Multidimensional control of surface acoustic wave generation via programmable interdigital transducer arrays

Domain: physics
Published: 2026-04-13
Editorial outcome: accept

Abstract
Fixed interdigital transducers (IDTs) are commonly limited to only generate a single type of surface acoustic wave (SAW). Here, we present a programmable IDT array architecture for multidimensional SAW generation, based on standard and chirped IDT array designs. Forty independently addressable IDT units are each modulated by a double-pole-double-throw switch to enable binary phase inversion. This system generates diverse SAW waveforms including non-diffracting Airy SAWs and dynamically focused SAWs. We achieve two-dimensional focus manipulation with sub-wavelength precision and extended focal depth, enabled by time-division multiplexing with chirped IDTs. By combining spatial phase encoding with spectral frequency multiplexing, our approach demonstrates multidimensional control over SAW generation, providing a platform for adaptive acoustic field control in applications such as reconfigurable microfluidics, tuneable metamaterials, and multifrequency sensing systems.

Introduction
Surface acoustic waves (SAWs) are mechanical waves that propagate along the surface of a solid material, with their amplitudes decaying exponentially into the bulk. Since their first observation by Lord Rayleigh in 1885 [1], SAWs have been widely utilized across various fields. In modern applications, SAWs are primarily generated using interdigital transducers (IDTs) deposited on piezoelectric substrates. By exploiting the inverse piezoelectric effect, an applied electric potential across the IDTs is converted into mechanical energy, producing SAWs that propagate along the substrate's surface. The unique properties of SAWs, such as low energy consumption, high sensitivity, and compatibility with integrated circuit technology, have facilitated their extensive applications in sensors [2−4], filters [5−7], acoustic microfluidics [8−12], particles manipulation [13−18], among others. Although conventional SAW devices with fixed geometries are the cornerstone of major applications such as radio frequency (RF) filters and stable sensor platforms, they lack the dynamic reconfigurability or programmability required for booming applications in microfluidics and particle manipulation. Therefore, the development of dynamically modulated SAWs is essential to address the evolving requirements in modern technologies and intricate operational environments.

Currently, SAW modulation is primarily achieved through two distinct approaches. The first involves the integration of tailored metastructures onto a pre-existing SAW wavefront [19−23]. As SAWs propagate through these metastructures, their phase or amplitude is modulated, thereby alerting their morphological characteristics. This method offers high flexibility, enabling precise control over SAWs and waveguiding [24] by adjusting the dimensions, arrangement, and defects within the metastructure units. However, strong wave attenuation occurs upon interaction with these structures, and their fabrication remains complex. The second approach modifies the geometric configuration and arrangement of the IDT fingers to achieve the various SAW characteristics, such as slanted-finger IDTs [25,26], focused IDTs [27,28], chirped IDTs [29,30], multiple IDTs [31,32], and IDT arrays [33]. This method simplifies fabrication and improves energy conversion efficiency, enhancing the overall performance and reliability of SAW devices. While recent programmable IDT platforms [31–33] have demonstrated the ability to generate arbitrary wavefields, they typically rely on multi-channel driving architectures with independently controlled inputs, which increase system-level hardware complexity compared to single-input solutions. The practical deployment of such multi-input systems is often hindered by their inherent hardware complexity and the need for precise synchronization of multiple channels, posing a potential barrier to their broader adoption.

To overcome this limitation, we report an innovative approach for multidimensionally controlled SAWs generation using a programmable IDT array, enabling both efficient generation and flexible modulation of multiple waveforms through phase and frequency tuning. By integrating an externally controlled encoding circuit, each IDT unit within the array operates independently, allowing for precise phase transitions via a switching mechanism. Additionally, a programmable chirped IDT array is introduced to generate multifrequency SAWs, where gradually varying electrode widths enable tailored frequency responses. Time-division multiplexing (TDM) is employed to enable concurrent signal transmission by allocating distinct time slots to individual data streams within a shared channel [34−36]. This technique sequentially samples multiple signals, assigns each to brief, non-overlapping temporal windows, and reconstructs them at the receiver through synchronized decoding. The chirped IDT array leverages TDM to superimpose multifrequency SAWs through temporally encoded excitations, generating tailored focused acoustic fields—the so-called “SAW needle”—for advanced microfluidic and sensing applications. Furthermore, two-dimensional manipulation of particles is demonstrated through the encoded switching control of IDTs arranged in a one-dimensional configuration. The proposed multidimensional SAW modulation approach offers several advantages, including simplified fabrication, enhanced regulatory flexibility, and highly reduced acoustic energy attenuation. These attributes render the SAW devices highly efficient and adaptable for a wide range of applications in acoustic wave-based technologies.

Results
Programmable IDT Array Design. In our design, both standard and chirped IDT configuration are miniaturized laterally to form individual IDT unit, each capable of discrete control. An IDT array is assembled by arranging these identical units in parallel, with their corresponding electrode pins. The fabricated IDT array is patterned onto a lithium niobate (LiNbO ) wafer using the photolithography technique. To enable selective control, the electrode pins of the IDT array are connected to a control circuit via a flat flexible cable (FFC), allowing each IDT unit to be independently modulated through discrete switches integrated within the control module. This configuration provides precise phase and frequency control over the generated SAWs. The generation and modulation of multidimensional SAWs are achieved through sequentially encoded control of the discrete switches. The resultant acoustic field distribution is characterized by a laser Doppler vibrometer (LDV) with the laser beam focused on the surface of the LiNbO wafer, as shown in Fig. 1a.

To ensure compatibility with the FFC, the electrode pins extracted from this array are arranged in a uniform lateral spacing configuration. Full details on the standard and chirped IDT arrays are described in Supplementary Note 1. Each IDT unit has a pair of electrode pins, resulting in a total of 80 pins for the entire array. After post-extension, these 80 pins are aligned in a uniform, equidistant manner, with spacing of 500 µm. Each pin has a width of 250 µm and a length of 4 mm, as shown in Fig. 1b.

The individual IDT unit is controlled by a double pole double throw (DPDT) switch, as illustrated in Fig. 1c. To ensure the system stability under amplified voltages (>50 V), relatively high frequencies (>7 MHz) and prolonged operation (>8 hrs), a manually controlled DPDT switch was selected in the experiment. The dual pins emanating from the IDT unit are affixed to the respective terminals C and D of the DPDT switch. The input signal, maintained at a floating potential, is applied to terminals A and F, while terminals B and E are grounded. By toggling the DPDT switch, terminals C and D can be connected either to A and B, or to E and F. This switching mechanism enables inversion of the electrical potential across the IDT unit, effectively inducing the phase-inversion in the generated SAW. This binary modulation of the wave’s phase is referred to as “1” for the initial phase state and “0” for the phase-inverted state. Consequently, this programmable phase modulation provides a versatile and efficient means of dynamically controlling SAW properties, facilitating precise wave manipulation for various applications. The detailed fabrication and integration processes for the SAW device with the standard and chirped IDTs are comprehensively described in Supplementary Note 2.

Phase and Frequency Validation. The core mechanism in this work is based on the superposition of SAWs generated by each individual IDT unit. To effectively control the wavefront of the resultant SAW, it is essential to establish phase coherence among the individual SAW through the modulation of DPDT switches. In our experiment, the superpositioned SAW was synchronized with the signal generator and analyzed using the LDV measurements. The implementation details regarding the experimental setup are provided in Supplementary Note 3. Distinct SAW signals emitted by the IDT unit under the two switching states, “1” and “0” of the DPDT switch are demonstrated in Fig. 2a. The time-domain signals corresponding to these states exhibit an exact phase difference of π, confirming that the SAWs generated from individual IDT units can be modulated in a binary phase manner by toggling the DPDT switch. This capability enables precise phase control, which is fundamental for achieving programmable wavefront manipulation.

To evaluate the frequency response of the chirped IDT array, a frequency sweep measurement was performed. All control module states were initially set to “1” to maintain phase uniformity across the chirped IDT units, thereby generating planar SAWs. Multiple measurements were taken at different points and averaged to minimize experimental errors. The collected data were subsequently smoothed and normalized, producing the frequency response curve shown in Fig. 2b. The results indicate that the chirped IDT array exhibits a broadband response, with activity between 6.58 MHz and 9.45 MHz. It is worth noting that the multiple peaks observed in Fig. 2b originate not from structural resonances, but Fresnel ripples—an inherent feature of any finite-length, broadband chirp signal in both time and frequency domains [37]. Within this range, Fresnel ripple peaks were identified at f = 7.20 MHz, f = 7.81 MHz, f = 8.35 MHz, and f = 8.78 MHz. This analysis provides a comprehensive characterization of the array’s frequency response, forming a foundation for future multifrequency modulation and applications.

Additionally, for the chirped IDT array comprising 40 units separated by a fixed gap, ensuring the continuity and smoothness of the superpositioned SAW is crucial. A detailed LDV scan was conducted with the starting point at ~3 mm away from the chirped IDT array along the SAW propagation path. The scanning area was 2 mm × 1 mm with a step size of 20 µm. The scanned results of planar SAWs at the four Fresnel ripple peak frequencies from f to f are illustrated in Fig. 2c−f. The x-direction scan spans 1 mm, covering approximately 5 IDT units, while the y-direction scan spans 2 mm, which corresponds to approximately 4𝜆 of the SAWs. As shown in Fig. 2c−f, no obvious misalignment was observed between the SAWs generated by discrete IDT units, confirming that their wavefronts remain collinear. Furthermore, the amplitude of the generated SAWs is uniform, with negligible fluctuations. According to the Huygens–Fresnel principle, each individual unit can be regarded as a point source radiating the secondary wavelet. When multiple units are arranged in close proximity with the interunit gap (10 µm) much smaller than the wavelength (500 µm), the coherent superposition of the secondary wavelets results in a stable, uniform primary wavefront. The minimal interunit gap reduces acoustic energy loss, facilitating the coherent superposition of SAWs from adjacent IDT units. Furthermore, when the input signals to the IDT units are out-of-phase, the corresponding secondary wavelets also maintain a consistent anti-phase relationship, which has been discussed in our previous work [38].

SAW Waveform Modulation. In the standard IDT array, each individual IDT unit enables binary phase modulation of the SAW through the control of its corresponding DPDT switch. By programmably encoding the phase states of the SAWs generated by each IDT unit, various types of the superpositioned SAWs can be achieved, tailored for specific acoustic wave manipulation and control applications. As a demonstration, we generated Airy-type SAWs using the programmable IDT array. Following a similar phase design in our previous work [38], we binarized the Airy function [39], assigning a phase value of 𝜋 to amplitudes greater than 0 and a value of 0 to amplitudes less than 0 [40,41], as depicted in Fig. 3a. The binarized Airy function was then correlated with the spatial phase distribution of the IDT units. Given the limited number of the IDT units (only 40) in our experiment, the number of units assigned to each individual binarized state is illustrated in Fig. 3b. Experiments and simulations were conducted within a 4 cm  2 cm area in front of the IDT array, covering the SAW propagation zone. The experimental and simulation results are shown in Fig. 3c−f, respectively. For clarity, the IDT arrays generating Airy SAWs are highlighted in Fig. 3c and e, with black and white blocks representing the states “1” and “0”, respectively. The digit within each block indicates the number of the IDT units assigned to each state. To simplify the encoding representation, adjacent digits in the sequence correspond to binarized phases 0 and . In Fig. 3c and e, the digit sequences “7, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2” and “2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 7” indicate the arrangement of the IDT unit from the bottom to the top. Upon activation of the IDT array, the generated SAW’s acoustic field was scanned using the LDV. The resulting acoustic field distributions, shown in Fig. 3c and e, exhibit the characteristics bending trajectory of the Airy SAW. Notably, the Airy SAWs in Fig. 3c and e bend in opposite directions due to the reversed digit sequences, confirming the programmable nature of our approach. The corresponding simulation results in Fig. 3d and f closely match the experimental observations validate the accuracy of our encoding method. This programmability offers great flexibility in generating various types of SAWs, expanding potential applications in acoustic wave engineering and related fields. Detailed information regarding the simulation model and parameter settings can be found in Supplementary Note 4.

Spatially Focal Positioning Modulation. The superposition of the curved main lobes from two symmetrical Airy SAWs can generate a focused acoustic field. By positioning two co-axial standard IDT arrays in opposite orientations, a focused standing SAW is formed. In our experiment, we mapped a 2 cm × 1 cm area between the two IDT arrays using the LDV for detailed analysis. The predefined digit sequences encoded in the IDT arrays allow for vertical control of the focal point within the focused standing SAW.

The scanned acoustic field distribution reveals the characteristics of the focused SAW, as shown in Fig. 4a. The encoded digit sequences for both IDT arrays in Fig. 4a are “3, 3, 4, 12, 4, 3, 3, 2, 2, 2, 2”. The rationale for the encoded digit sequences can be found in Supplementary Note 5. A distinct focusing effect is observed, with the focal region appearing elongated along the wave propagation direction (x-direction), indicating a notable depth of focus. In contrast, the focal width (lateral resolution) in the perpendicular direction (y-direction) is much narrower. This focused acoustic field forms the basis for controlling particle movement along the y-direction in subsequent experiments. To achieve focal point shifting, the encoding sequence was adjusted by shifting 4 IDT units in the -y direction. The new sequences “2, 2, 3, 3, 4, 12, 4, 3, 3, 2, 2” and “2, 2, 2, 2, 3, 3, 4, 12, 4, 3, 3,” successfully moved the focal point downward, as demonstrated in Fig. 4b and c. The results show a consistent downward shift of the focal point while maintaining lateral position and focal depth. By extracting the acoustic field distributions along dashed lines A, B, and C, the measured focal displacements d and d were 0.88 mm and 0.96 mm, respectively, closely aligning with the theoretical displacement of 0.92 mm (4 units × 0.23 mm). Simulated acoustic fields (Fig. 4e−g) further validated these findings, with simulated focal displacements l and l measured at 0.9 mm, shown in Fig. 4h. These results confirm that modifying the IDT array encoding sequence enables precise focal point control in the y-direction.

Theoretically, the number of the central IDT units determines the initial position of the main lobe of the Airy SAW and, consequently, the focal point position of the combined focused SAW [42]. To validate this, we altered the encoding sequences to induce lateral focus shifts. The left-side IDT digit sequence was set to “2, 2, 2, 3, 3, 4, 8, 4, 3, 3, 2, 2, 2,” while the right-side sequence was “2, 3, 3, 4, 16, 4, 3, 3, 2,” resulting in a leftward focal shift, as shown in Fig. 5a. This shift occurred because fewer central units on the left generated a shorter focal length, while the increased number of units on the right produced a longer focal length. When both sides were symmetrically encoded with the digit sequence “2, 2, 3, 3, 4, 12, 4, 3, 3, 2, 2,” the focal lengths became equal, centering the focal point, as shown in Fig. 5b. Reversing the asymmetry—setting the left and right sequences to “2, 3, 3, 4, 16, 4, 3, 3, 2” and “2, 2, 2, 3, 3, 4, 8, 4, 3, 3, 2, 2, 2,” respectively—resulted in a rightward focal shift, symmetric to the first case (Fig. 5c). Cross-sectional acoustic field distributions extracted along dashed lines A, B, and C from Fig. 5a−c, shown in Fig. 5d, indicate focal displacements d₁ and d₂ of approximately 3.91 mm and 3.8 mm, respectively, which closely match the design values. Corresponding simulations (Fig. 5e−g) confirm these results, demonstrating consistent focal shifts. The cross-sectional acoustic intensities along the x-direction (Fig. 5h) reveal lateral displacements l₁ and l₂ of approximately 4 mm, further aligning with the experimental observations. Such dynamic focal position manipulation enabled by programmable IDT array coding can be used for controlled particle movement. The working principle for the particle control and corresponding experimental demonstration are discussed in Supplementary Note 6.

Multifrequency Focal Depth Modulation. By modifying the chirped IDT array’s encoding, with the digit sequence “2, 3, 3, 4, 16, 4, 3, 3, 2”, a focused SAW is generated. The acoustic field distributions of the focused SAWs at four different frequencies were scanned using LDV over a 1.5 cm × 2.5 cm propagation area, with the results shown in Fig. 6a−d. At the frequency of f , the generated SAW exhibits a strong focusing effect, forming an elongated focal spot near the chirped IDT array, as depicted in Fig. 6a. As the frequency increases to f , the focus shifts along the +x direction while maintaining focusing characteristics, as shown in Fig. 6b. At the frequency of f , the focal point shifts along the +x direction, as shown in Fig. 6c. Finally, at the frequency of f , the focal point reaches its farthest position from the IDT array, meanwhile still exhibiting a distinct focusing effect, as seen in Fig. 6d. These results demonstrate that the focus position can be effectively controlled by adjusting the excitation frequency. Cross-sectional profiles along the y- and x-direction at the focal points, indicated by white dashed lines in Fig. 6a−d, are analyzed with the results shown in Fig. 6e and f, respectively. The amplitude values are normalized to the maximum at the focal point. The acoustic field distribution along the y-direction (Fig. 6e) reveals that the focal points at all frequencies overlap, with a focal width of approximately 2𝜆, indicating consistent focus positioning and excellent symmetry. In contrast, along the x-direction (Fig. 6f), the focal position shifts farther from the chirped IDT array as the frequency increases, reaching a maximum displacement of approximately 11 mm. The average full-width at half-maximum (FWHM) of the focal depth along the x-direction was measured individually for each operating frequency. The obtained values are as follows: 22𝜆 at f₁ = 7.20 MHz, 29𝜆 at f₂ = 7.81 MHz, 28𝜆 at f₃ = 8.35 MHz, and 28𝜆 at f₄ = 8.78 MHz, respectively. This confirms the strong frequency dependence of SAW focusing, enabling precise control over the focal position through frequency tunning. This approach provides a tunable method for concentrating acoustic energy at specific locations, which is highly beneficial for practical applications.

The frequency-dependent focal position of focused SAWs generated by two primary mechanisms. First, within the chirped IDT array, designed with progressively wider finger widths, the generated SAWs with different frequencies are position-dependent: the activation regions for lower and higher frequency SAWs are at the rear and front of the chirped IDT array, respectively. Second, focused SAWs arise from the superposition of symmetric main lobes of Airy SAWs. At higher frequencies, reduced acceleration and main lobe curvature push the focal point further from the source. Together, these mechanisms enable precise frequency-based control of the focal position.

To validate the modulation effect of multi-frequency excitation on the focused SAW, the TDM technique was applied to temporally concatenate four discrete Fresnel ripple peak frequencies, thereby generating TDM waveforms. The technical implementation scheme and corresponding spatial-temporal modulation characteristics are analyzed in Supplementary Note 7. The TDM is generated using MATLAB, and the corresponding code is provided in Supplementary Note 8. The location of the focused energy along the x-axis varies with the operating frequency, as shown in Fig. 6f. The SAW with a higher frequency has a longer focal length from the excitation source. The focal positions of SAWs vary with excitation frequency, leading to distinct energy distributions at each focal point when multifrequency components are superimposed. By adjusting the relative contributions of different frequencies, the focusing effect can be sustained across an extended propagation distance, thereby increasing the focal depth. Since the generated SAWs with frequencies of f₁ (7.20 MHz) and f₄ (8.78 MHz) have the nearest and farthest focal points, respectively, their signal weighting should be enhanced. Meanwhile, the generated SAWs with frequencies of f₂ (7.81 MHz) and f₃ (8.35 MHz) have the focused energy distributions that overlap with those of f₁ and f₄ to a large extent. Therefore, their relative contributions should be minimized to achieve a more uniform energy distribution along the x-axis across the four frequencies, thus extending the effective focal depth. A reference TDM signal with equal cycle allocations (f : f : f : f = 5:5:5:5) serves as a baseline configuration, where each ratio value indicates the number of wavelength cycles per frequency component. LDV scans over a 15 mm × 40 mm propagation area mapped the acoustic field distributions for various TDM configurations (Fig. 7a−e). All tested frequency ratios maintained strong focusing performance while demonstrating progressive focal depth extension. Cross-sectional intensity profiles along the propagation direction (x-axis) extracted from Fig. 7, enable quantitative comparison of focal depth variations across TDM configurations (Fig. 8). These profiles permit systematic evaluation of both focal depth and axial energy distribution for each frequency ratio combination.

The relationship between TDM signal composition and focal depth is quantified using FWHM analysis of the acoustic field profiles, as shown in Fig. 8. Increasing the proportion of f (8.78 MHz) from the baseline (5:5:5:5) to an optimized configuration (5:0:4:11) ratios results in the focal depth extension from 40λ to 43λ by temporally stitching the acoustic fields of generated SAWs with different frequencies. However, excessive f weighting reduces the focal depth to 27λ due to diminished near-field contributions from f (7.20 MHz). This nonlinear behavior results from unbalanced energy distribution: a dominant f components amplifies distal focusing but weakens proximal intensity, disrupting superposition across the extended focal depth. For the frequency combination of (5:0:4:11), the SAW energy assigned to the frequency of f₂ is 0, meaning that the f₂-frequency SAW has no contribution. This is likely because the f₂-frequency SAW energy distribution overlaps with those of f₁ and f₃, while its peak is higher than that of f₃ (see Fig. 6f). Therefore, to extend the focal depth, our proposed frequency-weighting strategy is to suppress f₂ and f₃ while increase f₄. As a result, we experimentally optimized (5:0:4:11) ratio to achieve the extended focal depth of 43λ with uniform energy distribution.

Methods
Simulation. Numerical simulations were performed using the Piezoelectricity module in COMSOL Multiphysics. A two-dimensional model of a 128° Y-X cut LiNbO₃ substrate was constructed to reduce computational cost while maintaining accuracy. Perfectly matched layers (PMLs) with a thickness of approximately one wavelength (500 μm) were applied around the substrate to absorb boundary reflections. The IDT array electrodes were modelled on the substrate surface and excited with either in-phase or out-of-phase voltage signals (20 Vₚₚ) to control the acoustic phase. The resulting acoustic field distributions were visualized by plotting the displacement field.

Experiment. The IDT arrays were fabricated on a 128° Y-X cut LiNbO₃ substrate using standard photolithography, followed by deposition of a 3-nm Cr adhesion layer and a 50-nm Au electrode layer via electron beam evaporation. The arrays consist of 40 independently addressable IDT units, each connected to a control module equipped with DPDT switches for binary phase inversion. SAWs were generated by applying AC signals (20 Vₚₚ, 7.98 MHz for standard IDTs; 5–12 MHz swept for chirped IDTs) from a signal generator (DG4102, Rigol, China). The out-of-plane displacement fields of propagating SAWs were measured using a LDV (PSV-500 Scanning Head, Polytec, Germany). The entire setup was mounted on a two-axis stepper motor translation stage with 10 μm positioning resolution.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Article title : « Multidimensionally Controlled Surface Acoustic Waves Generation via Programmable Interdigital Transducer\nArrays »\nWhat are the noteworthy results?\nThis study addresses the generation of two-dimensionally controlled surface acoustic waves (SAWs) using a programmable\ninterdigital transducer (IDT) array. The authors developed both a single-frequency and a broadband chirped IDT system with\nan aperture of 8.8 mm. The aperture is segmented into 40 parallel emitting units, each capable of on-demand phase\ninversion using double-pole double-throw (DPDT) switches. This 1-bit phase modulation of SAW emission wavefront\nenabled the generation of non-diffracting Airy SAWs and dynamically focused wavefronts. Furthermore, by incorporating\ntime-division multiplexing (TDM) with the chirped IDT array, the authors achieved extended focal depth.\nCurrently, the switches are operated manually, but the approach is amenable to automation. The system requires only a\nsingle-channel arbitrary waveform generator, and the fabrication of the IDT array is relatively simple.\nWill the work be of significance to the field and related fields? How does it compare to the established literature?\nThe work is of potential interest to the microfluidics and acoustic manipulation communities. Although programmable IDT\nconcepts have been previously explored, their representation in the literature remains limited, and the authors' overview\ngenerally reflects the current state. Nevertheless, the following reference should be added to improve completeness: DOI:\n10.1039/c9lc00465c. Given the modest requirements of the presented platform in terms of equipment and processing, the\napproach offers a resource-efficient alternative to more complex programmable IDT systems.\nOne of the central statements in the introduction may require revision for accuracy:\n“Despite their advantages, both approaches share the same fundamental limitation: once metastructures or IDTs are\nfabricated, they can generate only a single type of SAWs, lacking the flexibility to produce diverse waveforms within a single\ndevice.”\nThis statement is not universally applicable. Systems presented in [31, 32] are capable of generating arbitrary SAW fields\nwithin a single device (e.g., plane waves of arbitrary direction, focused beams, etc.). While it is true that the present approach\noffers advantages in implementation simplicity and hardware requirements, the claim should be reformulated to reflect the\nactual limitations more accurately.\nDoes the work support the conclusions and claims, or is additional evidence needed?\nThe experimental data, which include simulations, laser Doppler vibrometry (LDV) measurements and particle manipulation\nvideos, support the authors’ conclusions.\nAre there any flaws in the data analysis, interpretation and conclusions? - Do these prohibit publication or require revision?\nAlthough the main results are substantiated, the manuscript would benefit from improved consistency in presentation and\nterminology. For example, the use of the term “resonant frequencies” for the chirped IDT is problematic:\nLines 158–159:\nThe statement “Fig. 2c–f presents the scanned results of planar SAWs at the four resonant frequencies” should be revised.\nThe IDT used in the experiment is a hyperbolic-type chirped transducer, which operates over a broad frequency range and\ndoes not exhibit discrete resonances in the conventional sense.\nFigure below represents time and frequency-domain impulse response of the chirped transduces as described in\nSupplementary Note 1. The spectral peaks observed in the impulse response and the corresponding local maxima in the\nLDV measurements are not due to resonant behavior but rather arise from interference effects associated with the\nbroadband excitation. These features are consistent with Fresnel ripples, as described in [https://doi.org/10.1049/ip-f-\n1.1980.0018]. Such ripples are characteristic of broadband, spatially modulated emission and do not reflect intrinsic\nresonant properties of the structure.\nThe authors are advised to refer to these frequencies as “frequencies corresponding to Fresnel ripples” instead of “resonant\nfrequencies,” and to explicitly state that a hyperbolic-type chirped IDT is employed.\nfrom https://doi.org/10.1049/ip-f-1.1980.0018\nIs the methodology sound? Does the work meet the expected standards in your field?\nIn general, the overall idea is interesting, but several important issues remain:\n• The limitations of the approach (insertion loss, attenuation, etc.) are not discussed.\n• There is no comparison with existing methods in the literature.\nOther issues could be cites as follows:\n• Possible thermal effects or power limits to avoid IDT degradation are not addressed. In the demonstration video, did you\nquantify the power required to move the particles? Did you observe any thermal effects? Is there a power limit beyond which\nthe IDTs could degrade?\n• The MATLAB code used to generate the TDM signal is not shared or referenced.\n• No data on absolute SAW displacements is given.\n• The coupling effect between the IDTs is not considered.\n• No quantitative data on the power required to move the particles is provided, despite the demonstration video.\nIs there enough detail provided in the methods for the work to be reproduced?\nIn general, yes. However:\n• No insight into how programming sequences (like “2, 2, 3, 3, 4, 12, 4, 3, 3, 2, 2”) other than the first one are provided.\n• No details are provided on the simulation methodology, not even in the appendix. Are the beam steering phenomenon on\nY 128° LiNbO3 and other anisotropy processes (X-direction dependent K2, etc.) taken into account in the simulation? Some\nstrong limitation on beam divergence are observed on Y 128° LiNbO3 : https://doi.org/10.3390/s25041067\nOther remarks\n1.\nAccording to the provided artwork and references to the switches, the switches appear to have been operated manually.\nHowever, this is not explicitly stated in the article. In the reviewer’s opinion, it should be.\n2.\nEven if it may seem obvious, it would be better to explicitly state the relation between the single-unit aperture, the inter-unit\ngap, and the IDT operation wavelength.\n3.\nThe article contains numerous AI-style statements at the end of paragraphs. These self-repeating, self-promoting sentences\nmake the text difficult to read. A more neutral writing style would be preferable. For example:\n• “This co-design of excitation and measurement protocols enabled accurate reconstruction of the acoustic field distribution,\nthereby validating the ability of the chirped IDT array to generate multifrequency SAWs.” – This phrase is overly ambitious\nfor what is essentially a simple adjustment of LDV measurement settings.\n• “This approach effectively mitigates spectral crosstalk limitations in conventional multifrequency SAW systems while\nmaintaining phase coherence over extended propagation distances.” – The statement lacks supporting details and\nreferences. No phase coherence measurements over extended propagation distances are provided.\n• “This programmability offers significant flexibility in generating various types of SAWs, expanding potential applications in\nacoustic wave engineering and related fields.” – This self-promoting statement appears outside the introductory section and\nadds little informational value.\nAll three examples follow the same grammatical template, which contributes to a repetitive and uncritical tone.\n4.\nFor the sake of reader comfort, the authors are encouraged to cite the IDT unit length (i.e., the value of N_i × λ/2 for the\nstandard configuration) and the aperture of the fabricated IDT arrays.\n5.\nThe new sequences “2, 2, 3, 3, 4, 12, 4, 3, 3, 2, 2” and “2, 2, 2, 2, 3, 3, 4, 12, 4, 3, 3,” (FIG 4c) successfully moved the focal\npoint downward, as demonstrated in Fig. 4b and c. However, the sequence “2, 2, 3, 3, 4, 12, 4, 3, 3, 2, 2” cannot be identified\nin Fig. 4b. Please ensure the text and figures correspond accurately.\n6.\nIn Fig. 2(c–e), it is not clear where the scanning region is located relative to the IDT array.\n7.\nDid you observe any issues with the adhesion or possible delamination of the thin Cr/Au electrode layer (3 nm of chromium /\n50 nm of gold) during the bonding process, considering the relatively high temperature (140 °C) and pressure (180 MPa)\napplied for 10 seconds? In addition, could you explain the choice of these specific thicknesses (3 nm Cr and 50 nm Au)?\nWere they selected based on adhesion, electrical performance, or another technological constraint?\n8.\nS1. Does W, d and g have the same values for standard and chirped Programmable IDT Affays? They are not the same\nwhile looking at the figure S1 and nothing is said concerning their values for the chirped array. On the photo in figure S2 one\ncan see that they are the same, but it is better to explicitly indicate this in the text.\n9.\nA better summary of the supplementary notes is recommended. The main text is difficult to follow due to missing essential\ndetails. In particular, some general information about the particle manipulation experiments should be included in the main\narticle.\n10.\nLine 218: “A distinct focusing effect is observed, with the focal point appearing elongated along the wave propagation\ndirection (x-direction), exhibiting a notable focal depth. In contrast, the focal depth in the perpendicular (y-direction) is\nnarrower.”\nThe term “focal depth in the perpendicular (y-direction)” is somewhat ambiguous. A suggested rewording is:\n“A distinct focusing effect is observed, with the focal region appearing elongated along the wave propagation direction (x-\ndirection), indicating a notable depth of focus. In contrast, the focal width (lateral resolution) in the perpendicular direction (y-\ndirection) is significantly narrower.”\n11.\nThe relationship between the TDM signal composition and focal depth is quantified using full-width at half-maximum\n(FWHM) analysis. What is the average FWHM value of the focal depth for each frequency (f₁, f₂, f₃, f₄) used individually (7.20\nMHz, 7.81 MHz, 8.35 MHz, and 8.78 MHz), as shown in Fig. 6(f)? This information would be valuable to highlight the\nefficiency of TDM excitation in achieving an extended focal depth (i.e., forming a SAW needle).\n12.\nThe main article is difficult to understand without consulting the supplementary materials. However, the key insights should\nbe accessible from the main article alone. It is necessary to redistribute the information more effectively between the main\ntext and the supplementary materials, ensuring that the latter serves a truly supplementary role.", "reviewer_2": "In the manuscript, a programmable IDT array architecture is proposed for multidimensional SAW generation, enabling\ndiverse SAW waveforms through programable phase encoding for precise focus manipulation. It is a novel and useful work,\nhowever, there are some questions need to be addressed in the manuscript.\n1. Both the standard and chirped IDTs configuration are miniaturized laterally to form individual IDT unit. This results in a\nreduced acoustic aperture, which enhances diffraction effects and decreases acoustic energy. Could this affect the response\nof the IDT array? Please provide an explanation.\n2. Beam steering may occur during surface acoustic waves propagation. Could this phenomenon lead to undesired\ninterference between adjacent waves in the IDT array?\n3. Could the authors provide further justification for selecting numbers such as 2, 3, 4, 8, and 12 in the encoding process?\n4. In Section ‘Multifrequency Focal Depth Modulation’, the authors demonstrate that (5:0:4:11) is the optimized configuration\nratios, please clarify the rationale for this selection. Furthermore, Fig.7 and Fig.8 do not convincingly demonstrate that this\nratio provides the best trade-off between focal depth and energy uniformity. The authors should provide additional evidence\nto substantiate this conclusion.\n5. Color bars are missing from all simulation results.", "reviewer_3": "Review\nThe authors present a new type of SAW setup, combining several independent interdigital transducers (IDTs) with very\nsmall aperture next to each other, combined with a multiplexed, binary (i.e. two-state) phase-controlled electrical\nsignaling. This allows the flexible excitation and on-demand modulation of partial waves to realize complex Surface Acoustic Wave\nfields, e.g. for acoustofluidic actuation purposes. The manuscript is part of an actual trend towards higher acoustic wave field\ncontrol, the setup demonstrated is new and highly interesting for the broader acoustofluidics and microfluidics research\nsociety. The correct electric excitation itself, however, can be complex and may limit the adoption of the new method by less\nexperienced researchers, or labs with less extensive rf electrical device infrastructure. Investigations of the SAW excitation\nwere carried out by electrical measurement and laser-Doppler vibrometry. An experimental proof of particle manipulation is\ngiven. The manuscript is written in very good language and important details are provided (few are missing, as indicated\nbelow).\nMinor comments/requests:\n• It would be very interesting, to also see the |S11| plots of both IDT configurations, with and without the phase-switching\nboard.\n• Line 102: Please explain, what is meant by “post-extension”.\n• The simulation approach is not explained and should be provided in detail.\n• Line 334: “Discussion” should be changed into “Conclusion”\n• Details of the vibrometry settings during measurement of TDM configurations should be given"}, "author_response": "1. What are the noteworthy results?\nThis study addresses the generation of two-dimensionally controlled surface\nacoustic waves (SAWs) using a programmable interdigital transducer (IDT) array.\nThe authors developed both a single-frequency and a broadband chirped IDT\nsystem with an aperture of 8.8 mm. The aperture is segmented into 40 parallel\nemitting units, each capable of on-demand phase inversion using double-pole\ndouble-throw (DPDT) switches. This 1-bit phase modulation of SAW emission\nwavefront enabled the generation of non-diffracting Airy SAWs and dynamically\nfocused wavefronts. Furthermore, by incorporating time-division multiplexing\n(TDM) with the chirped IDT array, the authors achieved extended focal depth.\nCurrently, the switches are operated manually, but the approach is amenable to\nautomation. The system requires only a single-channel arbitrary waveform\ngenerator, and the fabrication of the IDT array is relatively simple.\nReply:\nWe sincerely appreciate the reviewer’s thorough and insightful summary of our\nwork. Regarding the reviewer’s comment, we would like to clarify that the\nmanual switch used in the current experiment was carefully selected to ensure\nsystem stability. Given the operating conditions—specifically, the relatively high\nfrequency (above 7 MHz), amplified voltage (exceeding 50 V), and prolonged\nduration (8 hours)—the DPDT switches were chosen for their reliable\nperformance in maintaining stable phase switching within the circuit under\nthese demanding conditions.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nPer the suggestion by the reviewer, we have added the following information:\n“To ensure the system stability under amplified voltages (>50 V), relatively high\nfrequencies (>7 MHz) and prolonged operation (>8 hrs), a manually controlled DPDT\nswitch was selected in the experiment.” Please refer to Line 3-5 from the bottom on\nPage 4 in the revised manuscript.\n2. Will the work be of significance to the field and related fields? How does it\ncompare to the established literature?\nThe work is of potential interest to the microfluidics and acoustic manipulation\ncommunities. Although programmable IDT concepts have been previously\nexplored, their representation in the literature remains limited, and the authors'\noverview generally reflects the current state. Nevertheless, the following\nreference should be added to improve completeness: DOI: 10.1039/c9lc00465c.\nGiven the modest requirements of the presented platform in terms of equipment\nand processing, the approach offers a resource-efficient alternative to more\ncomplex programmable IDT systems.\nReply:\nWe thank the reviewer for this positive feedback and for highlighting the\nsignificance of our work to the microfluidics and acoustic manipulation\ncommunities.\nWe also greatly appreciate the suggestion of the key reference DOI:\n10.1039/c9lc00465c and we have added this reference into our manuscript to\nprovide a more complete overview of the literature.\nPer the suggestion by the reviewer, we have added the mentioned reference in\nour revised manuscript, “and IDT arrays [33].” Please refer to Line 3 on Page 3\nand the added Ref. 33 in the revised manuscript.\n3. One of the central statements in the introduction may require revision for\naccuracy:\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\n“Despite their advantages, both approaches share the same fundamental\nlimitation: once metastructures or IDTs are fabricated, they can generate only a\nsingle type of SAWs, lacking the flexibility to produce diverse waveforms within a\nsingle device.”\nThis statement is not universally applicable. Systems presented in [31, 32] are\ncapable of generating arbitrary SAW fields within a single device (e.g., plane\nwaves of arbitrary direction, focused beams, etc.). While it is true that the present\napproach offers advantages in implementation simplicity and hardware\nrequirements, the claim should be reformulated to reflect the actual limitations\nmore accurately.\nReply:\nWe sincerely thank the reviewer for this critical and accurate observation. We\nagree that our original statement was overgeneralized and did not adequately\nacknowledge the capabilities of prior programmable IDT systems, such as those\npresented in references [31, 32], which can indeed generate diverse wavefields\nwithin a single device. We have thoroughly revised the statement in the\nintroduction to reflect a more precise and accurate comparison.\nPer the suggestion by the reviewer, we have modified the following information,\n“However, the wavefronts generated by conventional static devices are fixed and lack\npost-fabrication programmability. While recent programmable IDTs [31, 32] have\nbroken this paradigm, their reliance on multi-input systems presents a barrier to\nwidespread adoption.” Please refer to Line 5-8 on Page 3 in the revised\nmanuscript.\n4. Are there any flaws in the data analysis, interpretation and conclusions? - Do\nthese prohibit publication or require revision?\nAlthough the main results are substantiated, the manuscript would benefit from\nimproved consistency in presentation and terminology. For example, the use of\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nthe term “resonant frequencies” for the chirped IDT is problematic:\nLines 158–159:\nThe statement “Fig. 2c–f presents the scanned results of planar SAWs at the four\nresonant frequencies” should be revised. The IDT used in the experiment is a\nhyperbolic-type chirped transducer, which operates over a broad frequency\nrange and does not exhibit discrete resonances in the conventional sense.\nFigure below represents time and frequency-domain impulse response of the\nchirped transduces as described in Supplementary Note 1. The spectral peaks\nobserved in the impulse response and the corresponding local maxima in the\nLDV measurements are not due to resonant behavior but rather arise from\ninterference effects associated with the broadband excitation. These features are\nconsistent with Fresnel ripples, as described in\n[https://doi.org/10.1049/ip-f-1.1980.0018]. Such ripples are characteristic of\nbroadband, spatially modulated emission and do not reflect intrinsic resonant\nproperties of the structure.\nThe authors are advised to refer to these frequencies as “frequencies\ncorresponding to Fresnel ripples” instead of “resonant frequencies,” and to\nexplicitly state that a hyperbolic-type chirped IDT is employed.\nfrom https://doi.org/10.1049/ip-f-1.1980.0018\nReply:\nWe are deeply grateful to the reviewer for this exceptionally insightful and\ncorrect theoretical point. We sincerely apologize for the inaccurate use of the\nterm \"resonant frequencies\" in our original manuscript and fully agree with the\nreviewer's assessment. The spectral features we observed are indeed\ncharacteristic Fresnel ripples arising from the broadband, and not discrete\nresonances. We have thoroughly revised the manuscript to correct this flaw in\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nterminology and interpretation. We have replaced all instances of \"resonant\nfrequency\" in the manuscript with \"Fresnel ripple peak frequencies\" to more\naccurately describe the spectral features observed in the LDV measurements.\nPer the suggestion by the reviewer, we have added the following information, “It\nis worth noting that the multiple peaks observed in Fig. 2b originate not from structural\nresonances, but Fresnel ripples—an inherent feature of any finite-length, broadband\nchirp signal in both time and frequency domains [37].” Please refer to Line 3-5 on\nPage 7 in the revised manuscript.\n5. Is the methodology sound? Does the work meet the expected standards in your\nfield?\nIn general, the overall idea is interesting, but several important issues remain:\nThe limitations of the approach (insertion loss, attenuation, etc.) are not\ndiscussed. There is no comparison with existing methods in the literature.\nReply:\nWe greatly appreciate the reviewer for the insightful comments. To evaluate the\ninsertion loss, we have conducted additional experiments to further characterize\nthe performance of the device, including S-parameter measurements. Since the\nIDT array functions as an integrated electrode system, measuring the S₁₁\nparameter is more appropriate than evaluating insertion loss or attenuation,\namong other metrics. Therefore, we have supplemented the S₁₁ parameter and\nrelevant analysis. In addition, we have included a comparative analysis between\nthe proposed method and existing approaches in the revised manuscript.\nPer the suggestion by the reviewer, we have added the following discussion, “To\ncharacterize the performance of the IDT array electrodes, the S₁₁ parameter was\nmeasured, as this structure is individually wired and integrated with a backend\ndriving system. The S₁₁ response provides a direct evaluation of impedance matching\nat the input port of the driving system and reflects the actual output behavior of the\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nelectrodes. The backend driving system incorporates a critical and complex\nphase-switching board, whose presence significantly influences the performance of\nthe IDT array. Therefore, the S₁₁ parameters of both the standard and chirped IDT\narrays were measured under two conditions: with and without the integrated control\nmodule, as shown in Fig. S6. When the standard IDT array was connected without the\ncontrol module (i.e., directly wired without phase control capability), the S₁₁ response,\nindicated by the blue curve in Fig. S6a, exhibited a pronounced dip in the frequency\nrange of approximately 7 MHz to 8.5 MHz. The minimum value reached about –3 dB\nnear 7.8 MHz, which aligns well with the designed resonance frequency of 7.98 MHz.\nWhen the control module was connected to the IDT array, a resonant response near\n7.8 MHz was still observable in the S₁₁ spectrum, as shown by the red curve in Fig.\nS6a. However, the overall magnitude of S₁₁ increased, indicating much higher\nreflectivity and reduced overall efficiency of the device. This degradation primarily\nresults from the challenge in achieving perfect impedance matching between the IDT\narray and the complex backend control circuitry. To compensate for the reduced\nefficiency and ensure a sufficient signal-to-noise ratio during acoustic field scanning,\na relatively high driving voltage of 20 Vₚₚ was applied in the experiments. Similar\nbehaviors were observed in the chirped IDT array, as shown in Fig. S6b. Furthermore,\nthe chirped IDT array exhibits a notably broader operating bandwidth compared to\nthe standard IDT array, maintaining favorable performance across a frequency range\nfrom 6 MHz to 9.5 MHz, with its best performance also approaching –3 dB. This\nresult is consistent with the spectral response shown in Fig. 2b.” Please refer to Line\n1-6 from the bottom on Page 5 to Line 1-21 on Page 6 in revised SI.\nIn addition, we have added a comparative analysis between the proposed method\nand existing approaches in the revised manuscript, “However, the wavefronts\ngenerated by conventional static devices are fixed and lack post-fabrication\nprogrammability. While recent programmable IDTs [31, 32] have broken this\nparadigm, their reliance on multi-input systems presents a barrier to widespread\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nadoption.” Please refer to Line 5-8 on Page 3 in the revised manuscript.\n6. Other issues could be cited as follows:\n•Possible thermal effects or power limits to avoid IDT degradation are not\naddressed. In the demonstration video, did you quantify the power required to\nmove the particles? Did you observe any thermal effects? Is there a power limit\nbeyond which the IDTs could degrade?\nReply:\nWe thank the reviewer for this excellent question, which highlights critical\npractical considerations for deploying our technology in real-world applications\nlike acoustic manipulation. We employed a 20 V excitation voltage during the\npp\nacoustic field scanning using the LDV. Our measurements confirmed that under\nprolonged excitation (exceeding 4h) at this voltage, the device temperature\nremained stable below 60°C. Although a frequency shift of approximately 3%\nwas observed under these conditions, the performance of the IDTs exhibited no\nsignificant degradation, and stable signals could still be reliably measured. Given\nthat this frequency shift had negligible impact on the experimental outcomes,\nactive temperature compensation was deemed unnecessary. However, during\nparticle manipulation, the amplified voltage reached 60 V . Under these\npp\nconditions, the temperature in the IDTs region exceeded 110°C. Prolonged\noperation at such voltages could lead to cracking of the lithium niobate substrate\ndue to thermal stress. Therefore, the entire experimental process was strictly\nlimited to within 5 minutes to avoid thermal damage. Additionally, as the\nreviewer rightly pointed out, the significant temperature rise induced by the high\nvoltage used for particle manipulation can indeed lead to performance\ndegradation of the IDTs. This effect can also be observed in the supplementary\nvideo, where the motion of the particles appears less stable during the final\nsegment of the manipulation process.\n•The MATLAB code used to generate the TDM signal is not shared or referenced.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nReply:\nWe have separately provided a MATLAB file for generating the TDM signal. Please\nrefer to Supplementary Note 8 – MATLAB codes for TDM signal generation in\nrevise SI.\n•No data on absolute SAW displacements is given.\nReply:\nWe would like to provide further clarification regarding the reviewer’s comment\non the absence of absolute SAW displacement data. The raw data collected using\nthe LDV consists of voltage signals corresponding to the original electrical\noutput. These voltage signals can be converted into physical quantities such as\nvelocity, displacement, and acceleration. In this study, to facilitate clearer\ninterpretation by the readers, the displacement values derived from the\nconversion were subsequently normalized.\n•The coupling effect between the IDTs is not considered.\nReply:\nWe sincerely thank the reviewer for raising this critical methodological point.\nThe coupling effect between adjacent IDT elements is indeed a fundamental\nconsideration in array design, and we appreciate the opportunity to clarify this\naspect of our work. As shown in Fig. 2c–f, the planar wave formed by the\nsuperposition of sub-waves generated by multiple IDT units under in-phase\nexcitation exhibits rather high uniformity and stability across different\nfrequencies, with no observable crosstalk caused by coupling between adjacent\nsub-waves. This performance can be attributed to the fact that the distance\nbetween adjacent IDT units (10 µm) is significantly smaller than the wavelength\n(500 µm), which ensures stable and coherent superposition of in-phase\nsub-waves. Furthermore, when the input signals to the IDT units are in opposite\nphases, the corresponding sub-waves also maintain a consistent anti-phase\nrelationship, a phenomenon that has been discussed in our previous work [38].\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\n•No quantitative data on the power required to move the particles is provided,\ndespite the demonstration video.\nReply:\nWe thank the reviewer for highlighting the need for quantitative data to support\nthe particle manipulation demonstration. In Supplementary Note 4, we\nmentioned that a voltage of 600 mV was used in the particle manipulation\npp\nexperiments, which was amplified by a factor of 100 before being applied to the\nSAW device. Below we provide further details regarding this experimental setup.\nPer the suggestion by the reviewer, we have added the following information, “It\nis important to note that the relatively high amplified voltage applied to the device\ncan lead to a rapid temperature increase in the IDTs. The resulting thermal effect may\ncause performance degradation of IDTs, or even device fracture due to overheating in\nsevere cases. Therefore, the duration of particle manipulation was strictly limited to\nwithin 5 mins in our experiments.” Please refer to Line 7-11 on Page 9 in revised SI;\n“However, as observed in the final segment of the supplementary video (Fig. S9d–f),\nthe motion of the particles exhibits some instability, along with noticeable trajectory\ndeviations. This behavior can be attributed to the performance degradation of IDTs\ncaused by thermal effects under high driving voltage.” Please refer to Line 1-3 from\nthe bottom on Page 11 and Line 1-2 on Page 12 in revised SI;\n“The acoustic field distribution herein was normalized.” Please refer to Fig. 2b\ncaption on Page 6 in the revised manuscript;\n“According to the Huygens–Fresnel principle, each individual unit can be regarded as\na point source radiating the secondary wavelet. When multiple units are arranged in\nclose proximity with the interunit gap (10 µm) much smaller than the wavelength (500\nµm), the coherent superposition of the secondary wavelets results in a stable, uniform\nprimary wavefront. The minimal interunit gap reduces acoustic energy loss,\nfacilitating the coherent superposition of SAWs from adjacent IDT units. Furthermore,\nwhen the input signals to the IDT units are out-of-phase, the corresponding secondary\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nwavelets also maintain a consistent anti-phase relationship, which has been discussed\nin our previous work [38].” Please refer to Line 1-10 from the bottom on Page 7 in\nrevised manuscript.\n7. Is there enough detail provided in the methods for the work to be reproduced?\nIn general, yes. However:\n•No insight into how programming sequences (like “2, 2, 3, 3, 4, 12, 4, 3, 3, 2, 2”)\nother than the first one are provided.\nReply:\nWe are grateful to the reviewer for these insightful and critical comments, which\nhave helped us significantly improve the clarity and rigor of our methodology\nsection. To exploit the bending property of the Airy SAW near the main lobe,\ntwo symmetric Airy SAWs were designed to coincide at their main lobes,\nresulting in a focused SAW profile with enhanced energy concentration. Due to\nthe limited total number of available IDT units (40), the integer-item encoding\nwas approximated to achieve the desired focused sequence. We have accordingly\nsupplemented the corresponding section in the manuscript to provide a more\ndetailed explanation.\nPer the suggestion by the reviewer, we have added the following paragraph to\nexplain the selection of the IDT digit sequence, “By applying phase encoding to the\nexisting 40-unit IDT array, the desired SAW waveform—such as the Airy SAW\nencoded in Fig. 3—can be achieved. To exploit the bending property of the Airy SAW\nnear the main lobe, two symmetric Airy SAWs were designed to coincide at their main\nlobes, resulting in a focused SAW profile with enhanced energy concentration. Fig.\nS3a and b show the Airy function and its corresponding binarized phase distribution,\nrespectively [38,39]. The Airy function was truncated from x = -10 to x = 0.66 and\nthen symmetrically spliced at the main lobe to obtain the phase distribution of a\nfocused SAW, as shown in Fig. S3c. The corresponding binarized phase distribution is\npresented in Fig. S3d. Due to the limited total number (only 40) of IDT units, the\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nphase distribution could only be approximated to the nearest integers. As shown in\nFig S3e, the resulting digit sequence was determined as “2, 2, 3, 3, 4, 12, 4, 3, 3, 2,\n2”, where black and white squares represent phase values of 𝜋 and 0, respectively.”\nPlease refer to the added Supplementary Note 5 on Page 7 and 8 in revised SI.\n•No details are provided on the simulation methodology, not even in the\nappendix. Are the beam steering phenomenon on Y 128° LiNbO and other\n3\nanisotropy processes (X-direction dependent K , etc.) taken into account in the\n2\nsimulation? Some strong limitation on beam divergence are observed on Y 128°\nLiNbO : https://doi.org/10.3390/s25041067\nWe thank the reviewer for emphasizing the importance of anisotropy. As rightly\nnoted by the reviewer, lithium niobate exhibits anisotropic characteristics,\nmeaning that the SAW propagation velocity varies with different crystal cuts and\npropagation directions. We fully considered this aspect in our COMSOL\nsimulations. Specifically, the crystal cut of lithium niobate was explicitly set to\n128° Y-X cut in the model to ensure consistency in the simulated acoustic wave\nvelocity. Regarding the beam divergence phenomenon mentioned by the\nreviewer in the cited references, we would like to clarify that this aspect was\nconsidered during the design of our IDTs. While beam divergence tends to be\nmore pronounced in IDTs with narrower apertures, the overall aperture width in\nour IDT array design is sufficiently large to confine noticeable divergence effects\nprimarily to the edge regions of the structure. Therefore, we reasonably\nneglected its influence in the central region throughout our experimental\nanalysis. The results presented in Fig. 2c–f further confirm that the SAW\npropagation in the central area remains straight and stable, with no observable\nbeam divergence, thereby validating our design approach.\nAccordingly, we have also added the simulation model settings, “In our\nsimulations, we performed a frequency-domain analysis of the acoustic field\ngenerated by the designed IDT array using the Piezoelectricity module in COMSOL\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nMultiphysics. Given that SAWs propagate primarily along the substrate surface, a\ntwo-dimensional model was constructed in COMSOL to reduce computational cost\nwhile maintaining simulation accuracy. A simulation domain of 4 cm × 3 cm was\ndefined, and the material was set as LiNbO , as shown in Fig. S2. It is important to\n3\nnote that the LiNbO crystal orientation was specifically configured as 128° Y-X cut.\n(500 µm) were applied around the LiNbO substrate to absorb any reflected acoustic\n3\nwaves from the boundaries. Subsequently, the IDT array electrodes were constructed\non the substrate, with each electrode excited by either in-phase or out-of-phase\nvoltage signals to control the acoustic phase. By strategically arranging the\ndistribution of these voltage polarities, the desired acoustic field profile could be\nachieved. The applied voltage to the electrodes was set at 20 Vₚₚ.” Please refer to the\nadded Supplementary Note 4 on Page 6 and 7 in revised SI.\n8. According to the provided artwork and references to the switches, the switches\nappear to have been operated manually. However, this is not explicitly stated in\nthe article. In the reviewer’s opinion, it should be.\nReply:\nPer the suggestion by the reviewer, we have added the following details in the\nrevised manuscript, “To ensure the system stability under amplified voltages (>50 V),\nrelatively high frequencies (>7 MHz) and prolonged operation (>8 hrs), a manually\ncontrolled DPDT switch was selected in the experiment.” Please refer to Line 3-5\nfrom the bottom on Page 4 in the revised manuscript.\n9. Even if it may seem obvious, it would be better to explicitly state the relation\nbetween the single-unit aperture, the inter-unit gap, and the IDT operation\nwavelength.\nReply:\nWe thank the reviewer’s kind reminder. It is worth mentioning that in our work,\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nthe operating wavelength of the IDT is 500 µm, while the single-unit aperture\nand the inter-unit gap are 200 µm and 10 µm, corresponding to 0.4𝜆 and 0.02𝜆,\nrespectively. All these parameters have been mentioned in Supplementary Note 1.\nWe would like to clarify that there is no absolute relationship among these three\nparameters. The wavelength was determined the period of the IDTs. The\nsingle-unit aperture was then designed to be sub-wavelength, set at 200 µm, as a\ncompromise between integration density and fabrication feasibility. A smaller\naperture allows for more units within a given area but increases challenges in\nfabrication and circuit design. The inter-unit gap was minimized to the extent\npermitted by the fabrication process to prevent excessive separation, which\nwould lead to unwanted divergence of sub-waves and impair their superposition\nefficiency. In addition, as suggested by the reviewer in comment 11, for the sake\nof reader comfort, we have described all these geometric parameters of IDT\narrays using the wavelength as the unit.\n10. The article contains numerous AI-style statements at the end of paragraphs.\nThese self-repeating, self-promoting sentences make the text difficult to read. A\nmore neutral writing style would be preferable. For example:\n•“This co-design of excitation and measurement protocols enabled accurate\nreconstruction of the acoustic field distribution, thereby validating the ability of\nthe chirped IDT array to generate multifrequency SAWs.” – This phrase is overly\nambitious for what is essentially a simple adjustment of LDV measurement\nsettings.\n•“This approach effectively mitigates spectral crosstalk limitations in\nconventional multifrequency SAW systems while maintaining phase coherence\nover extended propagation distances.” – The statement lacks supporting details\nand references. No phase coherence measurements over extended propagation\ndistances are provided.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\n•“This programmability offers significant flexibility in generating various types of\nSAWs, expanding potential applications in acoustic wave engineering and related\nfields.” – This self-promoting statement appears outside the introductory section\nand adds little informational value.\nAll three examples follow the same grammatical template, which contributes to a\nrepetitive and uncritical tone.\nReply:\nWe sincerely thank the reviewer for this critical feedback on our writing style. We\nagree with the reviewer's observation and have removed all the\nabove-mentioned \"AI-style\" sentences.\nPer the suggestion by the reviewer, we have also modified the following sentence,\n“This signal concatenation strategy effectively extends the scope of SAW-based\nmanipulation, enabling diverse and flexible acoustic field control.” Please refer to\nLine 9-11 on Page 13 in revised SI.\n11. For the sake of reader comfort, the authors are encouraged to cite the IDT\nunit length (i.e., the value of N_i × λ/2 for the standard configuration) and the\naperture of the fabricated IDT arrays.\nReply:\nPer the suggestion by the reviewer, we have included the dimensional\nparameters of the IDT array in relation to 𝜆, such as “(0.02𝜆)”, “(0.44𝜆)”, “(0.4𝜆)”,\n“(0.02𝜆)”, “(0.25𝜆)”, “(0.5𝜆)”, and “(0.2𝜆).” Please refer to Supplementary Note 1\non Page 2 and 3 in revised SI.\n12. The new sequences “2, 2, 3, 3, 4, 12, 4, 3, 3, 2, 2” and “2, 2, 2, 2, 3, 3, 4, 12, 4, 3,\n3,” (FIG 4c) successfully moved the focal point downward, as demonstrated in Fig.\n4b and c. However, the sequence “2, 2, 3, 3, 4, 12, 4, 3, 3, 2, 2” cannot be identified\nin Fig. 4b. Please ensure the text and figures correspond accurately.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nReply:\nWe truely appreciate the reviewer for his/her meticulousness in identifying this\nerror. We have corrected the digit sequence of Fig. 4b. Please refer to the revised\nFig. 4b in our revised manuscript.\n13. In Fig. 2(c–e), it is not clear where the scanning region is located relative to\nthe IDT array.\nReply:\nPer the suggestion by the reviewer, we have supplemented the location\ninformation of the scanning region in the revised manuscript. “A detailed LDV\nscan was conducted with the starting point at ~3 mm away from the chirped IDT\narray along the SAW propagation path. The scanning area was 2 mm × 1 mm with a\nstep size of 20 µm.” Please refer to Line 11-14 on Page 7 in the revised\nmanuscript.\n14. Did you observe any issues with the adhesion or possible delamination of the\nthin Cr/Au electrode layer (3 nm of chromium / 50 nm of gold) during the\nbonding process, considering the relatively high temperature (140 °C) and\npressure (180 MPa) applied for 10 seconds? In addition, could you explain the\nchoice of these specific thicknesses (3 nm Cr and 50 nm Au)? Were they selected\nbased on adhesion, electrical performance, or another technological constraint?\nReply:\nWe thank the reviewer for these insightful questions regarding our fabrication\nprocess, which allow us to clarify our metallization choices. We did not observe\nany issues with adhesion or delamination of the Cr/Au electrode layer during the\nthermocompression bonding process. The FFC ensures excellent contact with the\nelectrodes, thereby guaranteeing reliable circuit conductivity. A 3 nm-thick Cr\nlayer was deposited as an adhesive interlayer to ensure strong bonding between\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nthe metal structure and the lithium niobate substrate, followed by a 50 nm-thick\nAu layer to provide excellent electrical conductivity. This thickness provides\nsufficient mechanical robustness to withstand the photolithography, lift-off, and\nbonding processes without breaking or becoming discontinuous. An excessively\nthick Au layer can increase the mechanical load on the IDTs, thereby adversely\naffecting their vibration performance. The mass loading from a 50 nm Au film is\nacceptable for lithium niobate and does not significantly perturb the SAW\npropagation or electromechanical coupling coefficient, unlike thicker metal\nlayers which can dampen the wave.\n15. S1. Does W, d and g have the same values for standard and chirped\nProgrammable IDT Arrays? They are not the same while looking at Figure S1 and\nnothing is said concerning their values for the chirped array. On the photo in\nFigure S2 one can see that they are the same, but it is better to explicitly indicate\nthis in the text.\nReply:\nWe appreciate the reviewer for this careful reading and for pointing out the need\nfor explicit clarification regarding the geometric parameters. We would like to\ntake this opportunity to clarify the following point: In structure S1, the values of\nW, d, and g of standard and chirped IDT arrays are identical. However, the\nstandard IDT array consists of 20 finger pairs, whereas the chirped IDT array\ncomprises 51 finger pairs. For the same number of finger pairs, the effective\nnumber of active fingers in chirped IDTs is fewer than that in standard IDTs.\nTherefore, the number of finger pairs in the chirped IDT was increased to ensure\nthat the signal intensities acquired by the LDV from both structures were\ncomparable.\nPer the suggestion by the reviewer, we have added the following information in\nrevised manuscript. “It is worth noting that for a given number of finger pairs,\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nchirped IDTs usually exhibit a much lower efficiency than standard IDTs. To ensure\nthat the measured signal intensities by the LDV for both chirped and standard IDTs\nare comparable, we purposely set that the standard and chirped IDT arrays contain\n20 and 50 finger pairs, respectively.” Please refer to Line 5-9 on Page 3 in revised\nSI.\n16. A better summary of the supplementary notes is recommended. The main\ntext is difficult to follow due to missing essential details. In particular, some\ngeneral information about the particle manipulation experiments should be\nincluded in the main article.\nReply:\nWe thank the reviewer for this critical suggestion to improve the manuscript's\nstructure and readability. We agree that a clearer guide to the SI and the inclusion\nof key experimental details in the main text are essential. Following the\nreviewer's advice, we have thoroughly reorganized and expanded the SI to make\nit more navigable. We have added two new standalone sections with descriptive\ntitles: “Supplementary Note 2 – Simulation Model Settings” and “Supplementary\nNote 3 – DT Digit Sequences Setting for Focused SAWs”. In addition, we have\nadded a new content in the SI dedicated to the S-parameters to further enhance\nthe depth and completeness of the SI.\nWe fully agree with the reviewer that general information on the particle\nmanipulation experiment is vital for understanding the application\ndemonstration and should be more appropriately placed in the main article.\nHowever, due to the strict length constraints imposed by the journal, we had no\nalternative but to include it in the SI. In the main text, we primarily focus on\ndemonstrating the underlying principles and experimental outcomes of SAW\nfield control using the IDT array.\nPer the suggestion by the reviewer, we have added the following supplementary\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nnotes, “Supplementary Note 4 – Simulation Model Settings” and “Supplementary\nNote 5 – IDT Digit Sequences Setting for Focused SAWs”. Please refer to Page 6-8 in\nrevised SI.\n17. Line 218: “A distinct focusing effect is observed, with the focal point\nappearing elongated along the wave propagation direction (x-direction),\nexhibiting a notable focal depth. In contrast, the focal depth in the perpendicular\n(y-direction) is narrower.”\nThe term “focal depth in the perpendicular (y-direction)” is somewhat\nambiguous. A suggested rewording is:\n“A distinct focusing effect is observed, with the focal region appearing elongated\nalong the wave propagation direction (x-direction), indicating a notable depth of\nfocus. In contrast, the focal width (lateral resolution) in the perpendicular\ndirection (y-direction) is significantly narrower.”\nReply:\nWe appreciate the reviewer for this precise and correct technical correction. Per\nthe suggestion by the reviewer, we have modified the following information in\nrevised manuscript. “A distinct focusing effect is observed, with the focal region\nappearing elongated along the wave propagation direction (x-direction), indicating a\nnotable depth of focus. In contrast, the focal width (lateral resolution) in the\nperpendicular direction (y-direction) is significantly narrower.” Please refer to Line\n1-3 from the bottom on Page 9 and Line 1 on Page 10 in the revised manuscript.\n18. The relationship between the TDM signal composition and focal depth is\nquantified using full-width at half-maximum (FWHM) analysis. What is the\naverage FWHM value of the focal depth for each frequency (f₁, f₂, f₃, f₄) used\nindividually (7.20 MHz, 7.81 MHz, 8.35 MHz, and 8.78 MHz), as shown in Fig. 6(f)?\nThis information would be valuable to highlight the efficiency of TDM excitation\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nin achieving an extended focal depth (i.e., forming a SAW needle).\nReply:\nWe thank the reviewer for this excellent suggestion, which is crucial for\nquantifying the performance of our TDM approach. We agree that providing the\nbaseline focal depth for each individual frequency is essential to highlight the\nefficiency of TDM in achieving an extended focal depth. As requested, we have\nmeasured the average FWHM of the focal depth (along the x-direction) for each\nfrequency used individually. The average FWHM value of the focal depth for each\nfrequency (f₁, f₂, f₃, f₄) used individually (7.20 MHz, 7.81 MHz, 8.35 MHz, and 8.78\nMHz) are 22𝜆, 29𝜆, 28𝜆 and 28𝜆, respectively. We have provided additional\ndescriptions regarding this aspect in the revised manuscript.\nPer the suggestion by the reviewer, we have added the following information in\nrevised manuscript. “The average full-width at half-maximum (FWHM) of the focal\ndepth along the x-direction was measured individually for each operating frequency.\nThe obtained values are as follows: 22𝜆 at f₁ = 7.20 MHz, 29𝜆 at f₂ = 7.81 MHz, 28𝜆\nat f₃ = 8.35 MHz, and 28𝜆 at f₄ = 8.78 MHz, respectively.” Please refer to Line 1-3\nfrom the bottom on Page 13 and Line 1-2 on Page 14 in the revised manuscript.\n19. The main article is difficult to understand without consulting the\nsupplementary materials. However, the key insights should be accessible from\nthe main article alone. It is necessary to redistribute the information more\neffectively between the main text and the supplementary materials, ensuring that\nthe latter serves a truly supplementary role.\nReply:\nWe sincerely thank the reviewer for this critical and constructive feedback\nregarding the balance of information between the main text and the SI. We fully\nagree that the main text should be self-contained and readily understandable,\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nwhile the SI should provide supporting depth. In response to this comment, we\nhave undertaken a major restructuring of the manuscript. We have added two\nnew standalone sections with descriptive titles: “Supplementary Note 2 –\nSimulation Model Settings” and “Supplementary Note 3 – DT Digit Sequences\nSetting for Focused SAWs”. In addition, we have added a new content in the SI\nregarding the S-parameter measurements to further enhance the depth and\ncompleteness of this work. However, due to the strict length restrictions imposed\nby Nature Communications, we had to make the difficult decision to place some\nimportant section in the SI. This allowed us to remain within the prescribed\nmanuscript limits while still making the experimental details accessible to\ninterested readers. The main article is intentionally focused on presenting the\ncore innovation of this work—the concept and implementation of programmable\nacoustic field shaping through phase encoding in IDT arrays, along with the key\nresults that demonstrate the capability and performance of the proposed\napproach.\nReviewer: 2\nComments:\nIn the manuscript, a programmable IDT array architecture is proposed for\nmultidimensional SAW generation, enabling diverse SAW waveforms through\nprogramable phase encoding for precise focus manipulation. It is a novel and\nuseful work, however, there are some questions need to be addressed in the\nmanuscript:\n1. Both the standard and chirped IDTs configuration are miniaturized laterally\nto form individual IDT unit. This results in a reduced acoustic aperture, which\nenhances diffraction effects and decreases acoustic energy. Could this affect the\nresponse of the IDT array? Please provide an explanation.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nReply：\nWe thank the reviewer for this insightful question, which gets to the very heart of\nthe design trade-offs in our system. The reviewer is absolutely correct that\nminiaturizing individual IDT units reduces the acoustic aperture, which, for an\nisolated emitter, would lead to increased beam divergence and reduced acoustic\nenergy density. However, in our array design, this effect is not a drawback but\nrather a fundamental feature that enables wavefront shaping. The key is that we\ndo not rely on the directivity of a single unit but on the collective interference of\nwaves from all elements. As the reviewer anticipates, the lateral width of each\nunit (200 µm) is significantly smaller than the operational wavelength (500 µm,\nratio = 0.4λ). This design deliberately makes each unit act as an approximate\npoint source of SAWs, characterized by a highly divergent wavefront. The\noperational principle of our array is the precise phase-controlled coherent\nsuperposition of wavelets emitted from each unit. By digitally controlling the\nphase (0 or π) of each point-like source, we can control their emissions to\nsynthesize a desired macroscopic wavefront across the entire array. As shown in\nFig. 2c–f, secondary wavelets generated by multiple units with identical phases\ncan interfere and combine to form a stable and uniform primary planar wave.\nThe resulting wave propagation—where every point on a wavefront can be\nconsidered as a source of secondary wavelets—is a manifestation of the\nHuygens-Fresnel principle. However, our design foundation is the active control\nof the primary sources (the array elements) to dictate the outcome of this\ninterference.\nAccordingly, we have added the following information: “According to the\nHuygens–Fresnel principle, each individual unit can be regarded as a point source\nradiating the secondary wavelet. When multiple units are arranged in close proximity\nwith the interunit gap (10 µm) much smaller than the wavelength (500 µm), the\ncoherent superposition of the secondary wavelets results in a stable, uniform primary\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nwavefront. The minimal interunit gap reduces acoustic energy loss, facilitating the\ncoherent superposition of SAWs from adjacent IDT units. Furthermore, when the input\nsignals to the IDT units are out-of-phase, the corresponding secondary wavelets also\nmaintain a consistent anti-phase relationship, which has been discussed in our\nprevious work [38].” Please refer to Line 1-10 from the bottom on Page 7 in the\nrevised manuscript.\n2. Beam steering may occur during surface acoustic waves propagation. Could\nthis phenomenon lead to undesired interference between adjacent waves in the\nIDT array?\nReply:\nWe greatly appreciate the reviewer’s question. Indeed, during the propagation of\nthe SAW, wave steering occurs only when the digit sequence is altered; otherwise,\nthe acoustic field remains in a steady state. Regarding the \"interference\"\nmentioned by the reviewer, it is indeed present but should not be considered\n\"undesired.\" This is because the manipulation of the acoustic field relies precisely\non the interference and superposition of multiple secondary wavelets generated\nby the IDT array. Therefore, interference between individual units is inherent and\nfundamental to the intended operation.\n3. Could the authors provide further justification for selecting numbers such as 2,\n3, 4, 8, and 12 in the encoding process?\nReply:\nWe are grateful to the reviewer for these insightful and critical comments, which\nhave helped us significantly improve the clarity and rigor of our methodology\nsection. To exploit the bending property of the Airy SAW near the main lobe,\ntwo symmetric Airy SAWs were designed to coincide at their main lobes,\nresulting in a focused SAW profile with enhanced energy concentration. Due to\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nthe limited total number of available IDT units (40), the integer-item encoding\nwas approximated to achieve the desired focused sequence. We have accordingly\nsupplemented the corresponding section in the manuscript to provide a more\ndetailed explanation.\nPer the suggestion by the reviewer, we have added the following paragraph to\nexplain the selection of the IDT digit sequence, “By applying phase encoding to the\nexisting 40-unit IDT array, the desired SAW waveform—such as the Airy SAW\nencoded in Fig. 3—can be achieved. To exploit the bending property of the Airy SAW\nnear the main lobe, two symmetric Airy SAWs were designed to coincide at their main\nlobes, resulting in a focused SAW profile with enhanced energy concentration. Fig.\nS3a and b show the Airy function and its corresponding binarized phase distribution,\nrespectively [38,39]. The Airy function was truncated from x = -10 to x = 0.66 and\nthen symmetrically spliced at the main lobe to obtain the phase distribution of a\nfocused SAW, as shown in Fig. S3c. The corresponding binarized phase distribution is\npresented in Fig. S3d. Due to the limited total number (only 40) of IDT units, the\nphase distribution could only be approximated to the nearest integers. As shown in\nFig S3e, the resulting digit sequence was determined as “2, 2, 3, 3, 4, 12, 4, 3, 3, 2,\n2”, where black and white squares represent phase values of 𝜋 and 0, respectively.”\nPlease refer to the added Supplementary Note 5 on Page 7 and 8 in revised SI.\n4. In Section ‘Multifrequency Focal Depth Modulation’, the authors demonstrate\nthat (5:0:4:11) is the optimized configuration ratios, please clarify the rationale\nfor this selection. Furthermore, Fig.7 and Fig.8 do not convincingly demonstrate\nthat this ratio provides the best trade-off between focal depth and energy\nuniformity. The authors should provide additional evidence to substantiate this\nconclusion.\nReply:\nWe sincerely appreciate the reviewers' critical comment, which pushes us to\nprovide a more rigorous justification for our optimization process and\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nconclusions. The selection of the (5:0:4:11) ratio was not arbitrary but resulted\nfrom a systematic exploration of the parameter space defined by the amplitude\nratios of the four frequency components (f₁, f₂, f₃, f₄), as shown in Fig.7. The\noptimization goal was to find the combination that FWHM while maintaining a\nhigh and uniform energy distribution along the extended focal zone.\nPer the suggestion by the reviewer, we have modified the following information:\n“From Fig. 6f, it can be clearly seen that the location of the focused energy along the\nx-axis varies with the operating frequency. The SAW with a higher frequency has a\nlonger focal length from the excitation source.” Please refer to Line 10-12 from the\nbottom on Page 14 in the revised manuscript;\n“Since the generated SAWs with frequencies of f₁ (7.20 MHz) and f₄ (8.78 MHz) have\nthe nearest and farthest focal points, respectively, their signal weighting should be\nenhanced. Meanwhile, the generated SAWs with frequencies of f₂ (7.81 MHz) and f₃\n(8.35 MHz) have the focused energy distributions that overlap with those of f₁ and f₄ to\na large extent. Therefore, their relative contributions should be minimized to achieve a\nmore uniform energy distribution along the x-axis across the four frequencies, thus\nextending the effective focal depth.” Please refer to Line 1-5 from the bottom on\nPage 14 and Line 1-2 on Page 15 in the revised manuscript;\nand “For the frequency combination of (5:0:4:11), the SAW energy assigned to the\nfrequency of f₂ is 0, meaning that the f₂-frequency SAW has no contribution. This is\nlikely because the f₂-frequency SAW energy distribution significantly overlaps with\nthose of f₁ and f₃, while its peak is higher than that of f₃ (see Fig. 6f). Therefore, to\nextend the focal depth, our proposed frequency-weighting strategy is to suppress f₂ and\nf₃ while increase f₄. As a result, we experimentally optimized (5:0:4:11) ratio to achieve\nthe extended focal depth of 43λ with uniform energy distribution.” Please refer to Line\n4-10 on Page 16 in the revised manuscript.\n5. Color bars are missing from all simulation results.\nReply:\nWe sincerely appreciate the reviewers' insightful comments. Per the suggestion\nby the reviewer, we have added a normalized color bar to both the simulated and\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nexperimental acoustic fields in “Fig. 3”, “Fig. 4”, “Fig. 5”, “Fig. 6”, and “Fig. 7”.\nPlease refer to the revised Fig. 3 on Page 9, Fig. 4 on Page 10, Fig. 5 on Page 11,\nFig. 6 on Page 13, and Fig. 7 on Page 15 in the revised manuscript.\nReviewer: 3\nComments:\nThe authors present a new type of SAW setup, combining several independent\ninterdigital transducers (IDTs) with very small aperture next to each other,\ncombined with a multiplexed, binary (i.e. two-state) phase-controlled electrical\nsignaling. This allows the flexible excitation and on-demand modulation of\npartial waves to realize complex Surface Acoustic Wave fields, e.g. for\nacoustofluidic actuation purposes. The manuscript is part of an actual trend\ntowards higher acoustic wave field control, the setup demonstrated is new and\nhighly interesting for the broader acoustofluidics and microfluidics research\nsociety. The correct electric excitation itself, however, can be complex and may\nlimit the adoption of the new method by less experienced researchers, or labs\nwith less extensive rf electrical device infrastructure. Investigations of the SAW\nexcitation were carried out by electrical measurement and laser-Doppler\nvibrometry. An experimental proof of particle manipulation is given. The\nmanuscript is written in very good language and important details are provided\n(few are missing, as indicated below)\n1. It would be very interesting, to also see the |S11| plots of both IDT\nconfigurations, with and without the phase-switching board.\nReply:\nWe greatly thank the reviewer for the suggestions. Measuring the |S | parameter\n11\nfor the different configurations is indeed a powerful way to characterize the\nelectrical performance and impedance matching of our system, and we agree that\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nit will add significant depth to the analysis.\nPer the suggestion by the reviewer, we have added the following discussion, “To\ncharacterize the performance of the IDT array electrodes, the S₁₁ parameter was\nmeasured, as this structure is individually wired and integrated with a backend\ndriving system. The S₁₁ response provides a direct evaluation of impedance matching\nat the input port of the driving system and reflects the actual output behavior of the\nelectrodes. The backend driving system incorporates a critical and complex\nphase-switching board, whose presence significantly influences the performance of\nthe IDT array. Therefore, the S₁₁ parameters of both the standard and chirped IDT\narrays were measured under two conditions: with and without the integrated control\nmodule, as shown in Fig. S6. When the standard IDT array was connected without the\ncontrol module (i.e., directly wired without phase control capability), the S₁₁ response,\nindicated by the blue curve in Fig. S6a, exhibited a pronounced dip in the frequency\nrange of approximately 7 MHz to 8.5 MHz. The minimum value reached about –3 dB\nnear 7.8 MHz, which aligns well with the designed resonance frequency of 7.98 MHz.\nWhen the control module was connected to the IDT array, a resonant response near\n7.8 MHz was still observable in the S₁₁ spectrum, as shown by the red curve in Fig.\nS6a. However, the overall magnitude of S₁₁ increased, indicating much higher\nreflectivity and reduced overall efficiency of the device. This degradation primarily\nresults from the challenge in achieving perfect impedance matching between the IDT\narray and the complex backend control circuitry. To compensate for the reduced\nefficiency and ensure a sufficient signal-to-noise ratio during acoustic field scanning,\na relatively high driving voltage of 20 Vₚₚ was applied in the experiments. Similar\nbehaviors were observed in the chirped IDT array, as shown in Fig. S6b. Furthermore,\nthe chirped IDT array exhibits a notably broader operating bandwidth compared to\nthe standard IDT array, maintaining favorable performance across a frequency range\nfrom 6 MHz to 9.5 MHz, with its best performance also approaching –3 dB. This\nresult is consistent with the spectral response shown in Fig. 2b.” Please refer to Line\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\n1-5 from the bottom on Page 5 to Line 1-21 on Page 6 and the added\nSupplementary Fig. 4 in revised SI.\n2. Line 102: Please explain, what is meant by “post-extension”.\nReply:\nWe sincerely appreciate the valuable question raised by the reviewer. As\nillustrated in Fig. 1b, the electrode structure of the IDT array consists of two\ndistinct parts: the IDT array itself, which is responsible for generating SAWs and\nthe extended electrodes, which serve as an external continuation of the array to\nfacilitate connection with the FFC. Therefore, the term \"post-extension\" refers\nspecifically to the 80 pins electrode array extended from the rear of the IDT\nstructure.\n3. The simulation approach is not explained and should be provided in detail.\nReply:\nWe sincerely appreciate the valuable comment by the reviewer. We have\nincluded detailed descriptions of the simulation setup and parameters in the SI.\nAccordingly, we have also added the simulation model settings, “In our\nsimulations, we performed a frequency-domain analysis of the acoustic field\ngenerated by the designed IDT array using the Piezoelectricity module in COMSOL\nMultiphysics. Given that SAWs propagate primarily along the substrate surface, a\ntwo-dimensional model was constructed in COMSOL to reduce computational cost\nwhile maintaining simulation accuracy. A simulation domain of 4 cm × 3 cm was\ndefined, and the material was set as LiNbO , as shown in Fig. S2. It is important to\n3\nnote that the LiNbO crystal orientation was specifically configured as 128° Y-X cut.\n(500 µm) were applied around the LiNbO substrate to absorb any reflected acoustic\n3\nwaves from the boundaries. Subsequently, the IDT array electrodes were constructed\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\non the substrate, with each electrode excited by either in-phase or out-of-phase\nvoltage signals to control the acoustic phase. By strategically arranging the\ndistribution of these voltage polarities, the desired acoustic field profile could be\nachieved. The applied voltage to the electrodes was set at 20 Vₚₚ.” Please refer to\nSupplementary Note 4 on Page 6 and 7 in revised SI.\n4. Line 334: “Discussion” should be changed into “Conclusion”.\nReply:\nPer the suggestion by the reviewer, we have changed “Discussion” into\n“Conclusion”. Please refer to the Line 13 on Page 16 in the revised manuscript.\n5. Details of the vibrometer settings during measurement of TDM configurations\nshould be given.\nReply:\nPer the suggestion by the reviewer, the MATLAB code for configuring the TDM\nsignals has been provided as part of the supplementary materials. Please refer to\nSupplementary Note 8 – MATLAB codes for TDM signal generation in revise SI.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nResponse to Referees\nREVIEWER REPORT(S):\nReviewer: 1\nComments:\nThe reviewer appreciates the authors’ positive reception of the previous\ncomments and the effort devoted to revising the manuscript. Most technical\npoints have been adequately addressed. However, several aspects of the\nintroduction and methodology still lack clear positioning and neutrality and\nrequire further refinement.\n1. Page 2, lines 43–46:\nThe assertion that conventional SAW devices “fail to meet the increasing\ndemands of complex and dynamic application scenarios” suggests that dynamic\nwavefront control is broadly required across SAW technologies. This is not the\ncase. Dynamic modulation is of high relevance in acoustofluidics, notably for\nparticle manipulation and droplet control, but it is not needed in major SAW\napplication domains such as RF filters or most sensor platforms, which rely on\nfixed-geometry resonant structures.\nThe authors are encouraged to clarify before the abovementioned statement that\nthe present work is motivated by applications in microfluidics and particle\nmanipulation, rather than implying a universal limitation of static SAW devices.\nReply:\nWe thank the reviewer for this precise and valuable correction. We agree that\nour original statement was overly broad and did not accurately represent the\nmany successful application domains for static SAW devices. Our intention was\nto highlight the limitation of static devices specifically for applications requiring\ndynamic wavefront control. To address this, we have revised the Introduction to\nclearly frame our work within the context of microfluidics and particle\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nmanipulation. The generalized claim has been replaced with the following more\nfocused statement:\nPer the suggestion by the reviewer, we have modified the following information:\n“Although conventional SAW devices with fixed geometries are the cornerstone of\nmature technologies such as RF filters and stable sensor platforms, they lack the\ndynamic reconfigurability required for emerging applications in programmable\nmicrofluidics and advanced particle manipulation.” Please refer to Line 17−21 on\nPage 2 in the revised manuscript.\n2. Page 3, lines 62–64:\nThe statement that multi-input systems “hinder dynamic modulation… under\nvarying operational requirements and environmental conditions” is not well\naligned with the practical context of acoustofluidic manipulation. Such\nexperiments are typically performed under stable laboratory conditions, where\nthe environment is controlled and operational requirements do not vary\ndynamically. The reviewer recommends removing or rephrasing this sentence to\nmore accurately reflect the true limitations of prior programmable-IDT\napproaches (e.g., hardware complexity, multi-channel synchronization), without\nattributing them to external environmental variability.\nReply:\nWe thank the reviewer for this astute observation. We agree that attributing the\nlimitation to varying environmental conditions does not accurately reflect the\ntypical stable context of acoustofluidic experiments and weakens our argument.\nWe have therefore removed the original phrasing and revised the relevant\nsentence in the Introduction to focus on the fundamental hardware-level\nconstraints of multi-channel systems.\nPer the suggestion by the reviewer, we have modified the mentioned reference in\nour revised manuscript, “The practical deployment of such multi-input systems is\noften hindered by their inherent hardware complexity and the need for precise\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nsynchronization of multiple channels, posing a barrier to their broader adoption.”\nPlease refer to Line 12−14 on Page 3 in the revised manuscript.\n3. Page 3, 59-62:\n“While recent programmable IDTs [31, 32] have broken this paradigm, their\nreliance on multi-input systems presents a barrier to widespread adoption.”\nThe revised sentence still requires clarification for accuracy and neutrality.\n• While the term “multi-input system” is technically applicable to Refs. [31, 32], it\nis too general to capture the actual complexity of these platforms. Both employ\nmulti-channel phased-array driving electronics with independent\namplitude/phase control, synchronization hardware, and calibration procedures.\n• The phrase “presents a barrier to widespread adoption” is not neutral. The\ncited works do not claim impracticality, and multi-channel architectures are\nwidely used in acoustofluidics, phased-array ultrasonics, and RF engineering. A\nmore balanced phrasing would simply note that such systems involve greater\nsystem-level complexity than single-input designs.\n• For completeness, Ref. [33] should be cited alongside [31] and [32].\nThe reviewer encourages the authors to refine this discussion so that it (i)\naccurately reflects the hardware demands of prior programmable IDT systems,\n(ii) maintains a neutral, evidence-based tone, and (iii) includes all relevant\nreferences.\nIf desired, a possible reformulation could be:\n“While recent programmable IDT platforms [31–33] have demonstrated the\nability to generate arbitrary wavefields, they typically rely on multi-channel\ndriving architectures with independently controlled inputs, which increase\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nsystem-level hardware complexity compared to single-input solutions.”\nReply:\nWe thank the reviewer for this meticulous feedback and for providing a precise\nand balanced reformulation. We agree completely that our previous phrasing\nwas both insufficiently specific and not fully neutral. The reviewer's suggested\ntext perfectly captures the technical distinction we intended to highlight.\nPer the suggestion by the reviewer, we have therefore replaced the original\nsentence with the reviewer's wording verbatim in the Introduction: “While recent\nprogrammable IDT platforms [31–33] have demonstrated the ability to generate\narbitrary wavefields, they typically rely on multi-channel driving architectures with\nindependently controlled inputs, which increase system-level hardware complexity\ncompared to single-input solutions.” Please refer to Line 8−12 on Page 3 in the\nrevised manuscript.\n4. Page 4, 107-109\nThe explanation regarding the use of manually actuated DPDT switches still lacks\nadequate technical justification.\n• The statement that manual switching “ensures system stability” must be\nsupported by measurements or engineering arguments (e.g., contact integrity\nover >8 h, thermal behavior, switching transients, EMI susceptibility).\n• Mechanical DPDT switches are generally not suitable for MHz-range operation\ndue to parasitic capacitance and limited isolation, potentially introducing leakage\nor phase distortion at >7 MHz.\n• Manual switching should be presented as a pragmatic, prototype-level choice,\nnot an optimized or ideal solution. Manual actuation limits timing reproducibility,\nincreases operator dependence, and precludes automation.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nThe authors are encouraged to briefly discuss possible automation\nstrategies—e.g., high-voltage RF relays, solid-state MOSFET/IGBT switches, or\ncommercial switching matrices—to better contextualize the scalability of the\nproposed approach.\nReply:\nWe thank the reviewer for these critical and highly relevant engineering points.\nWe have prepared a point-by-point response to address each of the reviewer's\ncomments in detail below.\n• The rationale for emphasizing system stability stemmed from a specific\nexperimental constraint: a complete two-dimensional LDV scan of the acoustic\nfield distribution over the entire measured area required a continuous\nacquisition period of more than 8 hours. Under such prolonged measurement\nconditions, any transient glitch, contact bounce, or unintended state change in\nthe switching network would have corrupted the entire dataset. Therefore, the\nselection of simple, robust mechanical DPDT switches was a deliberate choice to\nminimize the risk of such failures during this critical and time-intensive scanning\nphase. Throughout the experiments, the mechanical DPDT switches\ndemonstrated reliable stability without any operational anomalies.\n• We fully acknowledge the reviewer’s valid point regarding the problem of\nDPDT switches. The use of mechanical DPDT switches does introduce significant\nparasitic impedance and insertion loss. As noted in the SI (detailed in the\nSupplementary Fig. 4.), our system exhibits a relatively high loss. The measured\nS parameters confirm that the overall impedance matching is sub-optimal, and\n11\na substantial portion of the input RF power is not efficiently converted into SAWs.\nThis is indeed a primary factor contributing to the lower-than-ideal output\nefficiency observed in the system. Although the current experimental circuit\ncontrol system is not yet perfect, the results demonstrate that the primary\nobjective—programmable multiple channels control of SAWs—has been\nsuccessfully achieved.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nPer the suggestion by the reviewer, we have added the following information,\n“These components exhibit non-negligible parasitic capacitance and limited isolation\nat MHz frequencies. This degradation primarily results from the challenge in achieving\nperfect impedance matching between the IDT array and the complex backend control\ncircuitry. Consequently, a substantial portion of the input RF power is lost before\nreaching the piezoelectric substrate for SAW excitation, directly explaining the\nobserved reduction in overall electroacoustic conversion efficiency.” Please refer to\nLine 16−22 on Page 7 in the revised SI.\n• We fully agree that our original justification for manual switching was\ninsufficient. The use of mechanical DPDT switches in our current\nproof-of-concept prototype is indeed a pragmatic, sub-optimal choice driven by\nprototyping convenience and cost, not an optimized solution. However, we\nbelieve it is more practical to first ensure the functional realization of the\nmultiple channels system by leveraging the stability advantage of mechanical\nswitches, before advancing to automated solutions in subsequent stages.\nRegarding the high-voltage RF relays suggested by the reviewer, we had\npreviously tested them but observed persistent contact bounce during prolonged\nscanning sessions, which adversely affected data acquisition reliability.\nPer the suggestion by the reviewer, we have modified the following information,\n“This novel approach, combining multifrequency programmability and TDM,\nenables precise waveform control and dynamic focal point adjustment, thereby\nestablishing a versatile platform for advanced SAW-based modulation. Looking\nforward, the transition from manual to automated electronic switching (e.g., via\nintegrated RF-MEMS or solid-state switches) will unlock real-time, intelligent control\nof these wavefronts. This evolution will not only significantly enhance modulation\nspeed and adaptability but also greatly expand the application potential of\nprogrammable SAW systems, opening new avenues for practical implementations.”\nPlease refer to Line 15−23 on Page 17 in the revised manuscript.\n5. The authors are invited to state explicitly that the implemented chirped IDT\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nemploys a hyperbolic-type frequency modulation, distinguishing it from the\nwidely used linear chirped IDTs.\nReply:\nWe thank the reviewer for this comment, we wish to clarify that the chirped IDT\nimplemented in this work actually employs a linear frequency modulation (i.e., a\nlinear variation of the periodicity with the direction of wave propagation), not a\nhyperbolic one. We have stared this point in Supplementary Fig. 1b.\nTo enhance clarity on this issue, we have revised the relevant description in the\nfollowing discussion: “The broadband chirped IDT arrays are designed with a linear\nfrequency sweep. The periodicity of the interdigitated electrode fingers width and\nspacing gradually varies linearly along the SAW propagation, generating a\ncorresponding linear shift in the Fresnel ripple peaks.” Please refer to Line 1−3 from\nthe bottom on Page 3 and Line 1 on Page 4 in the revised SI.\nReviewer: 2\nComments:\nThe authors have addressed the concerns raised in my first-round review and\nmade substantive improvements to the manuscript. I recommend publication in\nNature Communications.\nReviewer: 3\nComments:\nThank you for addressing my comments 1, 2 and 4 in a satisfactory way. I would\nlike to kindly ask you to provide more information on the remaining two\ncomments:\n1. The simulation approach is not explained and should be provided in detail.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nReply:\nWe sincerely appreciate the valuable comment by the reviewer. We have included\ndetailed descriptions of the simulation setup and parameters in the SI.\nAccordingly, we have also added the simulation model settings, “In our\nsimulations, we performed a frequency-domain analysis of the acoustic field\ngenerated by the designed IDT array using the Piezoelectricity module in\nCOMSOL Multiphysics. Given that SAWs propagate primarily along the substrate\nsurface, a two-dimensional model was constructed in COMSOL to reduce\ncomputational cost while maintaining simulation accuracy. A simulation domain\nof 4 cm × 3 cm was defined, and the material was set as LiNbO3, as shown in Fig.\nS2. It is important to note that the LiNbO3 crystal orientation was specifically\nconfigured as 128° Y-X cut. Perfectly matched layers (PMLs) with a thickness of\napproximately one wavelength (500 µm) were applied around the LiNbO3\nsubstrate to absorb any reflected acoustic waves from the boundaries.\nSubsequently, the IDT array electrodes were constructed on the substrate, with\neach electrode excited by either in-phase or out-of-phase voltage signals to\ncontrol the acoustic phase. By strategically arranging the distribution of these\nvoltage polarities, the desired acoustic field profile could be achieved. The\napplied voltage to the electrodes was set at 20 Vₚₚ.” Please refer to\nSupplementary Note 4 on Page 6 and 7 in revised SI.\n=> A 2D in-plane model for the simulation of Rayleigh-SAW is very unusual,\nconsidering the strong out-of-plane component u3. Detailed information on all\nmodel boundary conditions, physics and geometry are required for the reader to\nunderstand your approach.\nReply:\nWe thank the reviewer for raising this crucial point regarding the simulation of\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nRayleigh-type SAWs, which have a significant out-of-plane displacement (u₃). The\nreviewer is correct that a conventional 2D in-plane model cannot capture this\ncomponent. In the COMSOL simulations, however, we can specify the total\ndisplacement output, which inherently combines both in-plane and out-of-plane\ncomponents, thereby achieving an equivalent representation of the full acoustic\nfield distribution. This effectively captures the distribution of acoustic energy\nwithin the field, rather than relying solely on the out-of-plane (u₃) component.\nPer the suggestion by the reviewer, we have added the more simulation details as\nfollow, “A new “Rotated System” node needs to be added, with the “Input method”\nset to “General rotation”. According to the crystal cut of lithium niobate and the\nmodeling orientation, the rotation angle 𝛽 should be specified as “-38[deg]”. This\nstep is critical, as it directly determines the accuracy of the simulated wave velocity.”;\n“The mesh type for the PML domain was set to “Mapped” to enhance computational\nefficiency and numerical stability.”; “In the “Electrostatics (es)” physics interface, two\n“Terminal” nodes should be added. One should be configured as the signal voltage\nterminal and the other as the ground terminal, each connected to the corresponding\nthe IDT electrodes.”; “To visualize the complete acoustic field distribution within a 2D\nmodel, a “2D Plot Group” should be created under the “Results” node. Within this\ngroup, add a “Surface” subplot and set the “Expression” to “solid.disp”.” Please\nrefer to Line 11−15, 18−19, and 22−23 on Page 8; Line 1−2, 4−7 on Page 9 in the\nrevised SI.\n2. Details of the vibrometer settings during measurement of TDM configurations\nshould be given.\nReply:\nPer the suggestion by the reviewer, the MATLAB code for configuring the TDM\nsignals has been provided as part of the supplementary materials. Please refer to\nSupplementary Note 8 – MATLAB codes for TDM signal generation in revise SI.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\n=> My original request was related to the settings of the vibrometer (brand,\nsetup, experimental settings), that were not mentioned so far. Please revise.\nReply:\nWe apologize for the misunderstanding and thank the reviewer for the\nclarification. The brand of vibrometer we have stated in “Supplementary Note 3 –\nFunctional Validation” of SI. We have now revised the SI to include the requested\nsetup details regarding the LDV settings used during the TDM configuration\nmeasurements.\nPer the suggestion by the reviewer, we have added the more setting details as\nfollow, “The SAW field distribution was measured using a LDV test system. The setup\nprimarily consists of a scanning vibrometer (PSV-500 Scanning Head, Polytec,\nGermany), a data acquisition card (PXIe-5160, National Instruments, USA), a\ncustom-built two-axis stepper motor translation stage, and a control computer. The\nprobe laser of the vibrometer was focused perpendicularly onto the LiNbO₃ substrate\nsurface, and a clearly detectable reflected signal was obtained.”, “The total number of\npoints in the TDM signal sequence was set to 2500. The generated TDM signal data\nwas converted into a format compatible with the signal generator for output. The\nsignal generator was configured with a cycle period of 2.5 µs (slightly longer than the\nTDM signal duration) and set to infinite loop mode, enabling continuous and stable\nTDM signal output. The data from the vibrometer scan was subsequently acquired\nusing a data acquisition card. The custom control system synchronized the acquisition\ncard with the vibrometer. The sampling rate was set to 1 GSa/s and the memory depth\nto 2.5K points, which precisely corresponds to the TDM signal length, generating a\nwaveform with a duration of 2.5 µs. To obtain a stable acquired signal, the number of\naverages was set to 200.” Please refer to Line 6−12 on Page 6; Line 1−10 on Page\n14 in the revised SI.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nResponse to Referees\nREVIEWER REPORT(S):\nReviewer: 1\nComments:\nThe reviewer appreciates the authors’ positive reception of the previous\ncomments and the effort devoted to revising the manuscript, in particular the\nremarks 1 to 4.\nConcerning the reviewer’s last remark 5, “The authors are invited to state\nexplicitly that the implemented chirped IDT employs a hyperbolic-type frequency\nmodulation, distinguishing it from the widely used linear chirped IDTs,” the\nreviewer does not agree with the correctness of the authors’ rebuttal. The\nauthors’ reply appears to conflate spatial chirp of the IDT geometry with\ntemporal (group-delay) frequency modulation. These two concepts are not\nequivalent in SAW theory and require clarification.\nIf the finger periodicity varies linearly with position along the propagation\ndirection:\np(x) = p + α x\n0\nthe local synchronous frequency satisfies:\nf(x) ∝ 1 / p(x)\nand the resulting group delay as a function of frequency is nonlinear\n(hyperbolic):\nτ(f) ∝ 1 / (f − f )\none.\nConversely, a linear group-delay (true linear-chirp) response:\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nτ(f) = τ + k f\n0\nrequires a quadratic spatial modulation of the finger periodicity:\np(x) = p + β x²\nTherefore, stating that a linear variation of the periodicity along propagation\nemploys a linear frequency modulation is, in a strict sense, theoretically\ninaccurate. Either the device implements a linearly chirped geometry with a\nhyperbolic impulse response, or it implements a quadratic chirp to achieve a\nlinear frequency–time mapping.\nIn addition, the phrasing “generating a corresponding linear shift in the Fresnel\nripple peaks” is incorrect. Fresnel ripples are intrinsic oscillatory features of the\nspectral response and do not undergo a “shift” in this sense; at most, their\nspacing or modulation may change. The current wording is therefore misleading\nand must be revised.\nReply:\nWe are truly grateful to the reviewer for this exceptional and enlightening\nclarification. The distinction the reviewer has drawn between the linear spatial\nchirp of the IDT geometry and the resulting hyperbolic temporal (group-delay)\nresponse is a fundamental and valuable theoretical point that perfectly\ncontextualizes our work. In light of this clarification, we completely agree with\nthe reviewer and have revised our manuscript accordingly. We now explicitly\nstate that the implemented chirped IDT, which is designed with a linearly\nvarying finger periodicity, p(x) = p₀ + αx, consequently resulting in a\nhyperbolic-type frequency modulation in its group-delay response, accurately\ndistinguishing it from a linear group-delay device.\nAccordingly, we have retracted our previous claim of “linear frequency sweep”\nand provided a more accurate description: “The chirped IDT employs a linear\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China\nspatial chirp, with its finger periodicity increasing uniformly along the propagation\ndirection. According to the well-established SAW theory [1], this linearly changed\nspatial periodicity inherently yields a hyperbolic frequency‑modulation characteristic\nin the temporal (group‑delay) domain.” Please refer to Line 3−7 on Page 4 and the\nadded Ref. 1 on Page 16 in the revised SI\nWe have removed the incorrect and misleading phrase “generating a\ncorresponding linear shift in the Fresnel ripple peaks.” As the reviewer rightly\npoints out, Fresnel ripples are stationary oscillatory features of the spectral\nresponse and do not “shift” in that sense.\nPer the suggestion by the reviewer, we have rephased our statement with\nphysically more accurate description: “The measured spectrum (Fig. 2b) displays\nclear Fresnel ripples, which are the characteristics of the device's broadband\nresponse.” Please refer to Line 8−9 on Page 4 in the revised SI.\nwww.sustech.edu.cn\n地址：中国广东省深圳市南山区西丽大学城学苑大道1088号，工学院南楼239室\nAddress: RM 239, South Tower, College of Engineering, 1088 Xueyuan Blvd., Nanshan District, Shenzhen, Guangdong, China"}]

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