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A configuration of a laser polarisation modulator based on isotropic acousto-optic interaction is proposed. Polarisation control is performed by a 2D acousto-optic cell based on one monoclinic single crystal. A possibility of implementing this modulator on the basis of a KY(WO4)2 crystal is demonstrated.

Batteryless, wireless, and packageless acoustic wave sensors are particularly desirable for harsh high-temperature environments. In this letter, an acoustic wave sensor based on a lithium niobate (Y + 128° cut, abbreviated LN-Y128) substrate with a buried platinum interdigital transducer (IDT) in an aluminum nitride (AlN) overlayer is investigated. Previously, it was demonstrated theoretically that due to the specific properties of LN-Y128, Rayleigh-type guided waves can propagate at the AlN/IDT(Pt)/LN-Y128 interface. Here, this structure is, for the first time, studied experimentally, including the growth and properties of the AlN layer onto irregular platinum IDTs. Both Shear Horizontal and Rayleigh-type waves have been identified after the AlN deposition and the velocities are consistent with the fitted SDA-FEM-SDA (a combination of finite element modeling with spectral domain analysis) simulations. Electrical measurements with a surface perturbation and temperature measurements show that the AlN/IDT(Pt)/LN-Y128 bilayer structure is promising as a packageless high-temperature sensor.

We demonstrate that anisotropy of Fresnel diffraction in a birefringent medium can be quantitatively characterized by a planar tensor. Eigenvectors of the tensor correspond to directions of minimum and maximum beam divergence. Zero eigenvalues exist for the fast eigenmode near the optic axis of biaxial crystals and correspond to autocollimated beam propagation. Applications of the beam diffraction tensor are demonstrated for analysis of noncritical phase matching in acousto-optics and three-wave mixing., Comment: 8 pages, 9 figures

The high acoustic wave velocities required for high-frequency SAW devices can be combined with strong piezoelectric coupling and low propagation losses if a thin plate of LiNbO3 (LN) is bonded to a high-velocity sapphire substrate. This paper presents a numerical investigation of acoustic modes propagating in an LN/sapphire substrate under a periodic Al grating, demonstrating the occurrence of longitudinal leaky SAWs (LLSAWs) with a unique combination of high velocities exceeding 10 000 m/s, an electromechanical coupling coefficient of 4.5%, and negligible leakage into the substrate. The leakage was suppressed by optimizing the LN plate and Al electrode thicknesses. Compared with conventional SAW substrates, the LN/sapphire substrate offers 2- to 2.5-fold higher frequencies for periodic electrode structures and enables the production of 6-GHz devices by standard photolithographic processes while the required LN plate and Al electrode thicknesses remain compatible with existing wafer bonding technologies. In the optimal LN/sapphire structure, LLSAW behaves as a perfect Rayleigh SAW unperturbed by interactions with spurious modes in a wide range of frequencies.

We designed a new configuration of acousto-optic spatial light modulator based on biaxial crystal KY(WO4)2 (KYW). This material has proved to be a good candidate to fill the gap between paratellurite having high acousto- optic efficiency and quartz having low efficiency but high laser-induced damage threshold. The modulator uses isotropic diffraction by a slow quasi-shear bulk acoustic wave propagating in the autocollimation direction. This ensures good compromise between acousto-optic figure of merit, which is only 30% less than in z-cut longitudinal- wave paratellurite, and high laser-induced damage threshold. The prototype modulator has the spatial resolution of 250 with the central frequency of 100 MHz and the aperture of 20 mm. The designed spatial light modulator is aimed at high-power ultrashort laser pulse shaping applications in near and middle infrared.

A layered structure combining a thin plate of lithium niobate (LN) with a langasite (LGS) substrate was numerically investigated as an advanced substrate material for surface acoustic wave (SAW) devices with improved characteristics, including capability of operating at high temperatures. The longitudinal leaky SAWs (LLSAWs) propagating with negligible attenuation and high velocities up to 6400 m/s were found in LN/LGS using an optimization technique previously applied to the LN/quartz structure. Compared with quartz, the use of LGS as a substrate imposes less constrains on bonding at elevated temperatures for fabrication of a layered structure. Due to the specific acoustic anisotropy of LGS crystals, low-attenuated high-velocity waves exist in a wide range of LGS orientations, including the commercially available SAW cut, when LGS substrate is combined with an LN plate. In the found optimal structures, the electromechanical coupling increased from 5.5% to 14.5%, with increasing LN thickness, making LN/LGS substrate suitable for application in SAW devices with a widely varying bandwidth. In addition, low shear bulk wave velocities in LGS provide a wide spurious-free frequency range in resonators using LLSAW.

Multilayered substrates, including thin plates of LiTaO3 (LT) bonded to silicon (Si) or glass wafers either directly or via intermediate layers, were numerically investigated as potential materials for surface acoustic wave (SAW) resonators with high quality (Q)-factor required for the next generation of mobile communication systems. The propagation velocities and electromechanical coupling coefficients of shear horizontally (SH) polarized acoustic waves were estimated as functions of LT orientation and thicknesses of all layers in LT/Si, LT/SiO2/Si, LT/glass, LT/AlN/glass and structures with several pairs of SiO2/AlN layers between LT and the glass wafer. Optimal combinations of cut angle, LT and electrode thicknesses, as well as the number and thicknesses of intermediate layers, required for the construction of resonators with improved performance were observed for each analyzed structure. In the resonators employing LT/Si and LT/SiO2/Si structures with 30°YX - 48°YX LT cuts, high electromechanical coupling k2, reaching 11.6%, can be combined with high velocities up to 4000 m/s, zero TCF at the resonant frequency and Q-factors that are considerably higher than in the LSAW filters using regular LT substrates. To understand the loss mechanisms that limit resonator Q-factors in LT/glass, mechanical displacements that accompany wave propagation in multilayered structures were visualized. Investigation of the nature of acoustic modes and their transformations with number and thicknesses of the layers revealed that the low-velocity glass wafer can be used as a supporting substrate if an intermediate AlN layer or alternating pairs of low- and high-velocity layers, for example SiO2/AlN, are introduced between LT and the glass wafer.

Acoustic wave propagation in single crystals, metamaterials and composite structures is a basic mechanism in acoustic, acousto-electronic and acousto-optic devices. Acoustic anisotropy of crystals provides a variety of device performances and application fields, but its role in pre-estimation of achievable device characteristics and location of crystal orientations with desired properties is often underestimated. A geometrical image of acoustic anisotropy can be an important tool in design of devices based on wave propagation in single crystals or combinations of anisotropic materials. We propose a fast and robust method for survey and visualization of acoustic anisotropy based on calculation of the eigenvalues of bulk acoustic wave (BAW) diffraction tensor (curvature of the slowness surface). The stereographic projection of these eigenvalues clearly reveals singular directions of BAW propagation (acoustic axes) in anisotropic media and areas of fast or slow variation of wave velocities. The method is illustrated by application to three crystals of different symmetry used in different types of acoustic devices: paratellurite, lithium niobate, and potassium gadolinium tungstate. The specific features of acoustic anisotropy are discussed for each crystal in terms of their potential application in devices. In addition, we demonstrate that visualization of acoustic anisotropy of lithium niobate helps to find orientations supporting propagation of high-velocity surface acoustic waves., 12 pages, preprint submitted to EPJ Plus

Bonded wafers combining a thin LiNbO3 plate with a quartz substrate were studied numerically as potential substrate materials for high frequency wideband SAW devices. Longitudinal leaky waves propagating with velocities up to 7000 m/s were investigated, and the multilayered structure was optimized to combine high velocity, high electromechanical coupling and negligible propagation losses. In the optimized structures non-attenuated waves can propagate with velocities V=5500-6200 m/s and coupling up to 18%. Examples of simulated admittances of SAW resonators demonstrate that in some optimal LiNbO 3 /quartz structures high quality factors Q>5000 can be achieved simultaneously at resonant and antiresonant frequencies if duty factor of electrode structure varies between 0.48 and 0.65. Due to sufficiently large optimal plate and electrode thicknesses, 40% and 5% of a wavelength, respectively, the found structures can be employed in SAW resonators operating at high frequencies, up to 5 GHz.

International audience; Multilayered structures based on wide bandgap nitride piezoelectric thin films are very attractive for high-temperature surface acoustic waves (SAW) sensor applications. In this respect, scandium aluminium nitride (ScAlN) films are of particular interest as they combine enhanced piezoelectric properties and slower acoustic waves velocities when the Sc content steadily increases up to 40%. This property offers the possibility to combine slow ScAlN films on fast substrates like sapphire, to generate higher-order SAW modes which often show a better electromechanical coupling coefficient k 2 compared to zero-order modes. In this letter, we show that low-attenuated longitudinal SAW can be generated in ScxAl1-xN/Sapphire structure, for x parameter varying in a large range. This theoretical result is then confirmed by the experimental investigation of SAW resonators based on highly-textured (002) Sc0.09Al0.91N films sputtered on c-cut sapphire substrates. It is finally shown that the use of electrodes based on metals with high density can lead to SAW structures offering a unique combination between a large bandgap over 5 eV, a k 2 value beyond 1% and a high SAW velocity near 10000 m/s.

We designed a high-efficient acousto-optic Q-switch based on a potassium yttrium tungstate crystal (KY(WO 4 ) 2 ), or KYW. Isotropic acousto-optic interaction along N m N g plane of dielectric axes of the crystal was used. The Q-switch operated at the wavelength of 2.1 μ m of a Ho:YAG laser with the diffraction efficiency over 60% at the RF driving power of 20 W. No laser damage of the crystal with antireflection coatings was observed at 12 J/cm 2 fluence for nanosecond pulses.

Scandium aluminum nitride (ScxAl1-xN) films are currently intensively studied for surface acoustic waves (SAW) filters and sensors applications, because of the excellent tradeoff they present between high SAW velocity, large piezoelectric properties and wide bandgap for the intermediate compositions with an Sc content between 10 and 20%. In this paper, the growth of Sc0.09Al0.91N and Sc0.18Al0.82N films on sapphire substrates by sputtering method is investigated. The plasma parameters were optimized, according to the film composition, in order to obtain highly-oriented films. X-ray diffraction rocking-curve measurements show a full width at half maximum below 1.5&deg, Moreover, high-resolution transmission electron microscopy investigations reveal the epitaxial nature of the growth. Electrical characterizations of the Sc0.09Al0.91N/sapphire-based SAW devices show three identified modes. Numerical investigations demonstrate that the intermediate compositions between 10 and 20% of scandium allow for the achievement of SAW devices with an electromechanical coupling coefficient up to 2%, provided the film is combined with electrodes constituted by a metal with a high density.

The formalism of planar diffraction tensor was applied to the analysis of anisotropy of bulk acoustic wave diffraction and to build a full map of anisotropic diffractional coefficients for three bulk acoustic wave modes propagating in lithium niobate. For arbitrary propagation direction the diffractional coefficients derived allow estimation of ultrasonic beam divergence in far-field. Analysis of obtained data revealed that the maxima of acousto-optic figure of merit for anisotropic diffraction in the YZ plane correspond to moderate diffractional spreading of the beams exceeding isotropic diffraction 2-3 times.

Quasi-collinear type of acousto-optic (AO) diffraction by bulk acoustic waves (BAW) is widely used for high-resolution tunable optical filters and dispersive delay lines for ultrashort laser pulse shaping. Most often, quasi-collinear paratellurite (TeO 2 ) AO filters are used due to high AO figure of merit of this material (V. Molchanov et al. Quant. Electron. 39:353, 2009). Lithium niobate (LN, LiNbO 3 ) collinear filters along Y-axis are known to provide a better spectral resolution or a shorter response time. A demand for higher spectral performance of AO filters is caused by progress in ultrafast laser technology and adaptive spectroscopy. The performance of a LN filter can be improved using quasicollinear diffraction. We aimed at design of a quasi-collinear AO filter in LN with maximum diffraction efficiency.

Multilayered structures with LT plates bonded to silicon or glass substrates via AlN, isotropic SiO 2 or their combinations, were theoretically investigated as potential materials for resonators with high Q-factors required for the 5th generation of mobile communication systems. Characteristics of SH-waves propagating under Al grating in such structures, including electromechanical coupling and propagation losses, were extracted from admittance functions simulated with SDA-FEM-SDA software. An upgraded version of the software was developed to visualize the waves in multilayered structures and understand the loss mechanisms and their dependence on the supporting substrate material, as well as on the number, type and thicknesses of the intermediate layers. The methods of loss reduction required to improve the Q-factors of acoustic wave resonators are discussed.

Surface Acoustic Wave sensors are a promising enabling technology to achieve temperature monitoring in extreme conditions, and especially at very high temperature, above 900°C. Applications in the air and space, chemical, steel, and automotive industries are notably expected. Although many of the technical challenges posed by the development of these sensors have been tackled and solved over the years, there is still no SAW sensor able to withstand very high temperatures for a long time on the market (yet). A possible alternative could be to combine a SAW transponder with a thermocouple ('SAW Hybrid'). The thermocouple would be read wirelessly using a SAW transponder, itself located at a place nearby where the temperature doesn't exceed 350°C. The feasibility of this concept was recently demonstrated, using a 400MHz device. However, the obtained sensitivity was very low, and an optimized Design is needed, to increase it. It is notably expected that a higher operating frequency will significantly improve the sensitivity. In this paper, we present an optimal Design of the SAW Hybrid AlN/LN multilayered structure, for operation at 2.45GHz, with buried Pt electrodes.

Acoustic wave characteristics are numerically investigated and compared in AlN/ZnO/diamond and Al 2 O 3 /GaN/sapphire with Pt electrodes. These structures have been previously reported as candidates for application in packageless sensors. They include a low-velocity guiding piezoelectric layer sandwiched between two high-velocity materials. The anisotropy of the combined materials, their symmetry and the ratio between bulk acoustic wave velocities in the sagittal plane are compared to find the selection criterion for optimal combination of materials enabling high coupling of the useful mode and suppression of parasitic modes. Acoustic fields have been visualized for the reported structures and for Si 3 N 4 /GaN/sapphire, an alternative structure suggested to be used in packageless sensors, to understand the correlation between the acoustic fields and the wave characteristics.

Multilayered structures can successfully replace single crystal substrates in high-performance surface acoustic wave (SAW) devices. A combination of high propagation velocity and strong piezoelectric coupling is required for acoustic modes used in wideband high-frequency SAW devices. These characteristics can be achieved simultaneously in SAW devices arranged on a lithium niobate (LN) thin plate bonded to quartz and using longitudinal leaky SAW (LLSAW) if the orientations of both the crystals and the plate thickness are optimized. This article describes an optimization procedure developed to find low-attenuated LLSAWs in layered structures that can be used in LN/quartz applications. The symmetry consideration of two crystals was followed by the optimization of the LN orientation to achieve the largest electromechanical coupling and by an analysis of quartz anisotropy as a crucial factor of the existence of nonattenuated LLSAWs. Finally, the quartz orientation and LN thickness were optimized by a rigorous numerical simulation of resonator admittances and by the extraction of LLSAW attenuation at resonant and antiresonant frequencies. The discovered structures enable the propagation of LLSAWs with velocities in the range of 5400–6000 m/s, electromechanical coupling up to 18%, and negligible attenuation. High ${Q}$ -factors can be achieved at resonance and antiresonance by the variation of the duty factor in the same layered structure. The specific behavior of the LLSAW attenuation with a variation of the LN thickness and quartz cut angle is illustrated by contour plots for each of the optimal structures discovered.

Dispersion of Lamb waves propagating in AlN plates with a periodic Al grating on the top surface and an Al electrode on the bottom surface is investigated using the numerical technique SDA-FEM-SDA, which combines finite element modeling (FEM) analysis of the electrode region with spectral-domain analysis (SDA) of the adjacent multi-layered half-spaces. Characteristics of zero-order and higher-order Lamb waves are presented as functions of plate thickness and spectral frequency, which varies in the first Brillouin zone. The structures of typical Lamb waves are examined via visualization of the instantaneous displacement fields in the AlN plate confined between the grating and the bottom electrode. The mechanism of building hybrid modes, which arise from intermode coupling between the counter-propagating Lamb waves of different symmetry and order, is illustrated by two examples of modes propagating with wavelengths λ = 3p and λ = 4p, where p is the pitch of the grating.

Orientations of langasite (LGS) with Euler angles (0°, μ, 90°) are potentially useful for applications in wireless SAW sensors because of wide variation of their temperature coefficient of frequency (TCF), between -50 and +50 ppm/°C, combined with high values of electromechanical coupling coefficient, especially if thick electrodes are utilized. The nature and characteristics of shear-horizontally polarized SAWs (SHSAWs) propagating in these orientations are investigated using a combination of numerical techniques: analysis of the BAW slowness surface and its effect on the SH-SAW structure; visualization of displacements that follow wave propagation in the grating; calculation of admittance of infinite periodic gratings; and analysis of SAW dispersion in the gratings, including possible interaction between SH-SAWs and parasitic Rayleigh SAWs. The characteristics of SH-SAWs propagating in symmetric cuts (velocities, localization depth, electromechanical coupling, etc.) are supplemented by analysis of propagation directions deviating from the YZ-plane toward the x-axis of LGS, for the temperature compensated cut with Euler angles (0°, 22°, 90°) and one more orientation for comparison. This extended analysis reveals that in actual devices, the anisotropy may be a reason for strong interaction between SH-SAWs and parasitic Rayleigh SAWs and cause degradation of the device's performance.

The mechanism of SAW transformation with variation of film thickness is investigated in a piezoelectric substrate with a metal grating overlaid by a dielectric film, via simulation and visualization of the acoustic fields. By way of example, two orientations of lithium niobate substrates are analyzed, YX-LN and 128°YX-LN, with a Cu grating and an isotropic silica glass overlay. The motions, which follow the wave propagation in the sagittal plane, are visualized within two periods of the grating, with added contour plots showing the shear horizontal displacements. The continuous transformation of the wave's nature is investigated for each wave propagating in the analyzed material structures when the film thickness is increased from zero to a few wavelengths. The examples of the SAW transformation into boundary waves and into plate modes of different polarization have been found and investigated. The behavior of the SAW characteristics in the grating is correlated with transformation of the wave structure with increasing overlay thickness.

The characteristics of plate modes propagating under Pt grating in rotated Y-cuts of LGS were simulated as functions of the cut angle and plate thickness. Quasi-symmetric and quasi-anti-symmetric modes, which can be excited in rotated YX-cuts, and SH-polarized modes propagating in rotated Y-cuts with propagation direction normal to the X-axis demonstrated high electromechanical coupling up to 2.7%, in some orientations combined with zero TCF. The variation of the mode characteristics with plate thickness was investigated in YX and YZ cuts as the typical examples of the two cut families. The effect of metal film at the plate bottom on electromechanical coupling of different modes was investigated.

There is a need for wireless sensors able to operate in the intermediate temperature range (ITR) between 300 °C and 600 °C. Surface acoustic wave (SAW) sensors are promising candidates to solve this issue. However, existing SAW sensors most often fail in the ITR, due to the quick degradation of the sensor housing in extreme conditions. A promising way to circumvent the issue is to use “package-less” devices, where the acoustic waves are guided in a multilayered structure where they are intrinsically protected from adverse environmental effects. We present here an innovative multilayered structure that fulfills all the basic requirements, to achieve a wireless and “package-less” SAW Sensor for the ITR. The structure is made of a thin AlN layer deposited on top of a Y + 128°LN substrate and equipped with buried Pt electrodes. Numerical simulations of the acoustic waves propagating in SAW resonators built on this structure reveal the existence of a useful Rayleigh-type SAW that propagates at the AlN/LN inter...

Rigorous analysis of plate modes propagating in LiTaO 3 plates was performed using the numerical technique SDA-FEM-SDA. The characteristics of zero- and first-order plate modes were calculated in rotated YX cuts of LT as functions of cut angle and plate thickness. Orientations providing high electromechanical coupling (up to 19%), zero TCF at resonance and high velocities (up to 19,000 m/s) were found and investigated. The wave motions following the propagation of some modes are visualized. The possibility of enhancement of some modes by deposition of metal film on the plate bottom surface and the sensitivity of higher-order modes to variation of plate thickness are discussed.

A numerical technique developed for simulation of admittance of a finite-aperture resonator is applied to three LGS orientations: YX-cut, SAW cut with Euler angles (0°, 138.5°, 26.7°) and STW cut, Euler angles (0°, 22°, 90°), with a periodic platinum grating. The degradation of a resonator performance is observed for each cut when a resonator aperture decreases from 100 to 20 wavelengths. The ripples of the admittance function are analyzed in correlation with the slowness surface varying with the electrode thickness. Some specific features of each analyzed orientation, such as strong anisotropy or interaction with parasitic modes, and their impact on the resonator performance are discussed. The minimum acceptable aperture is determined for each cut and the possibility of decreasing it without further degradation of admittance, by variation of electrode thickness, is analyzed.

The surface acoustic wave (SAW) propagation properties of zinc oxide (ZnO) films on silicon carbide (SiC) have been theoretically and experimentally characterized in the film thickness-to-acoustic wavelength ratio range up to 0.12. The experimental characterization of the SAW propagation properties was performed with a linear array of interdigital transducer (IDT) structures. The measurements characterized the velocity and propagation loss of two surface modes, a generalized SAW (GSAW) mode with velocities between 6000 and 7000 m/s, and a high velocity Pseudo-SAW (HVPSAW) mode with velocities between 8500 and 12 500 m/s. The experimentally determined characteristics of the two waves have been compared with the results of calculations based on published data for SiC and ZnO. Simulation of wave characteristics was performed with various values of the elastic constant C/sub 13/, which is absent in the published set of material constants for SiC, within the interval permitted by the requirement of positive elastic energy in a hexagonal crystal. The best agreement between the measured and calculated propagation losses of the HVPSAW has been obtained for C/sub 13/ near zero. Although for the GSAW mode the calculated velocity dispersion has been found nearly insensitive to the value of C/sub 13/ and consistent with the experimental data, for the HVPSAW, some disagreement between measured and calculated velocities, which increased with ZnO film thickness, has been observed for any C/sub 13/ value. Theoretical analysis of HVPSAW has revealed the existence of a previously unknown high velocity SAW (HVSAW). The displacement components of this wave have been analyzed as functions of depth and confirmed its pure surface, one-partial character.

Acoustooptic (AO) light dispersive delay lines (LDDL) are widely used in high-power ultrashort laser pulse amplification chains for pulse shaping. The geometry of AO interaction of LDDL is determined mainly by the acoustic beam propagation and photoelastic properties of the crystal. Propagation of bulk acoustic wave (BAW) beams depends on acoustic anisotropy of the crystal and is characterized by the planar tensor of diffraction, which can be considered as an extension of anisotropy parameter for 3D-space. Two nonzero eigenvalues of the tensor are compared for pure shear BAWs propagating in the symmetry planes of TeO2 and LiNbO3. The found combinations of BAW characteristics, including high velocity, low diffraction, and sufficiently large acousto-optic figure of merit, make lithium niobate more preferable for application in LDDL with rapid scan repetition frequency up to 100 kHz compared to TeO2.

International audience; Passive high-temperature sensors are a most promising area of use for SAW devices. Langasite (La3Ga5SiO14; LGS) has been identified as promising piezoelectric material to meet high-temperature SAW challenges. Because it is necessary to know the material behavior for an accurate device design, the frequency-temperature behavior of Rayleigh SAW (R-SAW) and shear-horizontal SAW (SH-SAW) LGS cuts is investigated on delay line and resonator test structures up to 700°C by RF characterization. In the range of the 434-MHz ISM band, the (0°,22°,90°) SH-SAW cut shows thermal behavior similar to the (0°,138.5°,26.7°) R-SAW cut. Associated with the (0°,22°,31°) cut, in which SAWs present mixed types of polarization, the (0°,22°,90°) SH-SAW orientation might allow differential measurements on a single substrate. In the temperature range of 400 to 500°C, delay line test devices using the SH-SAW cut show a considerable drop of signal. Theoretical analysis indicates that this newly described behavior might be a result of anisotropy effects in this cut, occurring in case of any slight misorientation of electrode alignment.

The exceptional wave theory developed in the last two decades is applied to trigonal crystals, widely used in surface acoustic wave devices: quartz, lithium niobate, and lithium tantalate. For quartz all crystallographic orientations where one of bulk acoustic waves satisfies the stress‐free mechanical boundary conditions, have been found and plotted on the stereographic projection of a unit wave normal sphere as ‘‘exceptional wave lines.’’ The possibility of existence and the main features of pure shear, quasishear, and quasilongitudinal exceptional waves are examined in three cut families with Euler angles (0°,θ,0°), (90°,90°,ψ), and (0°,θ,90°). These orientations are analyzed both without and with piezoelectric effect by means of analytical and numerical techniques. The obligatory existence of undamped surface skimming bulk waves or leaky waves is proved for selected cuts of trigonal crystals, such as a well‐known 41°‐rotated Y cut of lithium niobate. The behavior of these waves is compared in three crystals. A simple relation between elastic moduli of trigonal crystals with point symmetry of 32 or 3m has been derived, which allows the existence of a longitudinal type of exceptional waves. Such waves have been discovered in quartz. They are similar to those found earlier in lithium tetraborate and in both crystals they give rise to piezoelectrically coupled high velocity leaky waves with small attenuation.

Unknown LH type leaky and non-leaky waves were theoretically found and examined in lithium tetraborate. The waves have very promising parameters: high velocity, strong piezoelectric coupling, zero power flow angle and small temperature coefficients of delay. The theory of exceptional waves proved to be very useful to investigate the acoustic anisotropy and to search for the cuts where leaky and non-leaky SAW can exist.

We report on a surface-bulk hybrid acoustic mode, which exists within a limited frequency interval in some piezoelectric substrates within a periodic metal grating. These hybrid modes result from the coupling between a bulk wave and a counter-propagating surface (or leaky) wave. An example of such a hybrid mode, which propagates in 36°-YX cut of lithium tantalate, is described. The hybrid mode gives rise to an additional branch of dispersion relation. The Bragg reflection stop band occurs due to phase match between surface and bulk waves. The lower edge of this stop band manifests itself by a resonance of harmonic admittance, being a reason of undesired resonances in resonator filters.

The numerical technique based on a previously developed rational approximation of harmonic admittance of a periodic grating was applied to analysis of SAW behavior in platinum grating on langasite cut with Euler angles (0°, 138.5°, 26.6°). The approximation is able to take into account interaction between surface and bulk waves or between two SAW modes. SAW dispersion was calculated at different values of electrode thickness varying between 1% and 4% of wavelength. It was found that with increasing Pt thickness, SAW behavior in the grating is strongly affected by interaction between two SAW modes propagating in the same orientation. An additional stopband, which results from this interaction, occurs at certain detuning from synchronous reflection condition and can cause spurious resonances of the admittance function. Interaction between two SAW modes is also responsible for anomalously slow growth of reflectivity with increasing platinum thickness.

Since 70-ies, when the first delay lines and filters employing surface acoustic waves (SAW) were designed and fabricated, the use of SAW devices in special and commercial applications has expanded rapidly and the range of their working parameters was extended significantly (Hashimoto, 2000; Ruppel, 2001, 2002). In the last decade, their wide application in communication systems, cellular phones and base stations, wireless temperature and gas sensors has placed new requirements to SAW devices, such as very high operating frequencies (up to 10 GHz), low insertion loss, about 1 dB, high power durability, stable parameters at high temperatures etc. The main element of a SAW device is a piezoelectric substrate with an interdigital transducer (IDT) used for generation and detection of SAW in the substrate. The number of single crystals utilized as substrates in SAW devices did not increase substantially since 70ies because a new material must satisfy the list of strict requirements to be applied in commercial SAW devices: sufficiently strong piezoelectric effect, low or moderate variation of SAW velocity with temperature, low cost of as-grown large size crystals for fabrication of 4-inch wafers, long-term power durability, well developed and non-expensive fabrication process for SAW devices etc. Today only few single crystals are utilized as substrates in SAW devices: lithium niobate, LiNbO3 (LN), lithium tantalate, LiTaO3 (LT), quartz, SiO2, lithium tetraborate, Li2B4O7 (LBO), langasite, La3Ga5SiO14 (LGS) and some crystals of LGS group (LGT, LGN etc.) with similar properties. The SAW velocities in these single crystals do not exceed 4000 m/s, which limit the highest operating frequencies of SAW devices by 2.5-3 GHz because of limitations imposed by the line-resolution technology of IDT fabrication. The minimum achievable insertion loss and maximum bandwidth of SAW devices depend on the electromechanical coupling coefficient, which can be evaluated for SAW as k2≈2ΔV/V, where ΔV is the difference between SAW velocities on free and electrically shorted surfaces. The largest values of k2 can be obtained in some orientations of LN and LT. Ferroelectric properties of these materials are responsible for a strong piezoelectric effect. As a result, k2 reaches 5.7% in LN and 1.2% in LT, for SAW. For leaky SAW (LSAW) propagating in rotated Y-cuts of both crystals, the coupling is higher and can exceed 20% for LN and 5% for LT. However, LSAW attenuates because of its leakage into the bulk waves when it propagates along the crystal surface. As a

The numerical technique recently developed for simulation of SAW dispersion in periodic gratings was applied to langasite cut with Euler angles (0°,138.5°,26.6°) and platinum grating, when electrode thickness varies between 1% and 6% λ (SAW wavelength). Analysis has revealed that with increasing Pt thickness, the dispersion appears to be strongly affected by interaction between two SAW modes. It results in additional stopband, which occurs at certain detuning from synchronous reflection condition and manifests itself by additional resonances of admittance function if such detuning occurs in SAW resonator. The anomalous character of dispersion is not adequately described by the known COM models and can explain the slow growth of reflectivity with increasing electrode thickness.

A numerical technique, which combines FEM analysis of electrode area with matrix formalism applied to spectral domain analysis (SDA) of eigen modes in multi-layered substrate and multi-layered dielectric upper half-space, is described as an efficient tool of investigating the wave characteristics in periodic metal grating sandwiched between two multi-layered half-spaces, with arbitrary thickness of each layer. The universal character of the developed technique is illustrated by few examples of its application to different types of structure providing propagation of common SAW, boundary waves at interface, plate modes, normal modes in a thin film deposited over the grating etc. The transformation between the waves with continuously increasing film thicknesses can be observed.

The mechanism of SAW transformation with variation of film thickness is investigated in Piezoelectric/Metal grating/Dielectric structures via simulation of acoustic fields. By way of example, YX and 128°YX cuts of lithium niobate are considered as substrates, with Cu grating and isotropic SiO 2 as overlay. The motions, which accompany the wave propagation in the sagittal plane, are visualized, and the added contour plots show variation of shear-horizontal displacements. The transformation of the wave nature with SiO 2 thickness increasing from zero to few periods is observed for each wave propagating in the analyzed material structures. Examples of wave transformation into boundary waves and into normal modes propagating in SiO 2 film are demonstrated. The difference in the behavior of SAW modes in the grating is correlated with velocity versus film thickness dependences.

Different cuts of langasite were investigated theoretically and experimentally as candidates for high temperature sensors utilizing SAW resonators and reflecting SAW tags. Single port SAW resonators with central frequencies close to 170, 200 and 433 MHz with W, Ir and Pt electrodes of different thickness were fabricated and their characteristics were measured as functions of temperature. An approach to SAW device encapsulation, which helps to avoid stress development during heating to high temperatures, was suggested and tested. The damage of the langasite surface during heating to high temperature is strong in the cut family with Euler angles (0°, 138.5°, ψ), while orientations with Euler angles (0°, 90°, ψ) and (0°, 22°, ψ) were found to be more resistant to heating. In the latter cut family, two cuts, (0°, 22°, 31.5°) and (0°, 22°, 90°) can provide zero power flow angle and sufficient piezoelectric coupling. COM parameters of SAW resonators with W, Ir and Pt electrodes, including complex reflection coefficient, were calculated as functions of electrode thickness and measured in the wide temperature range. The frequency responses were described by COM equations and the fitted COM-parameters were compared to their simulated values. Resonators show high Q and their performance is perfectly described by COM equations

We report two numerical examples of high-velocity surface acoustic waves, a type of surface waves which was recently shown to exist if a thin film is present on a surface. The nonattenuated high-velocity surface waves have been found in diamond orientation with Euler angles (0°,0°,45°) and sapphire orientation with Euler angles (0°,−20.3°,0°), with zinc oxide film. In diamond, the wave has “symmetric” structure with displacement in the symmetry plane while, in sapphire, the example of a “nonsymmetric” solution is presented. The numerical analysis has confirmed that, in both examples, the wave has a true surface nature, with one-partial structure in a substrate.

Results of resonators constructed on rotated YX lithium niobate (LiNbO3), to provide minimum coupling of the spurious Rayleigh-type mode are reported. The resonator employs non-leaky waves which result when the metal grating's electrodes are sufficiently heavy to suppress attenuation of leaky waves. The coupling of two SAW modes propagating in rotated YX cuts was estimated as function of cut angle and electrode thickness, with Al or Cu as electrode material. The optimal orientation, 19degYX for Al grating or 20degYX for Cu grating, is compared with previously reported 15degYX cut. If the electrode thickness is optimized to suppress the spurious mode, in 15degYX the coupling of this mode grows fast with variation of frequency or electrode thickness because of close proximity between the velocities of two modes. In 19degYX cut the resonance of the spurious mode is located in the middle of the interval between the resonance and anti-resonance of non-leaky SAW mode. The spurious mode is made less sensitive to variations of frequency or metal thickness and provides better performance of resonator filters. This conclusion is confirmed experimentally..

Optimal cuts of LiTaO3 for application in plate mode resonators were found via rigorous numerical investigations of zero- and higher-order plate modes propagating parallel or normal to the X-axis in rotated Y-cuts of LiTaO3; the plates were tested with a periodic metal grating on top of the plate and metal electrode present or absent on the plate bottom. In some cuts, high electromechanical coupling coefficients up to 20% could be combined with low or even zero temperature coefficients of frequency (TCF). Other cuts ensured moderate coupling of 12%–14% and low TCF in addition to high velocity of a higher-order plate mode up to 20 000 m/s. Metallization of a plate bottom helped to enhance coupling of certain modes. Interaction of a plate mode with electrodes of an interdigital transducer or with periodic metal gratings used for its excitation and reflection in resonators is illustrated by examples of dispersion plots. The nature of the analyzed modes was studied via visualization of the mechanical displacements accompanying wave propagation.

A method of accurate approximation of the admittance of a periodic grating, in which a leaky wave propagates, is described. The two-parameter coupling-of-modes formalism, which considers the interaction between leaky and bulk waves, was applied, with both parameters assumed dependent on frequency. The complex-valued frequency dependent parameters, which characterize leaky wave dispersion, were extracted from harmonic admittance of infinite grating, with imaginary parts responsible for propagation loss. The method was verified for 36oYX, 42oYX and 48oYX cuts of lithium tantalate with aluminum electrodes of different thickness. Very accurate approximation of harmonic admittance was obtained for wide range of orientations and electrode thicknesses.

In order for SAW duplexers to successfully meet the stringent requirements of insertion loss and skirt steepness required for applications such as the US-PCS duplexer, new technologies are required to reduce the temperature coefficient of frequency (TCF). SAW duplexer manufacturers (1), (2), (3), (4) are aggressively pursuing various methods to accomplish this reduction in TCF, at the wafer level. Their methods will necessarily result in changes to other properties of importance to duplexer design. This paper examines the effect bonding of Lithium Tantalate (LT) to Silicon has on the properties of the leaky SAW (LSAW) resonators.

Two acoustic modes, which propagate in rotated YX-cuts of LiNbO 3, were investigated as functions of rotation angle. The main characteristics of these modes, including polarization vectors, were determined first for free surface, and then analyzed as functions of Al thickness, in a substrate with uniform film or periodic grating. The behavior of typical Rayleigh-type and Love-type modes, which propagate in 128degYX cut, is compared with acoustic modes propagating in 15degYX cut. Velocity versus rotation angle dependences, calculated at different Al thickness, demonstrate gradual transformation of LSAW into the non-leaky SAW, with increasing Al thickness, and interaction between two SAW modes

The transverse anisotropy of LSAW characteristics is numerically analyzed in some orientations of practical interest in LiTaO/sub 3/ and LiNbO/sub 3/ with Al grating. The detailed analysis of the slowness curves for LSAW propagating in the grating and in the substrate with uniform Al layer helps to estimate the frequency intervals, in which strong radiation of obliquely propagating waves can be expected in the grating and in the busbars, and explains the transversal pattern within the IDT aperture. The numerical results show good agreement with measurements previously reported by Koskela et al. (2001) and Knuuttila et al. (2003).

The propagation loss of high-velocity pseudo-surface (leaky) waves (HVPSAW) propagating in orientations of LiNbO/sub 3/ defined by the Euler angles (0/spl deg/, /spl mu/, 90/spl deg/), with periodic Al grating, has been numerically analyzed as function of three parameters, Euler angle /spl mu/, electrode thickness and metalization ratio. It was found that there is no combination of these parameters giving non-attenuated HVPSAW simultaneously at resonant and antiresonant frequencies, but there exists a wide area, within which the propagation losses at resonance and at antiresonance are both less than 0.001 dB//spl Lambda/. This area is located between orientations (0/spl deg/, 78.5/spl deg/, 90/spl deg/) and (0/spl deg/, 81/spl deg/, 90/spl deg/), with normalized Al thickness between 0.079 and 0.0875 and metalization ratio between 0.4 and 0.8. Orientation (0/spl deg/, 80/spl deg/, 90/spl deg/) was found to be the best choice to provide low propagation loss within wide interval of Al thicknesses. Metallization ratios of individual resonators within one resonator (ladder) filter can be varied to allow the propagation loss for each individual resonator to be minimized at predetermined individual frequency and provide improved performance of the HVPSAW filter.

A criterion of simultaneous minimization of propagation loss at resonant and antiresonant frequencies, previously developed for optimization of rotated Y-cuts of LiTaO/sub 3/ (LT) used in resonator SAW devices, is applied to rotated Y-cuts of LiNbO/sub 3/ (LN). The optimal angle versus thickness dependence was determined for periodic gratings with Al, Cu, and Au electrodes. The main characteristics of LSAW, such as velocity, average propagation loss, electromechanical coupling factor and reflection coefficient, have been estimated along the optimal lines. In particular, it was found that propagation loss tends to zero in 76/spl deg/YX cut with Al electrode thickness 0.055 wavelengths. Nonsymmetric orientations, which exist around symmetric cuts, were located and described in a simple relation between the Euler angles.

We suggest an approximation of the effect of the surface skimming bulk wave (SSBW) on harmonic admittance of periodic grating. The approximation is valid on both sides of cut-off frequency and predicts the existence of surface-bulk hybrid mode (SBH), if such mode occurs in the grating due to SAW/SSBW interaction. As an example, parameters of approximating function were calculated for 36/spl deg/X, Y+90/spl deg/ cut of quartz with Al grating and plotted versus metalization ratio a/p. They revealed the existence of SBH mode for a/p >0.685. The resonance frequency of additional resonance of harmonic admittance, which corresponds to this mode, was predicted with high accuracy from approximation of harmonic admittance around the cut-off frequency.

In resonator filters, it is often desirable to minimize propagation loss simultaneously at resonant and anti-resonant frequencies. Using this criterion, we found an optimal dependence of rotation angle on electrode thickness in wavelengths, in rotated YX cuts of LiTaO/sub 3/ with At grating. In particular, 48/spl deg/YX cut was found to be optimal for resonator filters with thick Al electrodes, about 10% wavelength. With rotation angle set to be optimal for the specified electrode thickness, the lines of nonsymmetric orientations were located, along which propagation losses at resonant and anti-resonant frequencies do not exceed 0.003 dB//spl Lambda/, electromechanical coupling coefficient is higher than 8% and power flow angle does not exceed 5/spl deg/.

An investigation is made of the specific features of the excitation of (pseudo) quasi bulk surface waves. Particular attention is focused on the analysis of wave fields associated with "non-physical" plane wave solutions. As illustrations, numerical computations have been performed for SH-waves and quasi-longitudinal leaky waves in quartz.