# Broadband surface acoustic wave attenuation in metals using chirp compression and dispersive interdigital transducers

Dame Fall, Marc Duquennoy, Nikolay Smagin, Zakariae Oumekloul, Mohammadi Ouaftouh

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Dame Fall, Marc Duquennoy, Nikolay Smagin, Zakariae Oumekloul, Mohammadi Ouaftouh. Broadband surface acoustic wave attenuation in metals using chirp compression and dispersive interdigital transducers. JASA Express Letters, 2025, 5 (9), 7 p. 10.1121/10.0039237. hal-05313629

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SEPTEMBER 05 2025

# Broadband surface acoustic wave attenuation in metals using chirp compression and dispersive interdigital transducers

Dame Fall ; Marc Duquennoy ; Nikolay Smagin ; Zakariae Oumekloul ; Mohammadi Ouaftouh

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JASA Express Lett. 5, 094001 (2025)

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# Broadband surface acoustic wave attenuation in metals using chirp compression and dispersive interdigital transducers

Dame Fall,ª Marc Duquennoy, Nikolay Smagin, Zakariae Oumekloul, and Mohammadi Ouaftouh

IEMN (UMR CNRS 8520), University Polytechnique Hauts-de-France, CNRS, University Lille, INSA HdF, F-59313 Valenciennes, France

dame.fall@uphf.fr, marc.duquennoy@uphf.fr, nikolay.smagin@uphf.fr, zakariae.oumekloul@uphf.fr, mohammadi.ouaftouh@uphf.fr

**Abstract:** This study presents a non-destructive method for estimating surface acoustic wave attenuation, which is highly sensitive to microstructural features, especially at high frequencies. The method uses a single wideband dispersive interdigital transducer (IDT) that remotely emits acoustic waves at the sample's edge. Chirp compression of the temporal displacement response is achieved by correlating the excitation signal with the spatial configuration of the IDT's electrodes. This technique generates high-amplitude pulses with a sufficient signal-to-noise ratio, critical for enabling accurate attenuation estimation over a frequency range (15–70 MHz). Results from nickel and aluminum demonstrate the method's effectiveness for rapid material characterization. © 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

[Editor: Joel Mobley]

https://doi.org/10.1121/10.0039237

**Received:** 18 July 2025

**Accepted:** 18 August 2025

**Published Online:** 5 September 2025

## 1. Introduction

Attenuation is an intrinsic material property governed by its physical characteristics, including elastic constants, microstructure, and internal damping mechanisms. Initial investigations into surface acoustic wave (SAW) attenuation began over five decades ago, notably with the optical probing technique developed by Lean and Powell,¹ who employed light diffraction by SAWs to perform non-contact attenuation measurements on piezoelectric substrates. Both theoretical and experimental studies have since advanced our understanding of the underlying phenomena. Auld's foundational work² on acoustic wave interactions in solids introduced key attenuation models involving viscosity and internal energy loss, both of which significantly affect SAW propagation. In 1978, Wakefield and Liesegang³ carried out one of the earliest experimental investigations of SAW attenuation on metal surfaces at a low frequency (~5 MHz), employing laser interferometry of standing surface waves to determine both attenuation coefficients and SAW propagation velocities.

Slobodnik⁴ pioneered the use of narrowband interdigital transducers (IDTs) on piezoelectric substrates to measure SAW attenuation. While effective, this method is inherently limited to piezoelectric materials. Consequently, alternative techniques suitable for a broader range of solids have emerged. For example, Tang et al.⁵ proposed a time-domain method combining Wiener filtering with damped least squares inversion to estimate attenuation in the 0.2–1.5 MHz range, minimizing boundary reflection artifacts. Nevertheless, their approach is restricted to relatively low frequencies, and this method remains sensitive to low signal-to-noise ratios (SNRs) and spectral overlap, which may compromise the accuracy of attenuation estimates.

Subsequent experimental studies, such as those by Every and McCurdy,⁶ applied scattering theory to quantify SAW attenuation in polycrystalline materials, particularly due to energy losses at grain boundaries. In the early 2000s, advancements in instrumentation and methodology further improved attenuation measurements. For instance, Mueller et al.⁷ revisited IDT techniques for thin-film systems, investigating the metal-to-insulator transition in V₂O₃ thin films on lithium niobate substrates. Recent opto-acoustic approaches, enabled by laser ultrasonics and heterodyne interferometry, have facilitated broadband, non-contact measurements. Notably, Ryzy et al.⁸ measured coherent SAW attenuation in polycrystalline aluminum from 10 to 130 MHz, attributing frequency-dependent behavior to grain-boundary scattering. Most recently, Fall et al.⁹ introduced a transverse-field vibrometric technique that captures total beam energy in the near field and extends accurate attenuation measurements from 10 to 50 MHz, while reducing positional error.

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<footnote>ª Author to whom correspondence should be addressed.</footnote>
These milestones demonstrate that SAW attenuation can be experimentally measured in the tens to low hundreds of megahertz range. However, obtaining precise attenuation data at high frequencies remains challenging due to increased scattering, material-dependent damping, and escalating experimental complexity.

Moreover, high-frequency measurement techniques present practical limitations. For instance, while laser-based SAW generation is broadband and contactless, it deposits substantial optical energy into the material, raising the risk of surface modification damage or thermal effects, particularly in non-metallic materials.¹⁰,¹¹ Additionally, laser-ultrasonic systems typically require high optical power densities on polished or transparent surfaces, which can induce local heating, ablation, or micro-cracking. Studies on borosilicate glass have shown that even moderate laser fluences can compromise SAW propagation and damage substrate integrity.¹²

Similarly, other techniques require the substrate or coating to be deposited directly onto the transducers. This process necessitates irreversible sample modification, introduces additional failure modes and uncertainties, permanently alters the surface, restricts use to specific substrate types, and compromises the possibility of sample reuse.¹³⁻¹⁵

In contrast, remote narrowband IDTs have been demonstrated to provide a non-destructive, no-preparation, and broadly material-compatible method for SAW attenuation measurements.¹⁶⁻¹⁸ These transducers leave surfaces intact and allow repeated measurements or downstream analysis without contamination. This approach was successfully applied to polydimethylsiloxane (PDMS)-silica coatings, providing reliable dispersion characterization up to 60 MHz and confirming suitability for fragile, transparent materials.¹⁸ However, their narrowband nature means that characterizing attenuation across a broad frequency range requires multiple devices and long setup times.⁹

To overcome these limitations, wideband dispersive remote transducers have been used. These transducers enable the effective acquisition of SAW dispersion curves for a variety of materials.¹⁹,²⁰ However, the relatively low amplitudes of SAWs generated by wideband IDTs compared to narrowband ones limit their applicability for attenuation estimation on substrates, coatings, thin films, and similar structures. To address this issue, a chirp compression technique using dispersive IDTs has been adopted. This method enables the generation of SAWs with sufficiently large displacement amplitudes for the intended application, an optimal SNR, and a wide frequency spectrum.

As an example, attenuation estimations on an aluminum sample were successfully performed over a frequency range of 15 to 70 MHz with a frequency resolution of 0.1 MHz. In order to validate these results using narrowband IDTs, it was necessary to design, fabricate, and use ten individual IDTs, each operating at a specific frequency, to estimate attenuation across this range with a 5 MHz resolution. This validation required about 60 min of measurement time, whereas the broadband approach achieved the same characterization in a single 6-min scan, a tenfold efficiency gain. Although this second measurement phase was time-consuming, it allowed for the verification and confirmation of the results obtained with the wideband transducer.

## 2. Chirp compression technique

The IDTs used in this study feature a wide bandwidth due to the gradual variation in electrode periodicity (Fig. 1). This spatial periodicity can follow various distributions; in this work, a linear frequency modulation (LFM) scheme is employed.²¹ The frequency variation with respect to electrode position is linear.¹⁹,²⁰,²² The chirp compression technique involves correlating a temporally linear frequency-modulated (chirp) excitation signal with the spatial distribution of electrodes that constitute the IDT [Figs. 1(a) and 1(b)].

For an IDT comprising N finger pairs, the impulse response $h(t)$ to a Dirac delta excitation $\delta(t)$ is given by²³,²⁴

$$h(t) = \pi \sqrt{2K_R C_1^{1/2} f_c^{3/2}} \cos(2\pi ft) \quad \text{with } 0 < t < N/f, \quad (1)$$

<figure><img src="image_8.png" /><figcaption>Fig. 1. Spatiotemporal correlations: electrode pattern (red), applied electrical signal (blue), and displacement induced by SAWs (green). (a) Eq. (5), (b) Eq. (6), (c) temporal response and frequency spectrum (log scale) of the normal displacement measured 1 mm from the transducer [Eq. (5)], and (d) Eq. (6).</figcaption></figure>
where N represents the number of finger pairs, K_R is the electromechanical coupling coefficient, C_1 is the capacitance per finger pair per unit length, and f is the instantaneous frequency,

$$h(t) = A_3 \sin(2\pi ft + \pi/2) \quad \text{with } A_3 = \pi\sqrt{2}K_R C_1^{1/2} f_c^{3/2}. \qquad (2)$$

Taking into account the length L of the active region of the IDT and the velocity V of the SAWs, the temporal duration D (D=L/V) of the signal, the linear temporal chirp s(t) is the signal with duration D defined by

$$s(t) = A\sin(2\pi ft). \qquad (3)$$

The instantaneous frequency f is given by

$$f = \left( f_c - \frac{B}{2} \right) + \frac{B}{2D} t, \qquad (4)$$

where f_c is the center frequency between the maximum operating frequency f_2 and the minimum operating frequency f_1 of the IDT [f_c = (f_1 + f_2)/2], and B is the bandwidth (B = f_2 - f_1).

By correlating the linear temporal chirp signal with the electrode configuration, the displacement at the output of the IDT is obtained via convolution, as described by Eqs. (5) and (6), where s(-t) is a time-reversed version of the signal s(t),

$$U(t) = h(t) * s(t), \qquad (5)$$

$$U(t) = h(t) * s(-t). \qquad (6)$$

Two responses are obtained: Eq. (5) yields a spread signal with a duration of approximately two-dimensional (2D) [Fig. 1(a)], while Eq. (6) produces a compressed pulse signal whose main lobewidth is defined by the duration τ (τ ≈ 1/B) [Fig. 1(b)].²⁵ This type of compression is known as the Klauder wavelet.²⁶

Temporal compression of the displacement response enables the generation of SAWs in the form of short pulses with high amplitude levels, a good SNR, and a wideband spectrum matching the operating bandwidth of the transducer. The power of the SAW signal generated with this pulse increases proportionally to D/τ.²⁶

### 3. Experimental configurations and procedures

For this study, a 99.99% pure aluminum plate (50 × 50 mm, 1 mm thick) and a 99.7% pure nickel plate (50 × 50 mm, 1 mm thick) were selected. The normal displacements of the SAWs were measured using a laser Doppler vibrometer (Polytec UHF-120; Polytec, Irvine, CA).²⁰

Initial SAW measurements were performed directly on the transducer to illustrate the two previously described responses. The transducer used was a dispersive IDT with 165 electrodes, a length L of 4 mm, and an aperture width w of 7 mm. The IDT consisted of gold electrodes deposited on a 128° Y-cut lithium niobate (LiNbO₃) substrate with X-propagation, a widely used piezoelectric material for broadband SAW generation.

The operating frequencies f_1 and f_2 are 15 and 150 MHz, respectively, corresponding to a bandwidth B of 135 MHz, a center frequency f_c of 82.5 MHz, and a period T_c (T_c = 1/f_c) of 12 ns. For excitation, temporal linear chirps s(t) and s(-t) were applied with a signal duration D = L/V of 1.1 µs and a peak-to-peak voltage amplitude A of 50 V.

Figures 1(c) and 1(d) show the normal displacements measured at 1 mm from the electrodes on the transducer surface, with the spectra calculated using a Fourier transform. They correspond to the convolution described by Eqs. (5) and (6), respectively.

The obtained spectra were identical. Pulse compression resulted in a signal with a peak amplitude five times greater than the maximum amplitude obtained with the spread signal, which had a duration of twice D, i.e., 2.2 µs. The duration τ of the mainlobe is given by 1/B, which corresponds to 7 ns.

In a second step, measurements were performed on the aluminum sample to compare the two responses previously described and defined by Eqs. (5) and (6). The applied excitations were the same as those previously used for measurements performed directly on the transducer. For these measurements, SAWs were generated by the IDT and transmitted to the sample's edge via a coupling medium. A thin layer of petroleum-based couplant ensured efficient acoustic transmission between the transducer and the sample. Figures 2(a) and 2(b) show the normal displacements measured on the aluminum sample at a distance of 1 mm from the IDT, corresponding to the convolutions described by Eqs. (5) and (6), respectively.

The SNR is significantly lower for the spread signal [Fig. 2(a)]. The average amplitude of the time-domain response is 20.7 pm, with an average noise level of 6.2 pm, corresponding to an SNR of 10.5 dB. The maximum amplitude achieved with the compressed signal is 400 pm, corresponding to an SNR of 36.2 dB. A better SNR is therefore achieved due to compression [Fig. 2(b)]. Additionally, the amplitude is four times greater than the maximum amplitude of the spread signal. Compression thus enables the generation of SAWs over sufficiently long distances (several millimeters), allowing attenuation estimations with adequate SNRs and amplitudes for the intended application. These two parameters are crucial for achieving optimal accuracy in attenuation measurements. However, the microstructure can vary between
<figure><img src="image_9.png" /><figcaption>Fig. 2. Time-domain response of the normal displacement measured 1 mm from the IDT on the aluminum sample, with noise level shown in red: (a) convolution as described by Eq. (5); (b) convolution as described by Eq. (6); (c) time-domain displacement response at Nx scan points on the aluminum sample corresponding to the convolution in Eq. (6).</figcaption></figure>

different aluminum samples and can significantly affect intrinsic attenuation characteristics, especially at higher frequencies. For example, grain size influences attenuation: beyond a certain frequency, waves are strongly attenuated when the wavelength becomes comparable to the grain size.²⁷,²⁸

## 4. Near-field attenuation estimation

The measured SAWs velocity V on the aluminum sample was 2901 m/s at a temperature of 22 °C. Considering the minimum operating frequency $f_1 = 15$ MHz, this velocity yields a maximum wavelength $\lambda_{max} = V/f_1$, allowing calculation of the minimum near-field length as $w^2/\lambda_{max}$, which results in a value of 253.4 mm. Attenuation measurements were conducted within the very near-field region to avoid distortion zones.⁴ As a precaution, the measurement zone was limited to 1/50 of the near-field length, corresponding to a distance of 5 mm from the transducer. Transverse displacement scans performed perpendicular to the propagation axis confirmed that the acoustic field remains laterally uniform within this region, indicating negligible beam spreading or lateral mode interference.⁹ The temperature was kept constant at 22 °C by an air conditioning system. Additionally, the measurement was conducted along the acoustic beam axis, and it was necessary to ensure that each scan plane remained perfectly aligned with the beam axis and that the transducer was not tilted.

In this study, a line perpendicular to the transducer was defined, consisting of $N_x$ scan points ($N_x = 5$) with a spacing $d_x$ ($d_x = 1$ mm). The distance between the electrodes and the first scan point, denoted $x_0$, was set to 1 mm, resulting in a total scan length of 5 mm. The procedure described by Eq. (6) and illustrated in Fig. 1(b) was selected to generate high-amplitude displacements in the form of short pulses, with an improved SNR.

Figure 2(c) shows the normal displacements of the SAWs propagating along the line perpendicular to the propagation direction, measured at the $N_x$ scan points on the sample as a function of time. A time-gating process was then applied to each recorded displacement signal. This gating is necessary to eliminate parasitic echoes caused by inter-electrode reflections and edge reflections.

## 5. Results and discussion

To estimate attenuation, displacements measured at the $N_x$ points were considered, corresponding to four surface acoustic wave (SAW) propagation distances: 1, 2, 3, and 4 mm. The time-domain responses recorded at these positions were processed using the Fourier transform to obtain the corresponding frequency spectra [Fig. 3(a)].

Taking the point $N_x = 1$ as the reference, with $u_0$ denoting the corresponding spectrum, d the SAW propagation distance, and $u_d$ the spectrum measured at distance d, the attenuation (in dB per unit distance) is given by

$$ \alpha = \frac{20}{d} \log \left( \frac{u_d}{u_0} \right). \qquad (7) $$

Attenuation values were estimated for four SAW propagation distances: 1, 2, 3, and 4 mm. A minimum propagation distance of 3 mm was required to ensure reliable estimation. Figure 3(b) shows the estimated attenuation in the aluminum sample, along with the frequency band used for the calculation. Spectra were derived from time-domain responses at $N_x = 1$ and $N_x = 5$, corresponding to a propagation distance of d = 4 mm. Attenuation was evaluated over the frequency range from $f_1 = 17.65$ MHz to $f_2 = 66.15$ MHz, with a frequency resolution of 0.1 MHz. Additionally, the spectrum recorded at 1 mm from the transducer [Fig. 1(d)] was used to assess the gain at the cutoff frequencies $f_1$ and $f_2$, corresponding to -5 and -2 dB levels, respectively [Fig. 3(b)].

Given the IDT's operating bandwidth and characteristics, the amplitudes of the generated surface acoustic waves (SAWs) at frequencies ranging from 15 to 17.65 MHz (corresponding to gains of -7 and -5 dB, respectively) are insufficient for reliable attenuation estimation. Above 66.15 MHz, the amplitudes of the SAWs decrease significantly. This is expected, as the energy of these waves is confined near the surface, within a depth on the order of the wavelength. When the grain size is comparable to the wavelength, the material's microstructure, including both grain size and the nature of grain boundaries (e.g., misorientation, boundary type), induces stronger scattering of the SAWs, leading to increased attenuation with frequency.
<figure><img src="image_10.png" /><figcaption>Fig. 3. (a) Spectra from time-domain responses at $N_x$ scan points on the aluminum sample. (b) Spectra for $N_x = 1$ (red) and $N_x = 5$ (orange), and attenuation in dB/mm vs frequency (green), with the frequency band for attenuation estimation marked by black dashed lines. (c) Normalized spectra from time-domain responses at $N_x = 1$ on the aluminum sample for ten narrowband IDTs listed in Table 1.</figcaption></figure>

To investigate the frequency-dependent behavior, metallographic analysis was performed on the nickel samples. The average grain size d was 54 µm, with a standard deviation of 13.7 µm, with no significant crystallographic texture. Given the SAW velocity in nickel (2756 m/s), the wavelength at 40 MHz is 69 µm, comparable to the grain size ($\lambda$ ≈ d), placing the sample in the stochastic scattering regime where grain boundary scattering dominates.

Similar conditions are reported for aluminum. Ryzy et al.⁸ observed a sharp increase in SAW attenuation above ~80 MHz in polycrystalline aluminum, consistent with the transition to scattering when the wavelength approaches grain size. This supports our interpretation that the ~70 MHz cutoff frequency is also governed by grain boundary scattering.

The observed attenuation trend exhibits a clear exponential dependence on frequency [Fig. 3(b)].

Additionally, attenuation was estimated using ten narrowband IDTs. For example, one transducer with a resonant frequency of 19.5 MHz was employed. This IDT comprised 50 electrodes, with a wavelength $\lambda$ of 200 µm and an aperture width w of 12 mm. A 25-cycle sinusoidal burst at 19.5 MHz was applied, with a peak-to-peak input voltage of 50 V. The maximum amplitude measured with this narrowband IDT was 3400 pm, corresponding to a SNR of 45.5 dB. The amplitude of the generated SAWs is eight times greater than that obtained with the broadband IDT. However, due to the limited spectral bandwidth, attenuation can only be estimated at the IDT's operating frequency of 19.5 MHz. Table 1 lists the design parameters of the ten narrowband IDTs used for attenuation estimation. Figure 3(c) shows the normalized spectra from time-domain responses of these IDTs, each centered between 15 and 70 MHz. These results highlight the limitation of narrowband transducers, which provide attenuation estimates only at center frequencies, unlike the continuous spectral data from the wideband method.

Figure 4(a) shows the attenuation estimates obtained using broadband IDTs for both the aluminum and nickel samples, along with the results obtained from narrowband transducers.

The curves show good agreement between the results obtained with the two measurement methods and reveal an exponential dependence on frequency. However, due to the narrow operating bandwidths of the IDTs, each providing an attenuation estimate at a single frequency, a minimum of ten IDTs is required to cover the 15 to 70 MHz range with a frequency resolution of 5 MHz. In contrast, a single broadband IDT, combined with the compression technique, enables direct estimation of attenuation over the entire frequency range with a frequency resolution of 0.1 MHz. This exponential trend is also observed in recent finite element method simulations by Grabec et al.,²⁹ based on a statistical digital twin of polycrystalline aluminum, which reported similar attenuation behavior over 10–130 MHz.

<table><caption>Table 1. Parameters of the ten narrowband IDTs.</caption><thead><tr><td>Center frequency (MHz)</td><td>Wavelength λ (μm)</td><td>Number of finger pairs (N)</td><td>Aperture width w (mm)</td></tr></thead><tbody><tr><td>14.6</td><td>266</td><td>25</td><td>12</td></tr><tr><td>19.5</td><td>200</td><td>25</td><td>12</td></tr><tr><td>24.2</td><td>160</td><td>25</td><td>4</td></tr><tr><td>29.1</td><td>133</td><td>25</td><td>3.3</td></tr><tr><td>34.1</td><td>114</td><td>25</td><td>2.8</td></tr><tr><td>39.2</td><td>99.6</td><td>25</td><td>2.5</td></tr><tr><td>44.2</td><td>88.6</td><td>25</td><td>2.5</td></tr><tr><td>48.7</td><td>79.7</td><td>25</td><td>2.5</td></tr><tr><td>58.8</td><td>66.4</td><td>25</td><td>2.5</td></tr><tr><td>68.4</td><td>56.9</td><td>25</td><td>2.5</td></tr></tbody></table>
<figure><img src="image_11.png" /><figcaption>Fig. 4. Attenuation in dB/mm as a function of frequency, obtained using broadband transducers in aluminum (green) and nickel (blue), in addition to those obtained using narrowband transducers (red).</figcaption></figure>

## 6. Conclusion

A chirp compression technique using dispersive IDTs has been presented for the measurement of SAW attenuation.

By correlating the temporal excitation signal with the spatial configuration of the electrodes, this method generates short-duration surface wave pulses with high displacement amplitudes while preserving a wideband frequency spectrum that matches the operational bandwidth of the transducer. This approach significantly improves the SNR of the generated SAWs, even at high frequencies, enabling accurate attenuation estimation. The minimum propagation distance required for attenuation estimation in the aluminum sample has been established.

Given the performance of the proposed method and the intrinsic damping characteristics of metals, attenuation was successfully estimated over a broad frequency range from 15 to 70 MHz for aluminum and from 15 to 40 MHz for nickel. Additionally, the wideband SAW excitation and compression technique significantly reduces measurement time compared to traditional narrowband IDTs, which require multiple tests to cover the same frequency range. Finally, this non-destructive method, employing remote IDT, applies to a wide variety of substrates, including fragile, transparent, or coated materials.

## Acknowledgments

This work was part of the RITMEA project, co-financed by the EU Development Fund, the French government, and the Hauts-de-France Regional Council, with support from the French RENATECH network. The authors thank Benoit Jorgowski for the micrographs.

## Author Declarations

### Conflict of Interest

The authors have no conflict of interest to declare.

### Ethics Approval

Ethics approval was not required.

## Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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