Electroacoustic shear waves in the hollow structure of two piezoelectric

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Abstract

The results of papers are presented in which dispersion properties of electroacoustic waves in the gap structure of two different piezoelectrics are considered. In particular, it is shown that in the presence of a difference of shear wave velocities in piezoelectrics there are no purely symmetric and antisymmetric modes, and the coefficients of the boundary localization of the shear wave will be significantly different. It is established that at a certain equal level of loss and gain (PT is a symmetrical structure) of two identical piezoelectrics of symmetry class 6, the symmetric and antisymmetric modes intersect. The intersection point defines an exceptional point of the PT-symmetric structure. Taking into account the unequal level of loss and gain in piezoelectrics results in either intersection, touching, or convergence of two modes at the point of their degeneracy (exceptional point) in the shear wave spectrum. As in the case of a purely PT-symmetric structure, the frequency dependence of the amplitude at an exceptional point of a quasi PT-symmetric structure (with a rather small difference in loss and gain levels) exhibits a very narrow peak, which opens up the possibility of creating hypersensitive sensors based on them.

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About the authors

E. A. Vilkov

Fryazino branch Kotelnikov Institute of Radio-Engineering and Electronics RAS

Author for correspondence.
Email: e-vilkov@yandex.ru
Russian Federation, Vvedensky Sq. 1, Fryazino, Moscow region

S. A. Nikitov

Kotelnikov Institute of Radio-Engineering and Electronics, RAS; Moscow Institute of Physics and Technology (National Research University); Saratov National Research State University named after N.G. Chernyshevskiy

Email: e-vilkov@yandex.ru

Лаборатория «Метаматериалы» Саратовского национального исследовательского государственного университета им. Н.Г. Чернышевского

Russian Federation, Mokhovaya Str., 11, build. 7, Moscow, 125009; Institutskiy per., 9, Dolgoprudny, Moscow region, 141701; Bol’shaya Kazach’ya Str., 112, Saratov, 410012

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Supplementary files

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2. Fig. 1. Problem diagram; A – antisymmetric mode, S – symmetric mode.

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3. Fig. 2. Spectrum of slot electrosonic wave modes for two identical piezoelectric crystals of class 4mm (BaTiO3), h = 10–5 cm. Curve 1 is the antisymmetric mode, curve 2 is the symmetric mode.

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4. Fig. 3. Dispersion spectra of the localization coefficients of the antisymmetric mode of slot electrosonic waves in the first (1) and second (2) crystals at = 1.01 and = 1 (upper dashed curve A is the antisymmetric mode, lower dashed curve S is the symmetric mode). h = 10–6 cm.

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5. Fig. 4. Dispersion spectra of the localization coefficients of gap electrosonic waves in the first (1 – BaTiO3) and second (2 – PbTiO3) crystals. h = 10–6 cm. The inset shows a fragment of the spectrum in the region of small values of the wave vector.

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6. Fig. 5. Spectrum of slot electrosonic wave modes (identical class 6 piezoelectric crystals). Taking into account gain and attenuation. h = 10–6 cm, K 2 = 0.25, = 0.025, ε = 8. Numbers designate the spectra of symmetric (S) and antisymmetric modes (A) for different levels of attenuation and gain: 1 (S, A) –αk= 10–6, 2 (S, A) – αk= 9.62.10–5, 3 (S, A) - αk = 10–3, 4 (S, A) - αk = 10–1. The wavenumber value marked with a green triangle corresponds to the wavenumber that determines the singular point for αk= 9.62.10–5.

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7. Fig. 6. Dependence of the amplitude of the electric potential of the symmetric mode at y = 0 (middle of the gap) on the frequency for αk = 9.62.10–5.

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8. Fig. 7. Spectrum of electroacoustic wave modes for two identical 4mm class piezoelectric crystals: BaTiO3 (a) and Ba2Si2TiO8 (b), separated by a gap of h = 10–5 cm. Arabic numerals indicate the spectra of the “symmetric” (thick curve) and “antisymmetric” modes (thin curve) for different levels of attenuation and amplification: 1 – ; 2 – 10–4, ; 3 – 10–3, . Thin dashed lines I and II represent the linear spectra of the electroacoustic wave on the metallized: s = kK 2 and non-metallized: s = k(K 2 )/(1 + ε) boundaries of the piezoelectric crystal (see Fig. 2).

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9. Fig. 8. Logarithmic dependence of the difference in the amplitudes of the electric potential Ф0 in the gap at y = ±h on the value .

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10. Fig. 9. Profile of the total potential modulus for two modes (curve 1 – symmetric mode, curve 2 – antisymmetric mode), when . The calculated parameters correspond to Fig. 7b. a – k = 24500 cm–1, b – k = 38761 cm–1, c – k = 49200 cm–1.

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11. Fig. 10. Profile of the total potential modulus for two modes ((curve 1 – symmetric mode, curve 2 – antisymmetric mode)), when . The calculated parameters correspond to Fig. 7b. a – k = 24500 cm–1, b – k = 38761 cm–1, c – k = 49200 cm–1.

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