Dynamic Nonreciprocity in Loss-Compensated Piezophononic Media

Aurélien Merkel, Morten Willatzen, and Johan Christensen

Phys. Rev. Applied 9, 034033 – Published 28 March 2018

Abstract

Violating time-reversal symmetry enables one to engineer nonreciprocal structures for isolating and rectifying sound and mechanical vibrations. Rectifying sound is commonly achieved in nonlinear media, but the operation is inherently linked to weak and distorted signals. Here, we show how a pronounced electron-phonon coupling in linear piezophononic media under electrical bias can generate full mechanical rectification of broad spectral width, which permits the isolation of pulsed vibrations while keeping the wave-front shape fully intact. In this context, we deliberately show how the acoustoelectric effect can provide active loss compensation against lattice anharmonicity and thermoelastic damping. Further, our predictions confirm tunable nonreciprocity at an ultralarge contrast ratio, which should open the doors for future mechanical diodes and compact ultrasonic transducers for sensing and imaging.

Received 20 August 2017
Revised 1 February 2018
Corrected 6 April 2018

DOI:https://doi.org/10.1103/PhysRevApplied.9.034033

Physics Subject Headings (PhySH)

Acoustic phonons Elasticity Electron-phonon coupling Piezoelectricity

Acoustic metamaterials Diodes Functional materials

Condensed Matter, Materials & Applied PhysicsFluid Dynamics

Corrections

6 April 2018

Correction: The email address was missing for the corresponding author at publication; the footnote has now been inserted.

Authors & Affiliations

Aurélien Merkel¹, Morten Willatzen², and Johan Christensen^1,*

¹Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28916 Leganés, Madrid, Spain
²Beijing Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Xueyuan Road No. 30, Haidian District, 100083 Beijing, China

^*Corresponding author. johan.christensen@uc3m.es

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Issue

Vol. 9, Iss. 3 — March 2018

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Images

Figure 1
A piezophononic layer acting as a highly nonreciprocal device when an electric field $E^{0}$ is applied. Maximal rectification $σ$ is reached when the ratio of opposite flowing energy fluxes is the largest. The approach is to let the forward flux (incoming from left, blue wave fronts) propagate undistorted and with high efficiency, while the backward flux (incoming from right, orange wave fronts) experiences very high attenuation. As a proof of principle, we take CdS to be the piezoelectric medium. The time convention is $e^{- i ω t}$ .
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Figure 2
Dispersion relation in dependence to the applied electrical dc bias $E^{0}$ in CdS as derived from Eq. (2). (a) Imaginary parts of the two wave numbers $k_{1} (E^{0})$ and $k_{2} (- E^{0})$ as a function of $E^{0}$ and for different carrier densities $n_{0}$ computed at their respective values of $f_{\max} (n_{0})$ . The gray area corresponds to the amplification zone, while the black dots mark the case for $n_{0} = 10^{13} {cm}^{- 3}$ . (b) Spectral dependence of the attenuation $- Im (k_{2})$ , where $f_{\max} (n_{0})$ is indicated by red dots, at constant electrical bias $E_{0} = - 155.5 kV / m$ . (c) Complex wave numbers as a function of frequency at a fixed electric field $E_{0} = - 155.5 kV / m$ and $n_{0} = 10^{13} {cm}^{- 3}$ . With correspondence to the previous panels, the red-dotted line marks the spectral region of maximal attenuation.
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Figure 3
Scattering properties of a piezophononic CdS layer (width $L = 1 cm$ ), which is computed as a function of frequency, without losses, and under an applied electric field $E^{0} = - 154.7 kV / m$ corresponding to $γ = 1.00$ (continuous curves). When losses are present, we present three different scenarios: $E_{0} = - 154.7$ , $- 156.2$ , and $- 158 kV / m$ corresponding to $γ = 1.00$ , 1.01, and 1.02, respectively (dashed curves). (a) Transmittance is plotted when ultrasound is incident either from right ( $R$ ) or left ( $L$ ) to the layer. (b) Spectral dependence of the contrast ratio $σ$ . (inset) Maximum contrast ratio $σ_{\max}$ as a function of the intrinsic carrier density $n_{0}$ in units of ${cm}^{- 3}$ , without losses.
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Figure 4
Comparison of the temporal evolutions of a short ultrasonic microsecond pulse for right and left incidences. The piezophononic layer has the same specifications as in the previous example, with losses and $γ = 1.01$ , while the Gaussian pulse is centered at 200 MHz and has a frequency bandwidth of 60 MHz. (a) Source signal. (b) Transmitted signals with left incidence (blue curve) and right incidence (orange curve). The amplitudes are normalized with the maximum amplitude of the source signal.
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