Uniform Thermo-Optic Tunability of Dielectric Metalenses

The field of low-loss dielectric metasurfaces has created a new paradigm of miniaturization for free-space optical elements. We study the effects of uniformly changing the refractive index of high-index metalenses. We experimentally demonstrate a modal refractive-index change $(\mathrm{\Delta }{n}_{\mathrm{MD}}=0.15)$ in the fundamental Mie resonances in an $\mathrm{In}\mathrm{Sb}$ resonator based on traditional thermo-optic effects. We develop a high aspect ratio metasurface design with simulated 75–90% transmission efficiency and 2π phase shift as a function of cylinder radius. A metalens is shown to have high (>60%) focusing efficiencies for large (up to 0.8) numerical aperture designs. The uniform thermal tuning of the metalens system is studied based on the variations in the spatial phase profile of the individual resonators. We demonstrate that both the operating wavelength $(\mathrm{\Delta }{\lambda }_f=500\mathrm{nm})$ and the focal length (Δf = 45 µm) can be dynamically modified based on the chromatic dispersion of the engineered metalens. The results show that static metasurfaces made of high-index semiconductors can be thermally actuated to tune the operating focal wavelength and focal length.

Figure 1

(a) Fundamental Mie resonances in $\mathrm{In}\mathrm{Sb}$ spheres appear as dips in measured reflectance spectra. The MD resonance dip shifts from 8.15 to 9.75 µm as the diameter of the sphere increases from 2.1 to 2.5 µm. The black arrow indicates this size dependent dispersion of the MD resonance. Inset shows a scanning electron microscope (SEM) image of the 2.1 µm diameter sphere. (b) Spectral shifts of the fundamental Mie resonances due to thermo-optic tuning of the $\mathrm{In}\mathrm{Sb}$ refractive index of a 2.4 µm diameter sphere. The spectra are vertically offset to illustrate the resonant wavelength shift. The refractive-index shift derived from the electric and magnetic dipole spectral resonances is plotted in the inset.

Figure 2

(a) Schematic of the metalens with a uniform etch depth (h = 6.5 µm) and varying cylinder radius focusing a 9-µm plane wave from inside an $\mathrm{In}\mathrm{Sb}$ wafer into free space. (b) Field plots showing the electric and magnetic field intensities at the resonance wavelength within the dielectric resonator. (c) Geometric dispersion in the transmission amplitude (red, left axis) and phase (blue, right axis) of a linearly polarized 9-µm light as a function of cylinder radius. A 2π phase shift with high transmission amplitude of approximately 85% is achieved. (d) The spatial phase function required to convert an incident plane wave into a transmitted focused wave. The spatial phase defined by Eq. (1) is fabricated by choosing the appropriate resonator radius as defined by Fig. 1.

Figure 3

(a) Electric field intensity at the focus of the metalens simulated with a focal length of 100 µm and N.A = 0.5. (b) Field-intensity line cut taken from Fig. 3 (white dashed line). (c) Focusing efficiency of metalenses with two different focal lengths (1 mm in red and 100 µm in blue) at varying NA values. (d),(e) Electric field intensity (in logarithmic scale) in the metalens [Fig. 3] structure at the center (d) and the first phase wrapping region (e) of the metalens, plotted on a logarithmic scale.

Figure 4

(a) Variations in the spatial (in units of inter-particle spacing) phase profile of an $\mathrm{In}\mathrm{Sb}$ metalens designed to focus 9-µm infrared light at a -mm focal length for an index of $n_{\mathrm{In}\mathrm{Sb}}=3.86$ are shown in pink. Taking the same array dimensions but changing the index to n = 3.72 (red) or 4.00 (blue) produces a change in the spatial phase profile. (b) Phase errors (Δϕ) at the 9-µm operating wavelength when the refractive index is changed to 3.72 (orange line) or 4.00 (blue line) from 3.86 (pink line). Any accumulation of phase error is “reset” due to the 2π phase or radius wrapping of the underlying design. (c) Variation of the focal wavelength—wavelength of highest intensity—as a function of the refractive index. (d) Focal-length dispersion with wavelength for three different metalens refractive indices. The focal wavelength and focal length disperse simultaneously based on the chromatic dispersion of the metalens system.