The Head: Ph.D. Nedospasov I.A.
Information on the specific scientific results achieved in the reporting period
The main result of this reporting period is reflected in paragraphs 1-3.
1. A theory has been developed that offers two approximate methods for estimating acoustic nonlinear parameters (ANP) for quasi-phase mixing processes using second-order nonlinearity of two intrinsic waveguide acoustic modes generating a leakage wave. For flowing waves with a high degree of localization in the waveguide, both methods give consistent results with a good degree of accuracy, which is demonstrated by the example of a system with generalized (two-dimensional) plate modes.
2. The first approach proceeds from the stationary solution of the equations of motion and boundary conditions for the displacement field obtained within the framework of perturbation theory. This approach requires solving a linear system of equations that is close to singular.
3. The second approach is based on the decomposition of the displacement field into resonant states (resonant state expansion) generated during the mixing process. It allows you to express ANP as an overlap integral, requiring normalization of the displacement field associated with the leakage wave.
4. Analytical dispersion equations describing generalized plate modes in a system consisting of three media half-space/plate/half-space are obtained.
5. Several algorithms have been implemented to find complex solutions to such analytical dispersion relations based on the Muller method and iterative approximation to complex roots.
6. The range of existence of nonlinear mixing processes in the resulting mode for the interlayer system between two half-spaces is estimated.
7. Using numerical simulation, the effects of diffraction of a surface acoustic wave on a system of metal layers located on the surface of a lithium niobate crystal forming a Fresnel lens are described. The far-field focusing field and phase shift at the boundary of the structure are compared with experimental measurements on visualization of acoustic fields.
8. Waves in wedge-type systems in contact with the film are described in detail. The cases of both acute-angled and obtuse-angled wedges with a film on one of the faces are considered.
9. Dispersion ratios in a silicon wedge with different opening angles with a nickel film on one of the faces are calculated.
10. Reflection coefficients are calculated for edges with a film when a surface acoustic wave falls on it.
11. The possibility of leakage waves in a wedge-film system is shown. The different influence of the film on the modes in wedges with different crystallographic orientations is noted.
12. Solutions have been obtained for displacement fields in the process of reflecting a surface acoustic wave from the boundary of a deposited film having a stepped geometry.
13. The problem of excitation of wedge leakage waves is solved both in a two-dimensional formulation by a power source and in a three-dimensional acousto-electronic device approximated to a real one with excitation by counter-pin (periodic) converters using the example of a lithium niobate crystal.
14. Orientations and frequency domains of existence of wedge and pseudocline (leaking) waves in a 90 degree wedge of lithium niobate have been found and evaluated.
15. The effect of metallization of piezoelectric wedge surfaces on the velocities and regions of existence of wedge and pseudocline waves is estimated.
16. The slowness surfaces for wedge waves in a lithium niobate crystal are calculated depending on the angle of rotation of the wedge geometry, which leaves one of the faces of the wedge unchanged (rotation in the plane of one of the faces). It is shown that the coefficient of electromechanical coupling for wedge waves reaches maximum values of 5 percent when rotated relative to a given axis.
17. The real static moments of forces arising in a piezoceramic tube are calculated, depending on the frequency, for the attenuation parameters for piezoceramics PZT-4 as close as possible to the experiment. The obtained theoretical results are compared with experimental measurements.
18. The dependences of the addmittance on the frequency for the most approximate attenuation parameters for a piezocreamic cylinder made of PZT-4 when excited immersed in the volume of the VSHP are calculated. The obtained theoretical results are compared with experimental measurements.
19. Localized acoustic modes in one-dimensional periodic piezoelectric structures based on both thin metal inclusions and recesses and grooves located on a half-space are studied in detail.
20. Based on the analysis of the fields of mechanical displacements, the correspondence of the above modes in structures with periodically arranged thin aluminum electrodes with Love and Sesave waves in homogeneous media was established.
21. It is shown that changes in mechanical and electrical boundary conditions have a strong effect on the behavior of dispersion curves near the boundary of the Brillouin zone. This allows you to manipulate the occurrence and width of forbidden zones. On the other hand, it was found that these effects are practically absent for non-piezoactive modes observed simultaneously in the same structure.
22. It is shown that more complex modifications of structures in the form of a combination of voids and grooves/columns also strongly change the appearance of dispersion curves. Wide bandgap zones appear in the structure, extensive ranges of modes with zero group velocity arise, and pseudo-waves also arise.
23. Generalized analytical expressions describing the reflection of an electromagnetic wave of arbitrary polarization (TE and TM) from a limited photonic crystal, taking into account the plate on which it is located, are obtained. It is shown that taking into account the glass substrate in the model leads to fast oscillations, and the photonic crystal leads to slow ones.
Description of the work performed in the reporting period and the scientific results obtained for publication on the RSF website
Theoretical calculations have been made to estimate the torque acting on the cylinder depending on the frequency. As expected, based on the results obtained in [Biryukov], the magnitude of the static moment is highly dependent on attenuation. Three different combinations of viscous and dielectric loss parameters were selected based on literature data [Bode]. It is shown that as the values of the loss parameters decrease, the peak of the admittance value in Fig. 1 narrows, and the value of the static moment at the resonance frequency increases. The assumption that the imaginary part of the modulus of elasticity PZT-4 largely dependent on frequency, as stated in [Bode], and the case of delta_m=0.0037, delta_e=0.0037 (dashed lines in Fig. 1) seems to be the closest to the experimental situation presented in [Biryukov], according to our analysis of loss mechanisms in PZT [Nedospasov]. However, the maximum value of the calculated static torque is still about 50 times greater than the measured one. The probable causes of the discrepancy between the simulated static moment values presented in the project [Nedospasov] and those measured in [Biryukov] are described, which are as follows: i) The constants of the PZT material from which the tube is made are poorly known, especially those associated with acoustic wave attenuation. ii) For modeling, it was necessary to change the geometry of the system, studied earlier in experiments. It was reduced to two dimensions, neglecting the dependence of all fields on the coordinate along the axis of symmetry of the cylinder. Another notable difference concerns metal electrodes. In the experiments, the electrodes were located on the outer surface of the cylinder, and in our modeling we buried the electrodes into the piezoceramic and in addition, their edges were rounded to reduce numerical errors.
Theoretically, the problem of diffraction of surface acoustic waves (SAW) on metal layers forming a Fresnel lens was studied. The initial creation of the structure was carried out on the basis of a known isotropic model. The finite element method solved the problem of exciting acoustic waves using interdigital transducers. A finite element scheme is constructed that uses symmetry in the propagation of SAWs with appropriate boundary conditions to reduce the computational requirements. A comparison was made for various electrical boundary conditions on the surface of the Fresnel lens. Numerical modeling was compared with a real experiment [Roshchupkin] on visualization of diffraction of surface acoustic waves using the example of SAW focusing in a lithium niobate crystal.
The frequency dependencies of the existence and localization of the leaky modes, as well as the quantitative characteristics of the leakage, were investigated. The dispersion curves of the wedge and pseudowedge modes in a rectangular silicon wedge with a nickel film, as well as the response amplitude along the dispersion curve, were calculated. It has been shown that dispersion curves in adjacent silicon wedges with a nickel film have a significantly different slope, both when comparing different modes, wedge and pseudowedge, and when comparing different adjacent configurations. It has been shown that on dispersion curves of pseudowedge waves, using the example of an obtuse symmetrical wedge of silicon with a film, configurations with a high degree of localization at certain wavelengths can be observed. In other words, a wedge waveguide with a film on leaky waves has a selective frequency character, that is, it has the properties of a filter that can be adjusted by the thickness of the film.
The process of scattering the surface harmonic wave on the edge of the wedge with the film, as well as on the transition half-space – half-space with the film, was studied. Due to the selective localization of the field of the leaky wedge wave at the edge with respect to the wavelength, the effect of an abrupt change in the reflection coefficient depending on the thickness of the film, which can be played by a sensor coating that reacts to environmental conditions, was found. In comparison with this effect, the transition half-space – half-space with a film practically does not change the already weak scattering characteristics as functions of the film thickness.
The coefficients of reflection and transmission of surface waves when surface waves incident on a wedge with a nickel film for different film thicknesses were obtained. A significant shift in the resonance angle of reflection was detected with a small change in the thickness of the film. Using the example of a 1 GHz sensor, the sensitivity of the proposed sensor based on the reflection of surface waves was estimated, equal to a 10% change in the reflection coefficient induced by 2 nm of the film thickness equivalent in terms of nickel parameters.
Waveguide structures based on a composite half-space/interlayer/half-space system, for which conditions for the existence of leaky modes localized near the edge are realized, have been analytically studied. [Georgiades].
Systems of the type edge of variable thickness (truncated edge) were investigated. Changes in the wave amplitude at different angles in such a structure were evaluated to enable a blocking effect when propagating certain modes that have a dispersion curve with a zero velocity group configuration.
Quasi-phasematched mixing processes of acoustic waves via second-order nonlinearity are analyzed with two perfectly guided waves generating a leaky wave. The efficiency of such processes is quantified by an acoustic nonlinearity parameter (ANP), defined as the linear growth rate of the leaky wave’s amplitude in the initial stage of its spatial evolution [RevLissend, Matlack]. Two approximate ways of estimating the ANP of such processes are suggested. The first starts from a stationary solution of the equation of motion and boundary conditions for the displacement field, obtained within perturbation theory. It is determined in a direct way and requires the solution of a near-singular linear system of equations. The second is based on the resonant state expansion of the displacement field generated in the mixing process [Allarov1 Alarov2 Muljarov Doost]. It allows to express the ANP in the form of an overlap integral, requiring normalization of the displacement field associated with the leaky wave. For leaky output waves with a high degree of localization at the waveguide, both methods yield results in good agreement, as demonstrated for an example system with generalized (2D) plate modes. The first approach has been applied to finite element calculations of the ANP for nonlinear mixing processes of (1D) edge waves in an elastic plate with rigid faces.
A number of one-dimensional phononic crystals, which are periodic thin-film structures of various geometries, consisting of sets of columns and metal inclusions located on a piezoelectric half-space, have been proposed and studied. Localized acoustic modes in one-dimensional periodic piezoelectric structures based on thin metal inclusions, notches, and grooves have been investigated. Based on the analysis of the fields of mechanical displacements, it was found that these modes in structures with periodic thin aluminum electrodes correspond to Love and Sezawa waves in homogeneous media. It has been shown that the change in mechanical and electrical boundary conditions has a strong effect on the behavior of dispersion curves near the boundary of the Brillouin zone. This allows to manipulate the existence of band gaps existence, as well as their width. On the other hand, it was found that these effects are negligibly small for non-piezoactive modes observed simultaneously in the same structure. More complex modifications of structures in the form of a combination of voids and grooves/columns also strongly affect the behavior of dispersion curves. In the structures appears wide band gaps, extensive ranges of modes with zero group velocity, and pseudo-waves branches. State-of-the-art technologies for deposition of films and objects of complex geometry make it possible to design acoustic waveguides with unique characteristics that are suitable for various applications, whether they are components of signal processing devices, sensors, or wavefront manipulation systems.
Calculations were performed for the problem of exciting the leaky waves in three-dimensional systems close to real ones using the example of a lithium niobate piezoelectric crystal. To do this, a number of small problems are sequentially solved, which are a simplified version of the structure under consideration. A two-dimensional eigenvalue problem was solved to determine the lowest frequency localized solutions in a piezoelectric wedge. The crystal orientation was selected as shown in Figure 9.2. In the initial position, the wave propagated along the Y direction, the Z direction was chosen vertically. Surface slownesses for wedge waves are calculated for rotation of the geometry about the Z axis for various cases of electrical boundary conditions. Values of electromechanical coupling coefficients were estimated on the basis of standard approaches in acoustoelectronics. The two-dimensional model was also investigated in the frequency range for existence in the spectrum of leaky waves in the form of a response to a force source. In order to simulate real devices, a similar study of a three-dimensional model was carried out. Three-dimensional models were developed to study the task of reflecting surface waves from the edges during excitation and detection using IDT.
Work has been done on the theoretical and experimental study of the features of the propagation of electromagnetic waves in layered media. For TE and TM cases of polarized radiation using a representation of the solution of the Hill equation in the form of Floquet-Bloch waves, formulas are obtained for reflection and transmission coefficients of a plane wave traveling through a limited one-dimensional photonic crystal with a stepped refractive index profile located on a thin dielectric plate. For angular transmission spectra of a limited one-dimensional photon crystal on a thin dielectric plate, a comparative analysis of measurement results and theoretical modeling is performed.