An atom-thin lens showed about 30% modulation in the strength of the second-harmonic signal at its focus under a control beam. The result came at control-beam fluences—the amount of beam energy delivered to each unit of area—below 10 µJ/cm2, while corresponding linear-regime focal modulation was less than 1%.
The study asks whether a monolayer WSe2 Fresnel zone plate lens can enable ultrafast, all-optical tuning of focusing efficiency through second-harmonic generation (SHG), the nonlinear light signal used to read the lens’s focus. In practical terms, it tests whether a single layer patterned with concentric rings can have its focused signal adjusted by light.
A lens built from rings
The device was 100 µm in diameter and contained 22 concentric rings. It was designed for 755 nm light and a 150 µm focal length. The WSe2 monolayer was obtained by Au-assisted exfoliation onto a 1 mm quartz substrate, then patterned with electron-beam lithography.
The same wavelength appeared in the optical characterization of the bare monolayer. Its photoluminescence peaked around 755 nm, and the second-harmonic signal was enhanced near that resonance. Fits gave linewidths of 36 meV for the neutral-exciton contribution and 56 meV for the trion contribution.
The focus was the test
With collimated 750 nm illumination, the measured focal length was 152 µm, compared with 150 µm in simulation. Linear focusing efficiency was about 0.06%, providing the baseline for the nonlinear measurement.
For nonlinear characterization, the diverging fundamental beam was matched to the lens’s 100 µm aperture. Transmitted SH light was collected through a confocal pinhole while the lens was scanned along the optical axis.
The pump-probe measurement used a 515 nm above-bandgap control beam across the lens aperture while the exciton-enhanced SH response was monitored. In bare-monolayer tests, the control-beam fluence ranged from 1.60 to 9.65 µJ/cm2; focal modulation was measured below 10 µJ/cm2.
The nonlinear SH focus had a focal length of about 200 µm. Its spot measured 2.73 µm horizontally and 2.11 µm vertically by full width at half maximum, a standard measure of spot size. The calculated focusing efficiency was about 9.3%, more than 150 times the linear-regime value.
That roughly 200 µm focal length was longer than the 150 µm design value. The authors attributed the difference and an asymmetric focal profile to the diverging-beam illumination conditions.
Fast response, careful reading
Time-resolved measurements showed a recovery with two fitted components: a fast component below 0.5 ps and a slow component of approximately 10 ps. The time units are picoseconds, or trillionths of a second.
The conclusion describes the modulation speed as picosecond-scale and calls it a nine-orders-of-magnitude improvement over previously reported electrical tuning. That is a reported comparison, not an independently quantified switching-time result: the document gives no formal switching-time distribution or confidence interval for it.
The 9.3% efficiency figure was calculated using a sheet nonlinear susceptibility of 0.091 nm2/V, a 100 µm beam diameter, half-area etching and corrections for losses in the setup. The uncertainty of those inputs was not reported.
Still a laboratory result
Those details matter because the evidence comes from optical measurements and numerical simulations of a fabricated monolayer WSe2 lens. The document describes the fabricated device in the singular, and it does not report how many independently fabricated lenses were assessed.
For the focal-modulation result, error bars were calculated as the standard deviation among three measurements. Formal hypothesis tests, confidence intervals and a rationale for the sample size were not reported.
The authors present nonlinear atomically thin lenses as a possible platform for active nanophotonics. Beam steering, optical switching and miniaturized nonlinear imaging are described as future prospects, not applications demonstrated in this experiment.
The document is an arXiv preprint, version 1, dated 25 Aug 2026; no journal or peer-review status is reported in the supplied metadata.
The acknowledgments report support from DFG, NWO and an ERC Starting Grant through named programmes and grants. The funders’ roles in study design, analysis or reporting are not reported.
Paper data and sources
Original title: Ultrafast tuning of the focusing efficiency of a nonlinear atomically thin lens
Authors: Rahil Rezwan, Bernardo Dias, Tom Hoekstra et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text