Geometric-Phase Metalens: Wavefront Shaping

Circular polarization

Real focus forms at z = f

Metalens design

Aperture radius R 2.4 mm

Focal length f 6.0 mm

Design wavelength λ 532 nm

Live readouts

Numerical aperture

0.37

Fresnel zones

≈ 25

Diffr.-limited spot

0.87 µm

Nano-antennas

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How it works

A geometric-phase (Pancharatnam-Berry) metasurface is a flat array of sub-wavelength birefringent nano-antennas, each acting as a tiny half-wave plate. Rotating an antenna to orientation θ(x,y) does not change its material or thickness — it imprints a purely geometric phase on circularly polarized light passing through it:

φ_PB(x,y) = 2σ·θ(x,y)      σ = +1 (LCP) or −1 (RCP)

To act as a lens of focal length f at design wavelength λ, the surface must reproduce the phase a real curved lens would add — the difference between a flat wavefront and a spherical one converging on the focus:

φ_lens(x,y) = −(2π/λ)·(√(x²+y²+f²) − f)
θ(x,y) = φ_lens(x,y) / (2σ)

Each antenna in the array below is rotated to exactly this θ; its color encodes φ_lens mod 2π, revealing the concentric Fresnel-zone rings characteristic of every flat lens. Because the phase depends only on rotation angle, the same fixed nanostructure acts as a converging lens for one circular-polarization handedness and a diverging lens for the other — flipping σ flips the sign of φ_PB, so RCP light sees the conjugate phase profile and diverges as if from a virtual point source behind the surface instead of converging in front of it.

R, f, λ sliders — redesign the metalens; the antenna rotations and zone pattern update live.
LCP / RCP — switches the incident handedness, flipping real focus ↔ virtual focus with no change to the hardware.
NA = R/√(R²+f²) sets the diffraction-limited spot radius ≈ 0.61λ/NA, the smallest point the metalens can focus light to.

The animated wavefronts show the physically correct spherical-cap shape a converging/diverging metalens produces (constant total optical path length to the focus); their propagation speed is set for legibility, not to real light-travel timing. This is the same geometric-phase mechanism used in real metalens holography and polarization-multiplexed flat optics research (Capasso group and others), where one metasurface encodes two independent wavefronts, selected by input polarization.

Incident plane wavefront Reshaped wavefront Focus (real or virtual)

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