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Metalens

A flat paraxial phase-gradient proxy with design-wavelength focal length, diffractive chromatic shift or an idealized achromatic band, and user-set focusing efficiency.

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In the real world

A metalens is a flat optical surface patterned with subwavelength structures. Those meta-atoms impose a position-dependent phase delay instead of relying on the curved entrance and exit faces of a glass lens. An ideal focusing phase profile at design wavelength λ₀ is hyperbolic rather than the quadratic profile of the paraxial limit:

ϕ(r,λ0)=−2πλ0(f02+r2−f0)(mod2π)\phi(r,\lambda_0) = -\frac{2\pi}{\lambda_0}\left(\sqrt{f_0^2+r^2}-f_0\right) \pmod{2\pi}
Ideal phase required to bring a normally incident plane wave to a focus f₀ from radius r.
NA=sin⁡ ⁣[arctan⁡ ⁣(D2∣f0∣)]\mathrm{NA} = \sin\!\left[\arctan\!\left(\frac{D}{2|f_0|}\right)\right]
Geometric numerical aperture in air for clear diameter D and focal length f₀.

The direction of that colour error is the surprising part, and worth holding on to: a metalens is chromatic the opposite way round from glass. A refractive lens has a higher index in the blue, so blue comes to a focus nearer than red. A diffractive surface has a focal length inversely proportional to wavelength, so red focuses nearer and blue further away. Their colour fringes therefore run in opposite directions — which is also why a diffractive surface can be used to cancel the chromatic aberration of a refractive one rather than compounding it.

A phase pattern fabricated for one wavelength normally has strong diffractive chromaticity: longer wavelengths focus nearer and shorter wavelengths focus farther away. Achromatic metalenses add engineered group delay, but bandwidth, aperture, NA, polarization response, and efficiency are coupled design constraints rather than independent knobs[1]. Practical focusing efficiency also sends some incident power into zeroth order, unwanted diffraction orders, reflection, absorption, and scatter[2].

In OpticalSetup

OpticalSetup treats the patterned surface as a zero-thickness paraxial phase-gradient proxy. In Chromatic mode, the nominal focal length f₀ is exact at the design wavelength and every sampled wavelength follows the ordinary diffractive scaling:

f(λ)=f0λ0λf(\lambda) = f_0\frac{\lambda_0}{\lambda}
The wavelength-dependent focal length used by the chromatic metalens trace.
u′=u−hf(λ)u' = u - \frac{h}{f(\lambda)}
Each sampled wavelength then uses the same paraxial ray-transfer relation as the ideal thin lens.

A broadband ray is expanded into the same weighted wavelength samples used by prisms and gratings, making axial color visible in the actual traced paths. Idealized achromatic band holds f=f₀ inside the chosen range and transitions continuously back to diffractive scaling outside it. Focusing efficiency attenuates the focused output by the configured power fraction.

Simplified vs. reality

No phase map or electromagnetic field is propagated. The simulator does not design meta-atoms, derive efficiency, show the unfocused zeroth order, validate group-delay feasibility, or calculate polarization conversion, PSF, MTF, Strehl ratio, diffraction-limited spot size, field angle, aberrations, substrate effects, or fabrication tolerances. Achromatic mode is explicitly an idealized system-level behavior, not proof that the selected diameter, NA, bandwidth, and efficiency can be fabricated together.

Related components

Thin convex lensThick spherical lensDiffraction gratingSLMObjective

References

  1. Arbabi et al., “Subwavelength-thick lenses with high numerical apertures and large efficiency,” Nature Communications 6, 7069 (2015)
  2. Khorasaninejad et al., “Metalenses at visible wavelengths,” Science 352, 1190–1194 (2016)

Further reading