is shown that for the pure yttrium-iron-garnet film the influence of the CUA effects on the dispersion characteristics of the surface waves is not very substantial.