Theory and computer simulation of the reflection and refraction of bulk acoustic waves in piezoelectrics under the action of an external electric field

The basic equations describing the conditions for reflection and refraction of bulk acoustic wave at the interface between acentric crystals subjected to the action of a uniform external electric field are reported. Numerical analysis of the effect of this field on the reflection and refraction anisotropy of bulk acoustic waves at the crystal/vacuum and piezoelectric/elastic-isotropic-medium interfaces is performed.     

Determination of the Surface Tilt Angle by Attenuated Total Reflection

Thin SiO₂ layers prepared by oxidizing an organo-silane in an Ar/O₂ rf plasma discharge produce parallel alignment for nematic liquid crystals with essentially zero tilt. In addition, if the rf plasma system is arranged to produce an Ar/O₂ beam, uniform parallel alignment can now be obtained with the director in the substrate plane at an angle perpendicular to the plane of incidence of the rf plasma beam. We have studied the aligning properties of such films using the evanescent wave generated by attenuated total reflection (ATR) on a thin gold film when a surface electromagnetic wave is excited. Liquid crystal cells were constructed on a high index glass prism with a 500 Å gold film and a 200 Å aligning layer. By following the ATR minimum as a function of applied electric field, the tilt at the interface of the liquid crystal and the aligning layer was calculated.     

Polariton dynamics of a bounded weak ferromagnet in an external dc electric field tangential to the interface

Using the example of a semibounded easy-plane weakly ferromagnetic crystal, magnetized tangentially to its surface, the conditions have been determined under which, with the application of an external dc electric field along the easy-magnetization axis, a number of anomalies arise at the transmission and localization of OA and TM electromagnetic waves through the interface between a nonmagnetic dielectric and a weak ferromagnet due to quadratic magneto-optical interaction.     

Approximation of local reflection in meridional schemes of Bragg focusing

The wave amplitudes in the vicinity of the focus in monochromatic focusing are calculated in the approximation where each point of the surface of a weakly bent single crystal reflects an X-ray wave as a planar crystal, while the reflection coefficient is a coordinate function of the deviation from the exact Bragg condition. These amplitudes are calculated for all the meridional diffraction geometries (those for plane and spherical waves and the Johann and aberration-free schemes). For all these schemes, the quantitative characteristic of the process of polychromatic focusing—the intensity integrated over the pass band—is introduced and calculated. The analytical expressions of polyprofiles necessary for the consideration of these schemes are also derived.     

Mutual transformation of light waves by reflection holograms in photorefractive crystals of the $$\bar 43m$$ symmetry

The mutual transformation of light waves in the case of their simultaneous diffraction from a bulk reflection phase hologram, which was formed in a cubic photorefractive crystal of the [`4]3m\bar 43m symmetry class, has been studied. The indicator surfaces of the polarization-optimized values of the relative intensity of the object wave, which make it possible to determine the amplification of this wave for any crystal cut, are constructed. The linear polarization azimuths at which the energy exchange between the light waves reaches a maximum are found numerically for crystals of different cuts.     

On neutron surface waves

It is shown that neutron surface waves do not exist. The difference between the neutron wave mechanics and the wave physics of electromagnetic and acoustic processes, which allows the existence of surface waves, is analyzed.     

Nonlinear dynamics of layer growth and consequences for protein crystal perfection

In situ high-resolution optical interferometry of lysozyme crystal growth reveals that under steady external conditions, the local growth rate R, vicinal slope p and step velocity are not steady but fluctuate by several times their average values. The variations in p, which is proportional to the local step density, indicate that these fluctuations occur through the dynamic formation of step bunches. Our previous work with unstirred solutions has shown that the fluctuation amplitude of R increases with supersaturation and crystal size (Vekilov et al., Phys. Rev. E 54 (1996) 6650). Based on scaling arguments and numerical simulations, we have argued that the fluctuations are the response of the coupled bulk transport and nonlinear interface kinetics to finite amplitude perturbations provided by the intrinsically unsteady step generation. In this paper, we emphasize the recently discovered spatio-temporal correlation between the sequence of moving step bunches and striations (compositional variations) in the crystal, visualized by polarized-light microscopy. Hence, these unsteady kinetics have detrimental effects on the perfection of the crystals, and means to reduce and eliminate them should be sought. To this end, based on the above conclusion as to the mechanism of the kinetic unsteadiness, we accelerated the bulk transport towards the interface by forced solution flow. We found that this results in lower fluctuation amplitudes. This observation confirms that the system-dependent kinetic Peclet number, Pe_k, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe_k can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities. Interestingly, on further increase of the solution flow velocities >500 μm/s, the fluctuation amplitudes in R increased again, while the average growth rate decreased. At low supersaturations, this leads to growth cessation. The growth instability, deceleration and cessation were immediately reversible upon reduction of the flow velocity. When solutions, intentionally contaminated with ∼1% of covalent lysozyme dimer were used, these undesirable phenomena occurred at about half the flow rates required in pure solutions. Thus, we conclude that enhanced convective supply of impurities to the interface causes an increase in step-bunching related defects, growth deceleration and, in some cases, cessation. Finally, we correlate the “slow protein crystal growth” to step bunch formation. We show that in the absence of significant step density variations, the kinetic coefficient for step propagation is as high as 4×10⁻³ cm/s, which is 1–2 orders of magnitude higher than the previously determined, apparent values for any protein.     

Bulk polaritons in a biaxial crystal at the interface with a perfect metal

The orientation of the plane where the tangential electric field component becomes zero is indicated for any plane bulk electromagnetic wave propagating in an infinite transparent medium of arbitrary anisotropy. Thus, the existence of this wave (bulk polariton) in this plane (interface with an ideal conductor) is ensured. The characteristics of such polaritons of two independent branches with coinciding wave normals (isonormal polaritons) or Poynting vector directions (isoray polaritons) are compared.     

The role of surface and interface structure in crystal growth

Crystal growth occurs at the interface of a crystal and its growth medium. Due to the abrupt termination at the surface, at the interface the properties of the crystal will typically deviate from the bulk and this can affect the growth behaviour. Also the properties of the growth medium at the interface will typically differ from the bulk. In growth from solution, for example, the liquid will show ordering induced by the crystal surface or have a different composition. Here techniques to study such growth interfaces will be discussed together with examples of the effect that the properties of the interface can have on the growth.     

Excitation of intense acoustic waves in hexagonal crystals

Resonant excitation of an intense elastic wave using reflection of a pump wave from a free surface of hexagonal crystal is described. A resonance arises in the case of specially chosen propagation geometry where the reflecting boundary slightly deviates from symmetric orientation and the propagation direction of an intense reflected wave is close to that of an exceptional bulk wave, which satisfies the free boundary condition in unperturbed symmetric orientation. It is shown that, in crystals with elastic moduli c ₄₄>c ₆₆, a resonance arises when the initial boundary is chosen parallel to the hexagonal axis 6, whereas in crystals characterized by the relation c ₄₄<c ₆₆ a resonance occurs when the initial boundary is orthogonal to this axis. The fraction of the pump energy transferred to the excited beam depends on the specific relations between the elastic moduli and can be rather significant for specially chosen crystals. Examples of crystals are presented in which the beam intensity can be increased by a factor of 5–10 at sufficiently high frequencies, with beam divergence remaining acceptable.     

Structure investigations of the Ge-GeO2 system by high-resolution electron microscopy

The crystal structure of thermally oxidized Ge was investigated by high-resolution electron microscopy (HREM), mainly the interface Ge/oxide. Under special conditions the reaction Ge + O₂ → GeO₂ which takes place at (111) surface planes leads to suitable thin crystal regions. The GeO₂ occurs normally as amorphous films on the crystal surface. Furthermore, hexagonal GeO₂ can grow at the interface Ge/oxide by a topotaxial reaction; the orientation relation between these two lattices was ascertained. Intensive electron irradiation was used to initiate and to observe structure changes in boundary regions.     

On existence of one-partial bulk waves in semi-infinite piezoelectric media

The conditions for the existence of one-partial bulk waves satisfying the boundary conditions on a mechanically free surface of a semi-infinite piezoelectric medium have been analyzed. In purely elastic media, similar wave solutions are known to exist along the propagation directions m which form lines on the sphere m ? m = 1, passing through all the available degeneracy points (acoustic axes). It is shown that in a triclinic piezoelectric half-space with a metallized surface, one-partial bulk waves may exist solely along isolated propagation orientations, whereas for a nonmetallized surface, such waves can exist only if an additional condition for the material constants of the medium is fulfilled. It is also shown that the one-partial bulk solution may not exist along an arbitrary acoustic axis in a piezoelectric. These conclusions are valid in the general case of unrestricted anisotropy, i.e., they do not take into account the material symmetry. In addition, the orientations providing the propagation of one-partial bulk waves because of the existing symmetry are specified for piezoelectric media of various symmetry classes.     

一维等离激元晶格中的能带结构调控

由于具有将电磁波聚集到深亚波长体积的能力,表面等离激元在纳米光子技术研究工作中得到了广泛的应用。根据其性质,表面等离激元基本可以分为两大类:沿金属与介质界面传播的表面等离极化激元(SPPs)和束缚在金属表面的局域表面等离激元(LSPRs)。SPPs和对应的自由空间电磁波之间存在明显的动量失配,光栅,即一维等离激元晶格,经常被用于弥补动量失配,从自由空间激发SPPs。LSPRs是指在外部光场激发下局域在单个纳米结构周围的表面等离激元。当LSPRs被激发时,会形成近场增强效应,增大对入射光的吸收和散射。事实上,一维等离激元晶格既支持SPPs又支持LSPRs,是研究表面等离激元及其光学性质的很好的基本结构。由于LSPR这个自由度的存在,其中存在着比光子晶体更丰富的能带结构。本文将以一维等离激元晶格为研究对象,分别从能带调控、表面晶格共振、连续域中的束缚态以及玻色-爱因斯坦凝聚四个方面阐述金属等离激元的新颖性质和最新进展。这些性质对于进一步推动表面等离激元的应用具有重要意义。     

Surface matter waves caused by the absorption of nonrelativistic particles

The existence of surface states of nonrelativistic particles at the interface between a vacuum and a layer of a material on a reflecting substrate, which are caused by the absorption in the layer rather than the presence of discrete levels, is established. The wave functions of such states (surface matter waves) are found and the domains of their existence in the complex plane of the “optical” potential (both attractive and repulsive) of the layer are determined. Threshold effects of the count of microparticles at the intersection of the boundaries of these domains are revealed. The spatial characteristics of the surface matter waves are calculated. An example of the layer composition providing the existence of such waves is given for ultracold neutrons. The increase in the loss of trapped ultracold neutrons owing to the excitation of the surface matter waves of these particles in the trap walls is discussed.     

Growth of SiGe bulk crystals with uniform composition by utilizing feedback control system of the crystal–melt interface position for precise control of the growth temperature

We developed an automatic feedback control system of the crystal–melt interface position to keep the temperature at the interface constant during growth, and demonstrate its successful application to grow Ge-rich SiGe bulk crystals with uniform composition. In this system, the position of the crystal–melt interface was automatically detected by analyzing the images captured using in situ monitoring system based on charge-coupled-devices camera, and the pulling rate of the crucible was corrected at every 1 min. The system was found to be effective to keep the crystal–melt interface position during growth even when the variation of the growth rate is quite large. Especially, the interface position was kept for 470 h during growth of Ge-rich SiGe bulk crystal when we started with a long growth melt of 80 mm. As a result, a 23 mm-long Si_0.22Ge_0.78 bulk crystal with uniform composition was obtained thanks to the constancy of the growth temperature during growth through the control of the interface position. Our technique opens a possibility to put multicomponent bulk crystal in a practical use.     

Peculiarities of quasi-longitudinal elastic wave propagation through the interface between isotropic and anisotropic media: Theoretical and experimental study

The peculiarities of elastic wave propagation in a bilayer medium are studied theoretically and experimentally. One (isotropic) layer was an acrylic glass plate, and the other (anisotropic) was a quartz single-crystal. In experiments, the elastic waves were generated by a piezoelectric transmitter and received by a piezoelectric transducer contacting the surface of the model medium. The propagation time of a quasi-longitudinal wave was determined using high-order statistics. In the general case, the incident elastic waves are split at the interface between the layers: beams undergo double reflection and triple refraction. The measured dependences of the propagation times of quasi-longitudinal split waves on the angles of refraction are in satisfactory agreement with the calculated ones. The calculation was performed by solving the Christoffel equation with allowance for the boundary conditions.     

Temperature distribution in growing semi-transparent crystals (II). Comparison of theory with experiments

Calculated temperature difference between the liquid/solid interface and bulk of the melt was compared with the wide-angle scattering (celluae density) of Al₂O₃ and YAG crystals. Celluae free coloured crystals were grown using higher energy losses from the upper part of the crystal and the melt. Colourless crystals were successfully grown under opposite conditions. The results are in accordance with the calculated temperature differences which are proportional to the actual temperature gradient at the interface.     

Crystals with an Open Wave-Vector Surface: Peculiarities of Reflection and Possibilities of Designing Flat Lenses

The frequency dependence of the reflection coefficient of MgF₂ crystal in the frequency range of 200–800 cm^-1 at different orientations of the optical axis has been investigated. The experimental data are compared with the calculation results. This comparison confirms that the wave vectors for the extraordinary wave have an open surface. This makes it possible to focus a divergent beam refracted at a flat boundary ori- ented perpendicularly to the optical crystal axis. The focusing effect of a plane-parallel MgF₂ crystal plate is calculated.     

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.