Can a flat lens focus all colours to the same spot?
By designing nanopillars that control both the phase and how phase changes with wavelength, the authors built flat lenses that focus a broad band of infrared light to nearly the same point.
Source
Broadband achromatic dielectric metalenses
Study at a glance
- Design
- Other — Theory of achromatic focusing limits plus design, fabrication and optical characterisation of several amorphous-silicon metalenses built from three meta-unit libraries
- N
- Four fabricated metalenses were characterised; no statistical sample.
- Population
- Amorphous silicon nanopillar metalenses on quartz operating in the near infrared
- Outcome
- Focal length versus wavelength, focal spot size versus diffraction limit, Strehl ratio, focusing efficiency
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What they did
The authors showed that each point on an achromatic flat lens needs a particular phase and a particular dispersion (change of phase with frequency), and plotted these needs in a 'phase-dispersion space'. From this they derived a limit linking lens radius, numerical aperture and bandwidth to the range of dispersion the building blocks can provide. They designed libraries of silicon pillars (solid, ring, concentric and cross shapes, 800 or 1400 nm tall), fabricated several metalenses, and measured their three-dimensional focal intensity with a tunable laser.
What they found
A lens 100 micrometres wide with a 200 micrometre focal length, built from the taller pillars, corrected chromatic aberration continuously from 1200 to 1650 nm and reached the derived limit; the shorter-pillar version worked over 1300 to 1650 nm with parasitic focal spots. Focal lengths shifted by only 2 to 5% across the band, focal spots were at or near the diffraction limit, and Strehl ratios exceeded 0.8 for the taller-pillar lenses. A high-NA lens (about 0.88) was also achromatic, but only over 1200 to 1400 nm, illustrating the trade-off.
The limits
What it doesn't show
Focusing efficiencies were lower than the best single-wavelength metalenses, owing to amplitude variation, phase mismatch, neighbour coupling and fabrication errors, and weak parasitic focal spots remained. Only on-axis focusing of a small singlet was tested, so off-axis aberrations and real imaging performance are not shown. The demonstration is in the near infrared; visible operation would require other materials.
Key terms
- Metasurface
- A flat layer of subwavelength structures that shapes light's phase, amplitude or polarisation.
- Chromatic aberration
- Blurring caused by different wavelengths focusing at different distances.
- Phase dispersion
- How the phase imposed by a structure changes with light frequency.
- Numerical aperture
- A measure of the range of angles a lens collects; higher NA gives smaller focal spots.
- Strehl ratio
- Peak intensity of a real focal spot relative to an ideal diffraction-limited one; above 0.8 counts as diffraction-limited.
Flashcards
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Quiz yourself
What does 'phase-dispersion space' plot for each meta-unit?
Common questions
Why are ordinary flat diffractive lenses chromatic?
Diffractive elements bend longer wavelengths more, so the focal length shifts strongly with wavelength (negative dispersion).
What is the key trade-off the paper identifies?
For a given set of building blocks, making the lens bigger, raising its NA, or widening its bandwidth all demand more dispersion range, so you cannot maximise all three at once.
Why did taller pillars help?
Taller pillars span a wider range of dispersion, expanding the region of phase-dispersion space that can be filled, which suppressed parasitic foci and widened the bandwidth.
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