Single-Element Focusing Transducer (SEFT) Overview

• SEFT is an ultrasonic emitter that uses a single active element with passive focusing mechanisms to generate a concentrated acoustic field.
• Architectures vary from curved piezoelectric emitters and flat pistons with Fresnel zone electrodes to flexural plates with binary masks and metamaterial-lens designs.
• SEFTs balance focal confinement, efficiency, and reconfigurability, making them applicable in imaging, neuromodulation, structural health monitoring, and other domains.

Searching arXiv for the cited SEFT papers to ground the article in recent literature. arXiv search query: "(Hasegawa et al., 2024) Single-Element Focusing Transducer SEFT airborne ultrasound" A Single-Element Focusing Transducer (SEFT) is an ultrasonic source that produces a focused acoustic field with one active element rather than multi-element phasing. In the recent literature, the term encompasses several nonidentical architectures: classical spherically or elliptically curved piezoelectric emitters, flat piston elements equipped with Fresnel-zone-type electrode patterning, flexurally vibrating plates combined with binary amplitude masks, single actuators embedded in metamaterial lenses, planar transparent devices that impose a converging spherical phase on a flat aperture, and radially poled tubular emitters whose geometry yields an on-axis maximum (Dev et al., 2019, Hasegawa et al., 2024, Isomura et al., 8 Jul 2025, Li et al., 5 Dec 2025). Across these forms, the common principle is that focusing is achieved by source geometry, passive spatial modulation, or dispersion engineering, rather than by electronically phased arrays.

1. Conceptual scope and nomenclature

In its broadest usage, a SEFT is “any ultrasonic emitter that uses one active piezoelectric element to produce a focused acoustic field” (Dev et al., 2019). Classical SEFTs achieve focusing by shaping the emitter or by adding a bulk acoustic lens in front of a flat “piston” element. In human trans-spinal focused ultrasound, by contrast, SEFT denotes “a spherically curved, single-piece piezoelectric emitter that focuses ultrasound at a geometric focal point determined by its radius of curvature” (Isomura et al., 8 Jul 2025). In structural acoustics, the term has been extended to a single actuator whose radiated field is reshaped by an embedded metamaterial acoustic lens, so that beamforming and steering are produced by passive wave control rather than multi-channel phasing (Semperlotti et al., 2013).

This range of usages shows that SEFT is a functional category rather than a single hardware archetype. A common misconception is that a SEFT must be a monolithic curved piezoelectric bowl. The literature does not support that restriction. Flat circular pistons with concentric Fresnel electrodes, flexural plates with purposely designed amplitude masks, and radially poled piezoceramic tubes all satisfy the single-element criterion while relying on different field-synthesis mechanisms (Dev et al., 2019, Hasegawa et al., 2024, Li et al., 5 Dec 2025). A plausible implication is that comparisons between SEFTs are most meaningful when organized by focusing mechanism and operational bandwidth rather than by the mere fact of single-element drive.

2. Principal architectures and focusing mechanisms

Recent work presents SEFTs as a family of devices whose focusing behavior is encoded either in curvature, electrode topology, passive masks, resonant surroundings, or source geometry.

Architecture	Representative implementation	Focusing mechanism
Spherically curved SEFT	Commercial reference: $C = 85$ mm, $A = 80$ mm; adapted design: $C = 80$ mm, $A = 55$ mm	Geometric focus set by radius of curvature
Fresnel lens transducer	Flat/piston transducer with concentric ring electrodes at $F = 13$ mm, $3.85$ MHz	Binary Fresnel zone activation on a flat element
Flexural plate plus mask	Square duralumin plate, $a = 87.6$ mm, $h = 1$ mm, driven at $27{,}877$ Hz	Amplitude-only hologram matched to measured source phase
Transparent planar SEFT	LiNbO$_3$, $A = 80$0 MHz, $A = 80$1 mm, $A = 80$2	Binary $A = 80$3-shifted interdigitated electrodes imposing converging spherical phase
Tube transducer	Radially poled PZT tube, $A = 80$4 mm OD, $A = 80$5 mm ID, $A = 80$6 mm height	Inward cylindrical radiation with on-axis maximum
Metamaterial-lens SEFT	Single actuator in a $A = 80$7 m $A = 80$8 $A = 80$9 m aluminum plate, $C = 80$0 mm	Dispersion engineering, defect-localized modes, hyperbolic EFCs

For curved emitters, focusing follows directly from equalized path length to the geometric focal region. This is the baseline model used in trans-spinal focused ultrasound, where the key design parameter is the f-number $C = 80$1, and where increasing $C = 80$2 can tighten the focus through narrow intervertebral acoustic windows (Isomura et al., 8 Jul 2025).

For flat single elements, focusing can be synthesized by spatially patterned activation. In the Fresnel lens transducer, concentric ring electrodes implement a binary Fresnel zone plate on the emitting face: active rings radiate, inactive gaps suppress radiation, and the constructive zones yield a converging beam without mechanical curvature (Dev et al., 2019). The transparent planar SEFT uses the phase of an ideal converging spherical wave truncated by a plane and discretized with interdigitated electrodes that alternate a phase shift of $C = 80$3, thereby generating a finite-aperture planar focused beam or focused vortex (Li et al., 14 Apr 2026).

In airborne ultrasound, one square flexurally vibrating plate is combined with a purpose-designed binary amplitude mask placed immediately above the plate. The mask transmits sub-aperture regions whose total phase produces constructive interference at the target, forming a focus without phase electronics (Hasegawa et al., 2024). In structural health monitoring, a single actuator is “made intelligent” by embedding a metamaterial acoustic lens around it; the lens converts an omni-directional field into a collimated or focused beam and enables frequency-selective steering by tuned sectors and hyperbolic equi-frequency contours (Semperlotti et al., 2013). In power ultrasound, a radially poled piezoceramic tube driven near the fundamental radial resonance radiates inward from the inner cylindrical wall, and the coherent superposition produces an on-axis maximum with cavitation distributed throughout the bore (Li et al., 5 Dec 2025).

3. Governing formulations and design laws

Despite their architectural diversity, SEFTs are commonly analyzed as surface-velocity or aperture-phase synthesis problems. For a flexurally vibrating plate radiating into air, the acoustic field can be written through a Rayleigh/Kirchhoff-Helmholtz integral,

$C = 80$4

or through the discrete point-source superposition model used in the airborne plate study,

$C = 80$5

The same work relates the plate’s flexural behavior to thin-plate theory through

$C = 80$6

Because the actual centrally bolted plate mode deviates from an ideal simply supported mode, the source phase and amplitude are measured rather than assumed (Hasegawa et al., 2024).

For Fresnel-type SEFTs, the defining law is the half-wavelength path-difference condition. The analytical Fresnel lens transducer uses

$C = 80$7

with the approximation

$C = 80$8

when $C = 80$9. In the airborne plate variant, this Fresnel logic is adapted to a nonuniform source phase: rings are replaced by a spatially irregular binary pattern derived from the measured total phase $A = 55$0, where

$A = 55$1

The binary mask is then selected by the criterion

$A = 55$2

with $A = 55$3 tuned to maximize focal amplitude (Hasegawa et al., 2024).

For frequency-tunable planar SEFTs, the focal shift follows from aperture invariance. The transparent device derives

$A = 55$4

which linearizes near $A = 55$5 to

$A = 55$6

This provides an approximate linear relation between focal length and driving frequency near the design one (Li et al., 14 Apr 2026).

For focused sensing and imaging, the relevant quantity is often not emitted pressure but spatial sensitivity. The optoacoustic simulation work formulates the Spatial Impulse Response,

$A = 55$7

and replaces explicit SIR calculation by direct computation of the Spatial Pulse Response,

$A = 55$8

This shift removes the singular $A = 55$9-kernel from the numerical integration and makes high-accuracy surface integration tractable with h-adaptive cubature (Bader et al., 2024).

4. Optimization, tuning, and simulation strategies

SEFT design in current work is strongly application-specific. In airborne ultrasound, the design workflow is empirical and holographic: the near-field airborne pressure amplitude and phase are measured $F = 13$0 mm above the plate on a $F = 13$1 mm grid over an $F = 13$2 mm $F = 13$3 $F = 13$4 mm area, the target focus $F = 13$5 is chosen, the total phase $F = 13$6 is computed, and a binary amplitude mask is laser-machined in $F = 13$7 mm square perforations in $F = 13$8 mm thick acrylic. Adjacent open squares are merged, and small isolated open islands are bridged for mechanical robustness (Hasegawa et al., 2024).

In human trans-spinal focused ultrasound, geometry optimization is framed as a focality-intensity trade-off. The computational study explored adapted SEFTs with $F = 13$9–$3.85$0 mm and $3.85$1–$3.85$2 mm in $3.85$3 mm steps, yielding $3.85$4 non-overlapping designs on the torso. A Pareto front search identified a “balanced” SEFT with $3.85$5 mm and $3.85$6 mm $3.85$7, while a “maximum-overlap” design used $3.85$8 mm and $3.85$9 mm $a = 87.6$0. Frequencies of $a = 87.6$1, $a = 87.6$2, and $a = 87.6$3 kHz were evaluated, with source peak pressure amplitude $a = 87.6$4 kPa in all scenarios. The balanced design increased beam overlap by up to $a = 87.6$5 relative to the commercial unit while maintaining target intensity above the empirical neuromodulation threshold, whereas the maximum-overlap design further improved overlap but dropped below threshold (Isomura et al., 8 Jul 2025).

Frequency tuning provides a different route to reconfigurability. The transparent planar SEFT fixes geometry at fabrication and then tunes the focal plane by detuning the drive frequency near the design frequency. With $a = 87.6$6 MHz, $a = 87.6$7 mm, and $a = 87.6$8, water-tank measurements showed measured focal shifts of $a = 87.6$9 mm at $h = 1$0 MHz and $h = 1$1 mm at $h = 1$2 MHz for the focused beam, and $h = 1$3 mm and $h = 1$4 mm for the focused vortex, with measured slopes of approximately $h = 1$5 mm/MHz and $h = 1$6 mm/MHz, respectively (Li et al., 14 Apr 2026).

Accurate numerical modeling is itself a design lever for SEFTs. The optoacoustic work uses a 3D h-adaptive cubature algorithm for SPR evaluation, with error control through the condition $h = 1$7. For a spherically focused circular piston with focal radius $h = 1$8 m and aperture radius $h = 1$9 m, the proposed SPR method achieved median RSE up to five orders of magnitude lower than a discretize-SIR plus discrete convolution reference at comparable computation times. In model-based reconstruction, more accurate SEFT modeling reduced the relative residual norm by $27{,}877$0, $27{,}877$1, and $27{,}877$2 in three scans and reduced noise artifacts in out-of-plane maximum intensity projections (Bader et al., 2024).

5. Performance characteristics, trade-offs, and limitations

SEFT performance is governed by a recurring trade-off between focal confinement, efficiency, and reconfigurability. The airborne plate SEFT experimentally demonstrated intensified foci at $27{,}877$3, $27{,}877$4, $27{,}877$5, $27{,}877$6, and $27{,}877$7 mm. Measured focal diameters were approximately $27{,}877$8–$27{,}877$9 mm at $_3$0 mm, with visible sidelobes and artifacts. Numerical simulations and measurements agreed, but absolute pressure values were not reported, and the study emphasized spatial distribution and relative focusing efficacy rather than SPL or efficiency (Hasegawa et al., 2024).

Amplitude-only Fresnel implementations share a similar limitation. In the analytical Fresnel lens transducer, the $_3$1 two-ring design within an $_3$2 mm $_3$3 $_3$4 mm tile at $_3$5 MHz and $_3$6 mm increased maximum $_3$7 from $_3$8 to $_3$9 and maximum $A = 80$00 from $A = 80$01 to $A = 80$02 in normalized arbitrary units relative to a uniform circular piston of the same footprint. At the same time, binary amplitude Fresnel plates typically exhibit higher sidelobe levels than curved piezos or refractive polymer lenses, and amplitude-only Fresnel lenses pass only about half the space and do not recover the power from “blocked” zones (Dev et al., 2019).

In spinal focused ultrasound, the principal limitation is anatomical sensitivity. Through the intervertebral acoustic window, the adapted SEFT achieved approximately $A = 80$03-fold higher intraspinal intensity and up to $A = 80$04 greater beam overlap than the commercial SEFT, but small misalignments produced severe losses: a $A = 80$05 mm vertical shift resulted in a reduction of target intensity by approximately $A = 80$06-fold, and shifts of $A = 80$07–$A = 80$08 mm relative to the T10–T11 intervertebral window decreased target intensity by factors of approximately $A = 80$09–$A = 80$10 when the beam exited the window (Isomura et al., 8 Jul 2025).

The tube transducer illustrates the opposite operating regime: high-power sonication rather than narrow focal confinement. At equal electrical input of $A = 80$11 W, the tube’s sonochemiluminescence maximum greyscale level was $A = 80$12, versus $A = 80$13 for the sonotrode. For both tube input powers, more than $A = 80$14 of bore pixels were in the combined “low + high intensity” bands, and at $A = 80$15 W, $A = 80$16 were “high intensity.” In the graphite-delamination case study, the tube achieved complete removal up to $A = 80$17 cm$A = 80$18 effective area in $A = 80$19 s at $A = 80$20 W, but at $A = 80$21 cm$A = 80$22 remaining mass increased to approximately $A = 80$23, indicating a throughput limit for a single tube and $A = 80$24 s exposure (Li et al., 5 Dec 2025).

These cases show that “single-element” does not imply a single performance envelope. Some SEFTs prioritize static focal precision, some maximize spatially distributed high intensity, and others trade peak intensity for overlap or for passive simplicity. This suggests that SEFT evaluation should be normalized to the intended acoustic pathway and task, not treated as a generic alternative to phased arrays.

6. Applications and domain-specific significance

SEFTs are used wherever one-channel hardware simplicity is valuable and application constraints permit passive or quasi-static focusing. In airborne ultrasound, the flexural-plate SEFT was motivated by nonlinear acoustic effects such as radiation force employed in acoustic levitation. The same work gives the standard relations

$A = 80$25

and the Gor’kov potential

$A = 80$26

Because the paper did not report absolute pressure at the focus, quantitative levitation thresholds could not be computed from the data, but the demonstrated $A = 80$27–$A = 80$28 mm focal spots support the interpretation that the approach is relevant to macroscopic radiation-force actuation and to applications where static or slowly reconfigurable foci suffice (Hasegawa et al., 2024).

In neuromodulation, SEFTs are being adapted to anatomically constrained paths. The human tsFUS feasibility study identifies the posterior intervertebral acoustic window as preferable in the thoracic spine and lamina-based sonication as preferable in the cervical spine, with thoracic window intensities averaging $A = 80$29 W/cm$A = 80$30 and cervical lamina intensities averaging $A = 80$31 W/cm$A = 80$32. The feasibility threshold used for comparison was $A = 80$33 W/cm$A = 80$34 inside the target, while the resulting in-target intensities remained far below the FDA diagnostic ultrasound limit of $A = 80$35 W/cm$A = 80$36. Thermal rise was not modeled, and the paper recommends thermal simulation for protocol finalization (Isomura et al., 8 Jul 2025).

In imaging and system characterization, SEFTs function as focused receivers as much as emitters. The optoacoustic SPR framework showed that precise system characterization and simulation improve image contrast and reduce noise artifacts in model-based reconstruction. The clinically representative focused concave element used there had elevational focusing radius $A = 80$37 cm, elevational arc length $A = 80$38 mm, width $A = 80$39 mm, center frequency $A = 80$40 MHz, and $A = 80$41 dB bandwidth $A = 80$42, underscoring the continued importance of single focused elements inside larger imaging assemblies (Bader et al., 2024).

In structural health monitoring, the embedded metamaterial-lens SEFT provides beamforming, focusing, and frequency-selective steering with a single actuator. Reported demonstrations include a collimated beam at $A = 80$43 for $A = 80$44 kHz, steering to $A = 80$45 at $A = 80$46 kHz and to $A = 80$47 at $A = 80$48 kHz, and sub-wavelength resolution in which two sources separated by $A = 80$49 m $A = 80$50 were distinctly imaged in the far field (Semperlotti et al., 2013).

In microfluidics and compact biomedical platforms, planar Fresnel and transparent SEFTs enable focusing without bulky curvature. The Fresnel lens transducer can also generate strong rotational fields through sectoring, while the transparent planar device provides precise axial tuning by frequency and co-aligned optical and acoustic access. In power ultrasonics, the tube SEFT addresses the classic trade-off between localized high intensity and weak distributed activity by delivering sonotrode-like or higher intensities distributed throughout its bore, making it compatible with high-throughput flow-based applications (Dev et al., 2019, Li et al., 14 Apr 2026, Li et al., 5 Dec 2025).

Taken together, these studies place SEFTs in a distinct position within ultrasonic engineering. They do not replace phased arrays for dynamic holography, multifocal synthesis, or aberration correction, but they provide focused fields with one active element across airborne acoustics, guided waves, optoacoustic imaging, neuromodulation, microfluidics, and power ultrasound. The most consistent theme is not a single geometry but a single-channel design philosophy: shift complexity from electronics to curvature, phase patterning, passive masking, or wave-structuring media, and accept the accompanying trade-offs in bandwidth, sidelobes, and reconfigurability.