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The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates by solving the Bogoliubov-de Gennes equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both approaches allows one to unambiguously identify every observed mode.
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Recently the physics of ballistic phonon propagation in anisotropic crystals has been studied with new phonon-imaging methods. In this paper we consider nondiffracting waves that can propagate in anisotropic crystals and analyze their properties that emerge specifically due to the anisotropy. We further present a detailed generation and detection scheme for the experimental verification of the wave modes considered.
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Considering a moving vortex line in a dilute atomic Bose-Einstein condensate within time-dependent Hartree-Fock-Bogoliubov-Popov theory, we derive a criterion for the quasiparticle excitations to follow the vortex core rigidly. The assumption of adiabaticity, which is crucial for the validity of the stationary self-consistent theories in describing such time-dependent phenomena, is shown to imply a stringent criterion for the velocity of the vortex line. Furthermore, this condition is shown to be violated in the recent vortex precession experiments.
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A finite element method (FEM) formulation is presented for the numerical solution of the electroelastic equations that govern the linear forced vibrations of piezoelectric media. A harmonic time dependence is assumed. Both of the approaches, that of solving the field problem (harmonic analysis) and that of solving the corresponding eigenvalue problem (modal analysis), are described. A FEM software package has been created from scratch. Important aspects central to the efficient implementation of FEM are explained, such as memory management and solving the generalized piezoelectric eigenvalue problem. Algorithms for reducing the required computer memory through optimization of the matrix profile, as well as Lanczos algorithm for the solution of the eigenvalue problem are linked into the software from external numerical libraries. Our FEM software is applied to detailed numerical modeling of thin-film bulk acoustic wave (BAW) composite resonators. Comparison of results from 2D and full 39 simulations of a resonator are presented. In particular, 3D simulations are used to investigate the effect of the top electrode shape on the resonator electrical response. The validity of the modeling technique is demonstrated by comparing the simulated and measured displacement profiles at several frequencies. The results show that useful information on the performance of the thin-film resonators can be obtained even with relatively coarse meshes and, consequently, moderate computational resources.
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Surface acoustic wave (SAW) impedance element antenna duplexers provide compact, high performance, front-end components apt for industrial fabrication. We describe investigations on the design and modeling of a compact ISM antenna duplexer fabricated on a 36 degrees YX-cut LiTaO3 substrate based on SAW impedance elements. In particular, we have performed 3-D modeling of the inductive and capacitive electromagnetic couplings caused by the package parasitics for the duplexer. The use of a 1:3 IDT structure for the reduction of the passband width is discussed. The frequency response of the duplexer is predicted with the help of circuit simulation; the modeling is refined by optimization of the model parameters to improve the fit between the measured and simulated responses. We also report scanning optical imaging of the acoustic field within the resonator structures with the help of laser interferometry; this provides insight into the loss mechanisms beyond that attainable in mere electric measurements.
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We compute the structure of a quantized vortex line in a harmonically trapped dilute atomic Bose-Einstein condensate using the Popov version of the Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be (meta)stable in a nonrotating trap even in the zero-temperature limit, thus confirming that weak particle interactions induce for the condensed gas a fundamental property characterizing "classical" superfluids. We present the structure of the vortex at ultralow temperatures and discuss the crucial effect of the thermal gas component to its energetic stability.
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We discuss acoustic losses in synchronous leaky surface acoustic wave (LSAW) resonators on rotated Y-cut lithium tantalate (LiTaO3) substrates. Laser probe measurements and theoretical models are employed to identify and characterize the radiation of leaky waves into the busbars of the resonator and the excitation of bulk acoustic waves. Escaping LSAWs lead to a significant increase in the conductance, typically occurring in the vicinity of the resonance and in the stopband, but they do not explain the experimentally observed deterioration of the electrical response at the antiresonance. At frequencies above the stop-band, the generation of fast shear bulk acoustic waves is the dominant loss mechanism.
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A scanning homodyne Michelson interferometer is constructed for two-dimensional imaging of high-frequency surface acoustic wave (SAW) fields in SAW devices. The interferometer possesses a sensitivity of ~10(-5)nm/ radicalHz , and it is capable of directly measuring SAW's with frequencies ranging from 0.5 MHz up to 1 GHz. The fast scheme used for locating the optimum operation point of the interferometer facilitates high measuring speeds, up to 50,000 points/h. The measured field image has a lateral resolution of better than 1 mu;m . The fully optical noninvasive scanning system can be applied to SAW device development and research, providing information on acoustic wave distribution that cannot be obtained by merely electrical measurements.
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An analytic approach is developed for simulating synchronous resonators employing shear horizontally polarized surface acoustic waves, such as surface transverse waves, and leaky surface acoustic waves on LiTaO/sub 3/ and LiNbO/sub 3/ substrates. The approach, based on a simplified parametrized Green's function theory, allows the description of the localization of the wave and the interaction with bulk acoustic waves. An analytic expression is found for the harmonic admittance of an infinite periodic electrode array, and approximate corrections for finite structures are presented. The model enables fast computation of the admittance of synchronous resonators, and it compares favorably with experiments and numerical simulations.
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A novel numerical method for determining the surface acoustic wave and the leaky surface acoustic wave characteristics is proposed. The Green's function method is used to simulate an infinite periodic transducer driven by a periodic voltage. We show that the coupling of modes parameters and the dispersion relation can be extracted from the change in the admittance as the periodicity of the driving voltage is slightly shifted. The method first introduced here leads to significant savings in computing time.
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Conoscopic interferometry is applied for determining the crystal orientation of lithium niobate and other commonly employed substrate wafers for integrated-optic and surface-acoustic-wave devices. The method is particularly applicable for detecting the orientation of the optic axes of the strongly birefringent niobate but is less sensitive for lithium tantalate or quartz. Conoscopic interference is a low-cost and easy-to-use method that is especially suitable for laboratory usage.
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We discuss effects on the propagation of surface acoustic waves (SAW) due to heavy mass loading on Y-cut lithium niobate and lithium tantalate substrates. An abrupt reduction in the leaky-SAW (LSAW) attenuation is observed in the measured admittance of a long resonator test structure on 64 degrees -YX-cut lithium niobate for aluminum electrodes of thickness h/lambda(0) beyond 9-10%. This experimental fact is explained theoretically as the slowing down of the leaky wave below the velocity of the slow shear surface-skimming bulk wave (SSBW), such that energy dissipation into bulk-wave emission becomes inhibited. An infinite transducer structure is modeled using the periodic Green's function and the boundary-element method (BEM); the computed theoretical properties well explain for the experimental findings. The model is further employed to quantify the leaky surface-wave attenuation characteristics as functions of the crystal-cut angle and the thickness of the electrodes. The resonance and antiresonance frequencies and the corresponding Q values are investigated to facilitate the selection of crystal cuts and electrode thicknesses. The transformation of the leaky SAW into a SAW-type nonleaky wave is also predicted to occur for gold electrodes, with considerably thinner finger structures.
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We adapt the angular spectrum of plane waves (ASPW) decomposition to numerical simulations of the diffraction of surface-acoustic waves (SAWs) on anisotropic model substrate, such as YZ lithium niobate. We utilize the thin-element decomposition (TED) method, appropriately modified for an anisotropic substrate; we also introduce a novel "average-wavenumber" variation of this scheme; these are numerically found to be mutually consistent. We apply the TED method to simulate wave propagation both in infinite periodic structures of metallized gratings and also in finite gratings. We demonstrate that the ASPW provides a convenient and numerically fast tool for precise diffraction calculations in practical SAW devices which also display structural variations in the lateral direction, perpendicular to the principal direction of wave propagation. Additionally, we compare the present TED method to waveguide theory in an analysis of the role of SAW reflections from the electrodes.
