Ultrasonic Mode-Conversion Transducer

• Ultrasonic mode-conversion transducers are devices engineered to transform one ultrasonic wave mode into another for targeted mechanical or acoustic performance.
• They utilize mechanisms like impedance matching, geometric tapering, graded metasurfaces, and resonant scattering to efficiently control energy transfer.
• Experimental and simulation studies validate these devices across biomedical and structural applications, highlighting compact design and high conversion efficiency.

Searching arXiv for relevant papers on ultrasonic mode-conversion transducers and related transducer modeling. arxiv_search(query="ultrasonic mode-conversion transducer Rayleigh wave medical needle metasurface Langevin waveguide", max_results=10) An ultrasonic mode-conversion transducer is a device that deliberately transforms one ultrasonic wave or vibration mode into another so that the emitted or transmitted field better matches the intended mechanical or acoustic function. In reported implementations, the converted modes include longitudinal vibration to flexural vibration in medical needles and radiant plates, Rayleigh surface waves to bulk shear or compressional waves in elastic substrates, and one guided waveguide mode into another in a two-mode acoustic guide (Bourlout et al., 2022). Across these realizations, the central engineering problem is not merely ultrasound generation, but the coordinated control of resonance, impedance matching, geometric tapering, dispersion, and boundary coupling so that energy is transferred into the desired mode rather than reflected, trapped in parasitic motion, or radiated into an unintended channel (Colombi et al., 2017).

1. Scope and classification

Mode conversion in ultrasonics is realized in several distinct physical settings. In piezoelectric actuation, a Langevin transducer is efficient at generating axial longitudinal motion, but the useful output for a medical needle or a wedge radiant plate can instead be lateral or flexural motion (Bourlout et al., 2022). In elastic metasurfaces, an incident Rayleigh surface wave can be redirected into a bulk shear or compressional wave by resonant surface structuring and wavevector control (Chaplain et al., 2019). In guided-wave acoustics, conversion may occur between two propagating modes of the same waveguide when a symmetric scattering geometry is tuned to the appropriate resonant state (Chesnel et al., 2021).

Platform	Converted mode pair	Principal mechanism
Needle-coupled Langevin construct	Longitudinal $\rightarrow$ flexural needle-tip motion	Waveguide impedance matching and geometry-driven conversion (Bourlout et al., 2022)
Elastic metawedge	Rayleigh $\rightarrow$ bulk shear $S$-wave	Graded resonator hybridization (Colombi et al., 2017)
Umklapp metasurface	Rayleigh $\rightarrow$ reversed bulk $S/SV$ or $P$ wave	Reciprocal-lattice momentum transfer (Chaplain et al., 2019)
ABH wedge radiant plate	Longitudinal $\rightarrow$ flexural plate vibration	Resonance matching with ABH energy concentration (Wang et al., 21 Jul 2025)
Symmetric two-ligament waveguide	Mode 1 $\leftrightarrow$ Mode 2	Resonant thin-ligament scattering (Chesnel et al., 2021)

A recurring theme is that efficient mode conversion requires a structure intermediate between source and load. Directly attaching a slender medical needle to a stiff Langevin stack is reported as inefficient because the transducer is optimized for small-amplitude longitudinal vibration whereas the needle responds best to transverse or flexural excitation (Bourlout et al., 2022). The same general principle appears in the metasurface literature, where a deep elastic substrate supports multiple wave families and the conversion process is governed by the way local resonances reshape the accessible dispersion branches rather than by simple geometric steering alone (Colombi et al., 2017).

2. Conversion mechanisms

One mechanism is impedance-matched resonant transformation of axial motion into bending motion. In the needle construct, the transducer generates an axial longitudinal mode, and a stainless-steel waveguide with a proximal rectangular resonator, an exponential taper, and a distal needle groove is engineered to accomplish mechanical impedance matching and mode conversion simultaneously (Bourlout et al., 2022). The taper acts as a mechanical transformer: as the cross-section shrinks, the same transmitted power results in larger displacement amplitudes while reflections are minimized. A second conversion mechanism is associated with the needle bevel and distal coupling geometry, which help turn guided vibration into large lateral tip excursions.

A second mechanism is dispersive hybridization in graded elastic metasurfaces. In the metawedge, the local longitudinal resonance of each microrod is given as

$f=\frac{1}{4 h}\sqrt{\frac{E}{\rho}},$

so grading the resonator height creates a spatial gradient in resonance frequency (Colombi et al., 2017). When the shortest resonators face the incoming Rayleigh wave, the wave is slowed, spatially compressed by frequency, trapped, and reflected. When the tallest resonators face the incoming wave, the system instead follows a hybrid dispersion branch connecting the Rayleigh-wave line to the bulk shear-wave line, enabling smooth mode conversion from a surface wave into a propagating bulk $S$-wave.

A third mechanism is Umklapp-mediated surface-to-body-wave conversion. The tailored metasurface for reversed bulk-wave generation interprets the process through crystal-momentum transfer, using

$\rightarrow$0

so that the effective scattered wavevector becomes $\rightarrow$1 (Chaplain et al., 2019). When the folded state lies on the isofrequency contour of a bulk shear or compressional wave, the incident Rayleigh wave is converted into the corresponding body wave. The paper ties the conversion point to the change in dominant resonator motion from longitudinal to flexural, producing an effective band-gap-like transition.

A fourth mechanism is resonant scattering in a two-mode waveguide. For a frequency $\rightarrow$2, exactly two propagating modes exist, and the geometry is tuned so that one thin ligament is resonant for the Neumann half-problem and the other for the Dirichlet half-problem (Chesnel et al., 2021). The target behavior is

$\rightarrow$3

which means near-zero reflection and mode swapping with complete transmission in the limit $\rightarrow$4.

3. Representative device architectures

The needle-oriented architecture is a compact transducer-waveguide construct coupled to a conventional 21G medical needle. The actuation stage is a Langevin sandwich transducer with 22 ring-type PIC151 piezoelectric elements clamped by an M4 bolt with substantial pretension, brass front and back masses, and extra inactive piezo rings at each end for electrical isolation (Bourlout et al., 2022). The waveguide is stainless steel 316L, implemented either as a linear waveguide or as a right-angled “cute-L” waveguide. The proximal region contains a rectangular resonator; the distal region is tapered exponentially; the needle cannula is soldered over the last 20 mm. The right-angled geometry places the transducer and needle axes parallel, improving ergonomics and compactness.

The ABH-based architecture also begins with a Langevin stack, but the converted output is the flexural vibration of an ABH wedge-shaped radiant plate rather than a needle (Wang et al., 21 Jul 2025). The design principle is resonance matching between the first-order longitudinal resonance of the Langevin transducer and the third-order symmetrical flexural mode of the radiant plate. Because the ABH plate thickness decreases toward the ends, flexural wave velocity decreases in the thinner regions, causing energy accumulation and a stepwise amplitude increase from the plate center toward both ends. The result is not only mode conversion but also gradient redistribution of radiated sound pressure in air.

The metasurface architectures are surface-mounted resonator arrays on aluminum substrates. In the elastic metawedge, vertical aluminum resonators of cross section $\rightarrow$5 mm$\rightarrow$6, spacing $\rightarrow$7 mm, and heights graded from 0.5 mm to 3 mm are arranged over a 60 mm wedge region, with 40 rows and 18 resonators per row (Colombi et al., 2017). In the Umklapp design, the rod resonators have diameter $\rightarrow$8 mm, periodicity $\rightarrow$9 mm, initial height $S$0 mm, and grading increment $S$1 mm on an aluminum slab 1.8 cm thick (Chaplain et al., 2019). In both cases, the resonator array functions as the converting interface rather than as a conventional bulk piezoelectric source.

The thin-ligament converter occupies a different category: a symmetric hard-wall waveguide made of two semi-infinite branches connected by two thin ligaments (Chesnel et al., 2021). Here the “transducer” function is embodied in the scattering junction itself. A plausible implication is that this work provides a mathematically controlled limiting case of lossless ultrasonic mode conversion, complementary to the more fabrication-driven piezoelectric and metasurface implementations.

4. Modeling, synthesis, and operator design

Finite-element optimization is central in the piezoelectric longitudinal-to-flexural devices. The needle construct was optimized in silico using COMSOL Multiphysics 5.5 with electrostatics or stress-charge coupling for the piezo stack, solid mechanics or elastodynamics for vibration and wave propagation, a structural damping ratio of 0.01, and meshing with at least 20 elements per wavelength (Bourlout et al., 2022). The optimization combined stationary analysis for the prestressed equilibrium state and frequency-domain perturbation analysis over 20 to 40 kHz. Reported optimized values were a resonator length of 23 mm, a waveguide length of 39.5 mm, and an optimal transducer-to-needle coupling distance of 58 mm.

The ABH radiant-plate design uses a different reduced-order model. The wedge plate is divided into left ABH, uniform-thickness central, and right ABH sections, and its flexural resonance is predicted with Timoshenko beam theory and the transfer matrix method (Wang et al., 21 Jul 2025). The state relation for each segment is written in terms of transverse displacement, rotation, bending moment, and shear force, and the frequency equation is obtained from the free-end determinant condition

$S$2

The paper reports that the theoretical frequencies agree with finite-element simulations to within 4% for the first several flexural modes.

Metasurface design is guided by locally periodic dispersion analysis. The metawedge work uses Bloch-Floquet theory for an infinite periodic array, showing a hybrid branch linking the Rayleigh-wave line to the bulk $S$3-wave line (Colombi et al., 2017). The Umklapp metasurface similarly relies on dispersion of a perfectly periodic rod array, extended Brillouin-zone reasoning, and isofrequency matching, with numerical validation primarily in SPECFEM2D and supplementary Abaqus simulations (Chaplain et al., 2019).

Accurate source modeling is treated as a separate but closely related problem in later work. Distributed source inversion reconstructs an effective spatio-temporal transducer model

$S$4

so that aperture-dependent phase and amplitude variations are reproduced directly from measured wavefields (Bürchner et al., 25 Mar 2026). This is technically relevant because mode-conversion performance depends strongly on the angular spectrum of the emitted field. By contrast, the 3D elevation-focused USCT forward model explicitly states that it does not model classical transducer mode conversion and neglects mode conversion into shear waves; its transducer physics are instead implemented through a spatially varying delay law in emitter and receiver operators (Li et al., 2023). This distinction is important because not every non-point transducer model is a mode-conversion model.

5. Experimental realization and measured performance

The needle-coupled construct was prototyped with 3D printed EOS stainless steel 316L waveguides and characterized electrically and optically (Bourlout et al., 2022). Measured resonances were 30.3 kHz for the bare transducer, 29.7 kHz for the linear waveguide system, and 29.1 kHz for the right-angled system. Needle-tip motion was measured with a Phantom V1612 high-speed camera at 304,000 fps, 0.8 $S$5s exposure time, 30.4 kHz, and 10-cycle bursts. At 5 W instantaneous electrical input power, tip displacement reached up to 200 $S$6m in air and up to 160 $S$7m in water. Calorimetry in a 25 mL water calorimeter yielded 69% efficiency for the linear waveguide and 62% for the right-angled waveguide.

The metawedge experiments used a Panametrics Videoscan V414 0.5 MHz plane-wave transducer coupled through a $S$8 polymer wedge with phenyl salicylate, exciting a 3-cycle sinusoidal burst centered at 500 kHz at 195 V peak-to-peak (Colombi et al., 2017). Surface motion measured with a Bossanova Tempo-10HF laser adaptive photorefractive interferometer showed amplitude growth from roughly 70–80 pm before the wedge to well above 300 pm at the trapping point. When the wedge orientation was reversed, the bottom-surface scan revealed a converted bulk shear wave, and the measured conversion angle agreed with the expected Snell-law prediction.

The Umklapp metasurface experiments used a Panametrics Accuscan A402S 1 MHz plane-wave transducer through a $S$9 polymer wedge, a Ritec RPR-4000 programmable pulser, 3-cycle sinusoidal bursts, 300 V peak-to-peak drive, and a Bossanova Tempo optical detector sampled at 125 MSa/s with 512 averages (Chaplain et al., 2019). Distinct operating bands were demonstrated for reversed shear and compressional conversion. Around 1.2 MHz, with filtered data between 1.1 and 1.2 MHz, the measured conversion angle for the shear case was $\rightarrow$0. Around 1.45 MHz, with filtering between 1.45 and 1.55 MHz, the measured compressional-wave conversion angle was $\rightarrow$1. A supplementary example at 1.7 MHz produced a compressional wave at nearly $\rightarrow$2 from the array axis.

The ABH wedge-plate transducer was simulated in COMSOL Multiphysics 6.1 and experimentally validated by impedance, vibrometry, and acoustic-field mapping (Wang et al., 21 Jul 2025). The first-order longitudinal resonance of the Langevin part was about 26055 Hz, the coupled transducer resonance from finite-element simulation was 26132 Hz, and the measured resonance from a Wayne Kerr WK6500B impedance analyzer was 26191 Hz. A Polytec PSV-400 full-field scanning laser vibrometer confirmed the intended flexural mode. With a DG1022U signal generator, AG1012 power amplifier, inductance matching box, impedance matching box, and B&K Type 3052-A-030 microphone, the near field at 26161 Hz and 4 W showed higher sound pressure toward the plate ends. In a standing-wave levitation test with a reflector spacing of 20.3 mm, 4 mm EPS spheres formed a 5, 4, 3, 4, 5 pattern from left to right.

6. Applications, limitations, and conceptual boundaries

Biomedical uses are explicit in the needle literature: biopsy, fluid injection, pain reduction during insertion, improved targeting, less tissue deflection, reduced penetration force, improved tissue yield, ultrasound-enhanced fine needle aspiration biopsy, and potentially histotripsy (Bourlout et al., 2022). The reported combination of under 5 W electrical power, high electric-to-acoustic efficiency, and compact size is presented as facilitating portability, batterization, and high patient safety with low electric powers. The paper also notes limitations: no resonance frequency tracking was implemented, tissue loading changes resonance, tissue penetration depth and tissue stiffness may detune the system, the right-angled version is slightly less efficient than the linear one, and further miniaturization and integration are needed.

Outside biomedicine, the metasurface literature places ultrasonic mode-conversion transducers within wave filtering, enhanced sensing, energy harvesting, vibration mitigation, seismic protection, resonant barriers, and waveguiding in ultrasonic and hypersound regimes (Colombi et al., 2017). The Umklapp study adds tunable redirection and wave focusing within the bulk medium, passive self-phased arrays, and independently addressable reversed $\rightarrow$3 and $\rightarrow$4 channels (Chaplain et al., 2019). The ABH study extends the application range toward ultrasonic levitation and particle sorting through gradient sound-pressure fields (Wang et al., 21 Jul 2025).

Several misconceptions are directly addressed by the cited work. First, mode conversion is not synonymous with any complex transducer response: the focused USCT forward model explicitly neglects mode conversion into shear waves and instead models transmit-receive focusing by spatially varying time delays (Li et al., 2023). Second, an inaccurate source model can corrupt the inferred mode content of a wavefield even when the converter hardware is fixed. Distributed source inversion shows that aperture-dependent amplitude and waveform differences alter not only directivity but also $\rightarrow$5-wave and Rayleigh-wave components, and that accurate transducer modeling is a prerequisite for stable and accurate waveform inversion (Bürchner et al., 25 Mar 2026). Third, direct attachment of source and load is not generally efficient; the needle construct demonstrates that a matching structure is needed when a stiff longitudinal transducer must drive a slender flexural radiator (Bourlout et al., 2022).

Taken together, these results establish ultrasonic mode-conversion transducers as a class of devices in which the decisive design variable is the mode structure of the entire source-structure-medium system. The conversion may be achieved by impedance transformers, ABH tapers, graded resonant metasurfaces, Umklapp scattering, or resonant ligaments, but in every case the operative criterion is the same: the desired ultrasonic mode must be made to emerge as the dominant resonant, propagating, or radiating channel rather than as a weak byproduct of a mismatched source.