Meta-q-plate for complex beam shaping

Abstract

Optical beam shaping plays a key role in optics and photonics. In this work, meta-q-plate featured by arbitrarily space-variant optical axes is proposed and demonstrated via liquid crystal photoalignment based on a polarization-sensitive alignment agent and a dynamic micro-lithography system. Meta-q-plates with multiple-, azimuthally/radially variant topological charges and initial azimuthal angles are fabricated. Accordingly, complex beams with elliptical, asymmetrical, multi-ringed and hurricane transverse profiles are generated, making the manipulation of optical vortex up to an unprecedented flexibility. The evolution, handedness and Michelson interferogram of the hurricane one are theoretically analysed and experimentally verified. The design facilitates the manipulation of polarization and spatial degrees of freedom of light in a point-to-point manner. The realization of meta-q-plate drastically enhances the capability of beam shaping and may pave a bright way towards optical manipulations, OAM based informatics, quantum optics and other fields.

Figure 1. Q-plate and OV generation.

Pictorial illustration of the optical action of a q-plate with q = 0.5 on an input left circularly polarized plane wave. The output beam is a right circularly polarized helical mode with OAM given by m = 1. The dark blue sticks on the q-plate depict the local LC directors. The circular arrows denote the polarization handedness from the point of view of the source. z indicates the light propagation direction and x is the polar axis.

Figure 2. Setup for meta-q-plate fabrication.

The dynamic micro-lithography setup consists of a light emission component, a dynamic pattern generation component, an image focusing component and a monitor component. A meta-q-plate with q = 1.5 and radially different initial angles (0 and π/2) is illustrated. Three out of all eighteen exposure sum-regions are shown as examples and corresponding polarizer angles are listed with the red arrows pointing the polar axis. CCD, charge coupled device; DMD, digital micro-mirror device.

Figure 3. Meta-q-plates and generated complex beams.

The micrographs (top), measured LC director distributions (middle) and output field patterns (bottom) of meta-q-plates: (a) array with q = 0.5, 1, 1.5 and 2 respectively, (b) azimuthally variant q and fixed α₀ (q = 3 @ 0 ≤ φ ≤ π/2 & π ≤ φ ≤ 3π/2, q = 1 @ π/2 < φ < π & 3π/2 < φ < 2π, α₀ = 0), (c) azimuthally variant q and fixed α₀ (q = 10 @ 0 ≤ φ ≤ π, q = 2 @ π < φ < 2π, α₀ = 0), (d) radially variant α₀ and fixed q (α₀ = 0 @ r ≤ 0.5r₀, α₀ = π/2 @ r > 0.5r₀, q = 1.5) (e) radially variant α₀ and fixed q, (α₀ = 0 @ r ≤ 0.1r₀, α₀ = π/2 @ r > 0.9r₀, and from the centre to the edge, α₀ increases with an interval of π/18 every 0.1r₀, q = 1.5), (f) radially variant q and fixed α₀, (q = 2 @ r ≤ 0.1r₀, q = 6.5 @ r > 0.9r₀, and from the centre to the edge, q increases with an interval of 0.5 every 0.1r₀, α₀ = 0). All scale bars indicate 100 μm. The colour bar for director distribution indicates the director varying from 0 to π, and the colour bar for output field pattern indicates the relative optical intensity.

Figure 4. Simulation and experimental verification.

Simulated LC director distributions (top) and corresponding output transverse profiles (bottom) of meta-q-plates with: (a) n = 5, q = 2~4, (b) n = 7, q = 2~5, (c) n = 9, q = 2~6. The colour bar for the director distribution indicates the director varying from 0 to π, and the colour bar for the transverse profile indicates the relative optical intensity. The simulated transverse profiles (top) and the corresponding experimental results (bottom) of the meta-q-plate with n = 10, q = 2~6.5 under the incident polarization of (d) left and (e) right circular handedness. (f) Simulated (top) and experimental (bottom) Michelson interferograms obtained by the output beam with a spherical linearly polarized reference wave.