Thermally reconfigurable metalens

Abstract

Reconfigurable metalenses are compact optical components composed by arrays of meta-atoms that offer unique opportunities for advanced optical systems, from microscopy to augmented reality platforms. Although poorly explored in the context of reconfigurable metalenses, thermo-optical effects in resonant silicon nanoresonators have recently emerged as a viable strategy to realize tunable meta-atoms. In this work, we report the proof-of-concept design of an ultrathin (300 nm thick) and thermo-optically reconfigurable silicon metalens operating at a fixed, visible wavelength (632 nm). Importantly, we demonstrate continuous, linear modulation of the focal-length up to 21% (from 165 μm at 20 °C to 135 μm at 260 °C). Operating under right-circularly polarized light, our metalens exhibits an average conversion efficiency of 26%, close to mechanically modulated devices, and has a diffraction-limited performance. Overall, we envision that, combined with machine-learning algorithms for further optimization of the meta-atoms, thermally reconfigurable metalenses with improved performance will be possible. Also, the generality of this approach could offer inspiration for the realization of active metasurfaces with other emerging materials within field of thermo-nanophotonics.

Keywords: dielectric nanoresonators; metasurfaces; thermo-optical effects; tunable metalenses.

Figure 1:

Thermally reconfigurable phase control: Principle and analytical phase design. (a) Schematic illustration of a thermally reconfigurable metalens. Each nano-structure exhibits a resonance mode that locally induces a phase delay. All together these meta-atoms shape a converging wavefront with focal length f ₀, which can be modulated with the temperature thanks to thermo-optical effects (schematic shows a decrease in focal length). (b) Schematic illustration of the thermo-optical effect. Thermally induced changes of the refractive index cause a shift of the resonance mode of a meta-atom (top). The associated change in phase delay results in a phase shift Δϕ at the operating wavelength λ _op (bottom). (c) Lateral and top views of a nanofin (left) as well as its 3D rendering, indicating also the illumination conditions (right). $\left(l_1,{\mathrm{w}}_1\right.$ , $\left.l_2,{\mathrm{w}}_2\right)$ , gap, h, p and θ are the width and the length of the nanopillar 1 and 2, the gap between the two nano-pillars, the height of the nano-pillars corresponding to the initial c-Si film thickness, the nano-fin lattice period and the angle of rotation of the nanofin structure respectively. g = 0.060 μm, h = 0.300 μm, p = 0.350 μm. (d) Required phase profile at different temperatures to satisfy: Initial focal length f ₀ = 200 μm at T ₀ = 20 °C; final focal length f ₀ + Δf = 155 μm at T _max = 260 °C. (e) Required phase shift $\mathrm{\Delta }\varphi \left(r,T\right)$ between the phase profile at T ₀ = 20 °C and the phase at temperature T. (f) Numerical simulation of the maximum focal length variation over the initial focal length (%) as a function of the numerical aperture NA achievable with a maximum phase variation of Δ^max ϕ ∼ 100 deg and with different ML radiuses (left). Maximum focal length variation over the initial focal length (%) as a function of NA achievable with a ML radius R = 15.75 μm and for different Δ^max ϕ values (right). The chosen metalens design values are indicated with a black circle (f ₀ = 200 μm, Δf = −45 μm and Δ^max ϕ = 102 deg).

Figure 2:

Study of the thermo-optic response of nanofins with different geometrical parameters and relative rotation. (a) Schematic illustration of a unit nanofin NF # structure and its geometrical parameters; $\left(l_1,{\mathrm{w}}_1\right.$ , $\left.l_2,{\mathrm{w}}_2\right)$ , g, h, p and θ are the width and the length of the nanopillar 1 and 2, the gap between the two nano-pillars, the height of the nano-pillars corresponding to the initial c-Si film thickness, the nano-fin lattice period and the angle of rotation of the nanofin structure respectively. gap = 0.060 μm, h = 0.300 μm, p = 0.350 μm. (b) ϕ(θ, T, #) and Δϕ(θ, #) are a 3D and 2D matrices representing the phase parameter space used for the wavefront design. (c) Left and center 2D metalens phase profile at 20 °C and 260 °C respectively. (c) Right metalens phase shift between 260° and 20 °C. (d) Left and center 1D projection of the 2D plots (c) left and center respectively. Circle markers represent the actual ML phase value at a specific radial position overlapped to the theoretical phase values displayed with a continuous line (blue and red color indicates 20 °C and 260 °C respectively. (d) Right 1D projection of the 2D plots in (c) right. Circle markers represent the actual ML phase shift value at a specific radial position overlapped to the theoretical phase shift values displayed with a continuous black line. Different gradual colors in plot (c) and (d) represent different nanofin (#1–6). Notice that the nanofin #4 has not been selected by the algorithm for the ML design. All the phase shift profiles are computed with respect to the initial temperature T ₀ = 20 °C. All the nanofin structures have been studied with COMSOL numeric simulations to retrieve their phase and transmission efficiency at different temperatures and rotation angles θ.

Figure 3:

Thermally tunable metalens performance and deviation from an ideal lens. (a) Beam propagation focused by the designed ML. 2D intensity profiles along the XZ propagation plane at increasing temperatures. (b) 1D projection of the intensity profiles along the Z propagation direction at increasing temperatures. (c) Point spread function (PSF) 2D profile at the focal plane (XY) at increasing temperatures. (d) 1D projection of the PSF at all simulated temperatures. All the intensity profiles are normalized by the maximum intensity value at each temperature. (e) Focal length f at increasing temperatures. The focal length position of our designed metalens is compared with the focal length position extracted from the beam propagation of the ideal ML and with the effective linear focal length assumption. (f) PSF full width at half maximum (FWHM) of our designed ML at increasing temperatures. The FWHM of our designed ML is compared with the FWHM expected from an ideal ML and with the theoretical diffraction limit extracted from the Gaussian approximation of the Airy disk (σ ∼ 0.42λ/2NA and $\text{FWHM}=2\sqrt{2\ln (2)}*\sigma$ ). (g) Focusing efficiency η of our designed metalens at increasing temperature. η is computed as the transmitted field intensity over an integration area with radius R _i = 15.75 μm equal to the ML radius divided by the input field intensity at the ML plane (z = 0 μm). The average transmission efficiency of our designed ML over all temperature is 26%. The efficiency of our designed ML is compared with the efficiency expected by an ideal lens. With ideal lens we refer to a lens with an ideal phase profile and with 100% transmission efficiency. All the conversion efficiency values are computed with the same integration radius R _i = 15.75 μm.