Ultra-thin high-efficiency mid-infrared transmissive Huygens meta-optics

The mid-infrared (mid-IR) is a strategically important band for numerous applications ranging from night vision to biochemical sensing. Here we theoretically analyzed and experimentally realized a Huygens metasurface platform capable of fulfilling a diverse cross-section of optical functions in the mid-IR. The meta-optical elements were constructed using high-index chalcogenide films deposited on fluoride substrates: the choices of wide-band transparent materials allow the design to be scaled across a broad infrared spectrum. Capitalizing on a two-component Huygens’ meta-atom design, the meta-optical devices feature an ultra-thin profile (λ0/8 in thickness) and measured optical efficiencies up to 75% in transmissive mode for linearly polarized light, representing major improvements over state-of-the-art. We have also demonstrated mid-IR transmissive meta-lenses with diffraction-limited focusing and imaging performance. The projected size, weight and power advantages, coupled with the manufacturing scalability leveraging standard microfabrication technologies, make the Huygens meta-optical devices promising for next-generation mid-IR system applications.

The surface currents can be related to the surface electric and magnetic polarizabilities ( , where a time dependence jt e  is assumed, E/H represent the average electric/magnetic fields tangential to the surface S, and ω denotes the angular frequency. Furthermore, the complex reflection (R) and transmission (T) coefficients of a normally incident plane wave can be related to the polarizabilities of a periodic metasurface via 3 (6) where µ and ε are the permeability and permittivity of the free space, respectively. According to Eqs. 5 and 6, it can be concluded that arbitrary phase modulation and near-unity transmittance can be achieved by engineering the dielectric resonators with suitable polarizabilities 4,5 . shows that the ED resonance is red-shifted towards longer wavelength when Ly increases while fixing Lx = 2 µm. Meanwhile, the spectral position of the magnetic resonance remains almost unchanged. In contrast, Supplementary figure 3b illustrates that the magnetic resonance is redshifted when increasing Lx and fixing Ly = 1.2 µm, whereas little spectral shift is observed for the electric resonance despite its transmission amplitude change. The ability to independently tune the ED and MD resonances permits us to engineer the meta-atom's transmission properties (phase and amplitude) by varying the dimensions of the rectangular block.
In Supplementary Figs. 3a and 3b, the ED and MD resonances are spectrally separated, and the transmittances at the target wavelength (λ0 = 5.2 µm) are low. In comparison, Supplementary figure 3c plots the transmission spectra of resonators with partially overlapping ED and MD resonances, which leads to improved transmission at the wavelength of interest. Ideally, when the two resonances completely overlap, unity transmittance can be achieved 6,7 . In our HMS, the metaatoms are designed to be slightly off-resonance to obtain desired phase shifts (between 0 to 2) while maintaining high transmission efficiencies. Figures 1b and 1c plot numerically simulated rectangular resonator transmission phase and amplitude as functions of Lx and Ly at λ0 = 5.2 µm. The choice of the dimension range (0.5 -2 m) limits the aspect ratio of the meta-atom structures to be less than 1.3, which significantly simplifies the fabrication process and improves processing yield. The same data set in Figs. 1b and 1c are also plotted in Supplementary figure 3d, which shows the phase distribution with corresponding transmission amplitude for the rectangular cells. Optimal meta-atom designs presented in Fig. 1d correspond to the data points which give rise to the maximum transmittance in Supplementary figure 3d. As we allude to in the main text, Supplementary figure 3d and Fig. 1d illustrate the presence of a "low-efficiency gap" where the rectangular meta-atoms suffer from low optical transmittance. Such low-efficiency gaps also account for the limited efficiencies of previously reported dielectric HMS devices [8][9][10][11] , which comprise meta-atoms of a single type of geometry with only size variation.

Supplementary Note 3 -Transmission properties of H-shaped meta-atoms
To overcome the "low-efficiency gap" issue discussed in Supplementary Note 2, we devised a new type of unit cell, i.e., the H-shaped resonator. Here we first illustrate that both electric and magnetic resonances can be spectrally tailored by varying Lxd and Lyd, the width and length of the dielectric bar as shown in the rectangular resonators. Thus, a full 2π phase coverage with high transmission can be realized with our two-component HMS design which include both rectangular and H-shaped resonators to generate arbitrary wavefront. Supplementary table 1 summarizes the dimensions of the meta-atoms used in our HMS meta-optical devices. Given that the PbTe meta-atoms exhibit slanted sidewalls, the dimensions listed in Table S1 are measured at the bottom of the PbTe blocks. To

Supplementary Note 4 -Beam deflector measurement protocols
Supplementary figure 6 illustrates the testing setup for the metasurface beam deflector. The angle-resolved optical scattering measurement was performed by mounting an InAsSb infrared detector (PDA10PT, Thorlabs Inc.) on a custom-made semi-circular slider track with an angular accuracy of 0.1°. The beam deflector device under test was placed at the center of the semi-circular track, and the zerodegree incidence angle and baseline laser power were calibrated by aligning the detector to the laser beam without the beam deflector in place. The laser beam was chopped at a frequency of 1,728 Hz. The chopped detector signal was transmitted to a lock-in amplifier (SR810, Stanford Research Systems, Inc.) and then recorded by a computer. The infrared image of the diffracted spots shown in Fig. 3e inset was taken by a liquid nitrogen cooled InSb focal plane array (FPA, Santa Barbara Infrared, Inc.).

Supplementary Note 5 -Cylindrical meta-lens measurement protocols and results
Supplementary figure 7a sketches the setup for mapping the output optical intensity profile from the HMS cylindrical lens. The laser was normally incident on the cylindrical lens with its metasurface side facing the detector. A precision pinhole with a diameter of (5 ± 1) m (P5S, Thorlabs Inc.) was attached to the front window of the detector (PDA10PT, Thorlabs Inc.) to limit the detector signal to only coming from light falling on the pinhole aperture. The detector was mounted onto a motion stage driven by two-axis servo actuators (TRA25CC, Newport Corporation). The intensity distributions shown in Figs. 4d-f were obtained by raster scanning the detector in the x-z plane. The scanning step size was fixed to 1 m. Since the absolute distance between the pinhole and the lens surface can only be assessed with a measurement accuracy of a few tens of microns, all data collected using the pinhole scanning method (e.g. Figs. 4d-f and Fig.  4j) are referenced to the focal spot position at 5200 nm wavelength, which is taken as 500 m away from the meta-lens, the design value. Nevertheless, the longitudinal chromatic aberration (slope of the line in Fig. 4j), which only hinges on the relative position of the focal spot, is accurate. It is also worth noting that the detector used in this experiment is thermo-electrically cooled to -30 °C and hermetically sealed in a package to prevent moisture condensation on the detector's active surface. As a result, the pinhole aperture is not in direct contact with the detector's active surface, leading to an effective reduction of the measurable numerical aperture to about 0.60.
To quantitatively assess the focusing quality, the focal spot profiles acquired using the pinhole scanning procedures were compared with simulation results. In the simulation, spatial distributions of light intensity at the focal plane of a diffraction-limited cylindrical lens were first calculated following the Huygens-Fresnel principle. The collected optical power through the pinhole was calculated by integrating the simulated light intensity at the focal plane over the pinhole aperture area. The results at three wavelengths (5110 nm, 5200 nm, and 5290 nm) are shown in Figs. 4g-i.

Supplementary Figure 7. Schematic diagrams of measurement setups for (a) mapping the output optical intensity profile from the HMS cylindrical lens; and (b) quantifying the numerical aperture of the cylindrical meta-lens.
Since our HMS cylindrical lens has a designed NA of 0.71, we employed an alternative scheme illustrated in Supplementary figure 7b to accurately quantify its light collection ability. The laser was incident normally onto the device from the substrate side. Instead of using the single-element detector, we employed a large-area thermal sensor (S302, Thorlabs Inc.) to capture the output light from the meta-lens and the optical power collected by the sensor was monitored by a power meter (PM100D, Thorlabs Inc.). The thermal sensor was mounted on a two-axis linear motion stage. The insets in Supplementary figure 7b show three representative traces of the signal recorded as the thermal sensor position was scanned along the x-axis and at three different z positions with respect to the output beam (labeled as 1, 2, and 3, respectively). At position 1, the output beam width is larger than the width of thermal sensor's active area, and thus the sensor signal peaks when the sensor is aligned to the center of the beam. At position 3, the thermal sensor can intercept all the energy within the output beam from the meta-lens, and the x-scan signal trace exhibits a "flat-top" shape. The threshold position, labeled as "2" in the figure, coincides with the transition from a peaked trace to a "flattop" one: this is when the beam width exactly equals the sensor's active area size. The lens numerical aperture was deduced from simple geometric relations of the distance between the thermal sensor and the lens as well as the width of the sensor's active surface.
Supplementary figure 8 displays a set of x-scan sensor signal traces from the NA measurement. The z-scan step size between the neighboring traces is 0.2 mm. The trace corresponding to the threshold position is marked with red color. The measurement yields a lens NA of (0.71 ± 0.01), in almost perfect agreement with the original design.

Supplementary Note 6 -Aspheric meta-lens measurement protocols and results
Supplementary figure 9a illustrates the configuration for measuring the focal spot profiles of the aspheric meta-lens (Figs. 5d-i). The focal spot formed by the meta-lens was imaged onto a liquid nitrogen cooled InSb focal plane array (Santa Barbara Infrared, Inc.) via a microscope comprising Lens 1 (C037TME-E, Thorlabs Inc.) and Lens 2 (LA8281-E, Thorlabs Inc.). Lens 1 (an aspheric black diamond-2 lens) has a numerical aperture of 0.85, larger than that of the metalens to ensure that all light from the meta-lens focal spot was captured.
The microscope provides an overall magnification of 80, which was calibrated using a USAF-1951 resolution target. The resolution target was fabricated in-house via lift-off patterning of thermally evaporated metal tin films on a double-side polished CaF2 substrate. A similar setup was used to evaluate the focusing efficiency of the lens except that the focal plane array was replaced with a thermoelectrically cooled single-element detector (PDA10PT, Thorlabs Inc.) in conjunction with an optical iris (aperture diameter ~ 100 m) and a lock-in amplifier to precisely quantify the total optical power within the aperture. We then take the encircled optical power falling within the second minimum of the Airy disk as the focused power. The fraction of the focused power over the total power within the aperture was quantified based FPA images taken over the entire aperture area. The focusing efficiency is defined as the ratio of the focused power to the total incident power on the meta-lens. We note that unlike the case of the cylindrical lens, divergence angle of the output beam from Lens 2 is reduced by the microscope such that the detector can collect all the optical power from the meta-lens focal spot. The on-axis focal spot profiles (Fig. 5k) were recorded by translating the position of the metalens along the optical axis while fixing the locations of Lens 1, Len 2, and the FPA. The (absolute) Strehl ratio at each lens position along the z-axis was computed following protocols described in Supplementary Note 7. At each wavelength, the focal spot of the lens was taken as the on-axis location where the Strehl ratio reached maximum. Supplementary figure 10a plots the measured wavelength-dependent focal lengths of the aspheric meta-lens. The data suggest a longitudinal chromatic aberration of -0.12 m/nm, close to that of the cylindrical flat lens (-0.11 m/nm) as both types of lenses are constructed out of the same set of meta-atoms. The focal tolerance (focal depth) was defined as the z-range where the Strehl ratio is above 80% of the Strehl ratio at the focal plane. For instance, at 5200 nm the Strehl ratio gauged at the focal plane is very close to unity, and therefore the focal tolerance encompasses data points in Fig. 5l with Strehl ratios greater than 0.8. Supplementary figure 10b shows the measured focal tolerances at different wavelengths.
To test the imaging capability of the meta-lens, a setup illustrated in Supplementary Figure 9b was utilized. To suppress laser speckles, a single-side polished silicon wafers was inserted into the optical path as an optical diffuser to decrease spatial coherence of the illumination light. After passing through the diffuser, the laser light was focused by a silicon lens (LA8281-E, Thorlabs Inc.) to illuminate the USAF-1951 resolution target. The meta-lens was then deployed as the objective lens of an infrared microscope, and an off-the-shelf mid-IR compound lens (Asio Lens 40494-AA1, Janos Technology, LLC) acts as a tube lens to project the image onto the focal plane array.

Supplementary Note 7 -Quantifying focusing performance of the HMS aspheric lens
Focusing performance of the meta-lens is characterized by the Strehl ratio as well as the modulation transfer function (MTF). The Strehl ratio compares the generated focusing wavefront with a reference wavefront from a diffraction-limited lens. The (absolute) Strehl ratio S is defined as the ratio of the peak intensity of a measured PSF (Imeasured) to the peak intensity of a PSF generated by an aberration-free lens with the same F/# (Idiffraction): To calculate the Strehl ratio, the measured intensity profiles of the measured focal spot (Figs. 5d-i) are normalized such that the total optical power within a given area on the image plane equals that of the diffraction-limited focal spot 12 . An optical system with a Strehl ratio exceeding 0.8 is commonly regarded as diffraction limited (approximately 0/4 optical path difference) 13 . At each wavelength, the measured focal lengths (Supplementary Figure 10a) were used to calculate the corresponding diffraction-limited PSF. The Strehl ratios calculated from measurement data at the wavelengths of 5050 nm, 5110 nm, 5200 nm, 5290 nm, 5380 nm, and 5405 nm are shown in Fig.  5j.
Uncertainty in the Strehl ratio calculations primarily results from uncertainties in the focal length of the lens. We estimate that the absolute values of focal lengths presented in Supplementary  Figure 10a have an error bar of ~ 20 m, which translates to ~ 2% variation of the Strehl ratio based on our simulations. MTFs of the meta-lens at multiple wavelengths were computed from Fourier transform of the measured focal spot profiles 14 (Figs. 5d-i) and displayed in Supplementary figure 11. The diffraction-limited MTFs plotted in the same figures for comparison were calculated for an aberration-free ideal lens of the same aperture size (1 mm by 1 mm) as the meta-lens. The diffraction-limited MTF simulations were performed using the Zemax software (Zemax, LLC) following the Huygens-Fresnel principle. We note that the Fraunhofer approximation is not valid in the model given the large NA of the meta-lens, and therefore the diffraction-limited optical transfer function of the lens cannot be straightforwardly computed by taking auto-correlation of the pupil function 15 .

Supplementary Note 8 -Towards further enhancing optical efficiencies: loss mechanism analysis and new Huygens meta-atom designs
In this section, we seek to estimate the sources of optical losses in the HMS devices and proposed means to further improve the efficiencies of these devices. First of all, all the devices we have measured are fabricated on CaF2 substrates without anti-reflection (AR) coatings. By applying an AR coating to one-side of the substrate (the side without metasurfaces), the Fresnel reflection (up to ~ 3%) can be eliminated. We also compared the theoretical efficiencies of the beam deflector and the aspheric lens to those of experimentally measured values. For the beam deflector, the measured efficiency is ~ 7% lower than the theoretical calculation. For the aspheric lens, the discrepancy is ~ 5% (after taking into account the 3% Fresnel reflection loss). Therefore, the imperfect fabrication results in 5-7% efficiency loss.
We also examined the potential to further increase the theoretical efficiency limit based on the two-component meta-atom design. Supplementary figure 12 inset illustrates the new meta-atom design alongside the set currently used in the fabricated devices. In the new design, the same ultrathin profile of the meta-atoms (650 nm thickness) is maintained and the meta-atom geometries are optimized to enhance their optical efficiencies. The main differences between the two designs include: 1) the original meta-atom #8, which has a considerably lower efficiency than other metaatoms, is replaced with an H-shaped cell in the new layout; and 2) the dimensions of other atoms are slightly modified. Supplementary table 2 summarizes the new meta-atom structural dimensions, and Supplementary figure 12 compares the simulated optical transmission for the new design with that of the original meta-atoms. Our model shows that the new meta-atom design can boost the optical efficiencies of the HMS devices by an additional 4% to reach an overall efficiency of 87%.