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In this paper, we discuss flat programmable multi-level diffractive lenses (PMDL) enabled by phase change materials working in the near-infrared and visible ranges. The high real part refractive index contrast (Δn ∼ 0.6) of Sb₂S₃between amorphous and crystalline states, and extremely low losses in the near-infrared, enable the PMDL to effectively shift the lens focus when the phase of the material is altered between its crystalline and amorphous states. In the visible band, although losses can become significant as the wavelength is reduced, the lenses can still provide good performance as a result of their relatively small thickness (∼ 1.5λ to 3λ). The PMDL consists of Sb₂S₃concentric rings with equal width and varying heights embedded in a glass substrate. The height of each concentric ring was optimized by a modified direct binary search algorithm. The proposed designs show the possibility of realizing programmable lenses at design wavelengths from the near-infrared (850 nm) up to the blue (450 nm) through engineering PMDLs with Sb₂S₃. Operation at these short wavelengths, to the best of our knowledge, has not been studied so far in reconfigurable lenses with phase-change materials. Therefore, our results open a wider range of applications for phase-change materials, and show the prospect of Sb₂S₃for such applications. The proposed lenses are polarization insensitive and can have the potential to be applied in dual-functionality devices, optical imaging, and biomedical science. 

In this work, we explore inverse designed reconfigurable digital metamaterial structures based on phase change material Sb₂Se₃for efficient and compact integrated nanophotonics. An exemplary design of a 1 × 2 optical switch consisting of a 3 µm x 3 µm pixelated domain is demonstrated. We show that: (i) direct optimization of a domain containing only Si and Sb₂Se₃pixels does not lead to a high extinction ratio between output ports in the amorphous state, which is owed to the small index contrast between Si and Sb₂Se₃in such a state. As a result, (ii) topology optimization, e.g., the addition of air pixels, is required to provide an initial asymmetry that aids the amorphous state's response. Furthermore, (iii) the combination of low loss and high refractive index change in Sb₂Se₃, which is unique among all phase change materials in the telecommunications 1550 nm band, translates into an excellent projected performance; the optimized device structure exhibits a low insertion loss (∼1.5 dB) and high extinction ratio (>18 dB) for both phase states. 

We designed, fabricated, and characterized a flat multi-level diffractive lens comprised of only silicon with $\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}=15.2\mathrm{m}\mathrm{m}$, focal $\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}=19\mathrm{m}\mathrm{m}$, numerical aperture of 0.371, and operating over the long-wave infrared (LWIR) $\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{m}=8\text{µ<\#comment/>}\mathrm{m}$to 14 µm. We experimentally demonstrated a field of view of 46°, depth of focus $><\#comment/>5\mathrm{m}\mathrm{m}$, and wavelength-averaged Strehl ratio of 0.46. All of these metrics were comparable to those of a conventional refractive lens. The active device thickness is only 8 µm, and its weight (including the silicon substrate) is less than 0.2 g. 

We demonstrate three ultra-compact integrated-photonics devices, which are designed via a machine-learning algorithm coupled with finite-difference time-domain (FDTD) modeling. By digitizing the design domain into “binary pixels,” these digital metamaterials are readily manufacturable using traditional semiconductor foundry processes. By showing various devices (beam-splitters and waveguide bends), we showcase our approach's generality. With an area footprint smaller than λ₀², our designs are amongst the smallest reported to-date. Our method combines machine learning with digital metamaterials to enable ultra-compact, manufacturable devices, which could power a new “Photonics Moore's Law.” 

It is generally assumed that correcting chromatic aberrations in imaging requires multiple optical elements. Here, we show that by allowing the phase in the image plane to be a free parameter, it is possible to correct chromatic variation of focal length over an extremely large bandwidth, from the visible (Vis) to the longwave infrared (LWIR) wavelengths using a single diffractive surface, i.e., a flat lens. Specifically, we designed, fabricated and characterized a flat, multi-level diffractive lens (MDL) with a thickness of ≤ 10µm, diameter of ∼1mm, and focal length of 18mm, which was constant over the operating bandwidth of λ=0.45µm (blue) to 15µm (LWIR). We experimentally characterized the point-spread functions, aberrations and imaging performance of cameras comprised of this MDL and appropriate image sensors for λ=0.45μm to 11μm. We further show using simulations that such extreme achromatic MDLs can be achieved even at high numerical apertures (NA=0.81). By drastically increasing the operating bandwidth and eliminating several refractive lenses, our approach enables thinner, lighter and simpler imaging systems. 

A lens performs an approximately one-to-one mapping from the object to the image plane. This mapping in the image plane is maintained within a depth of field (or referred to as depth of focus, if the object is at infinity). This necessitates refocusing of the lens when the images are separated by distances larger than the depth of field. Such refocusing mechanisms can increase the cost, complexity, and weight of imaging systems. Here we show that by judicious design of a multi-level diffractive lens (MDL) it is possible to drastically enhance the depth of focus by over 4 orders of magnitude. Using such a lens, we are able to maintain focus for objects that are separated by as large a distance as $\sim <\#comment/>6\mathrm{m}$in our experiments. Specifically, when illuminated by collimated light at $\mathrm{\lambda <\#comment/>}=0.85\text{µ<\#comment/>}\mathrm{m}$, the MDL produced a beam, which remained in focus from 5 to 1200 mm. The measured full width at half-maximum of the focused beam varied from 6.6 µm (5 mm away from the MDL) to 524 µm (1200 mm away from the MDL). Since the side lobes were well suppressed and the main lobe was close to the diffraction limit, imaging with a horizontal × vertical field of view of ${40}^{\circ <\#comment/>}\times <\#comment/>{30}^{\circ <\#comment/>}$over the entire focal range was possible. This demonstration opens up a new direction for lens design, where by treating the phase in the focal plane as a free parameter, extreme-depth-of-focus imaging becomes possible. 

Flat lenses enable thinner, lighter, and simpler imaging systems. However, large-area and high-NA flat lenses have been elusive due to computational and fabrication challenges. Here we applied inverse design to create a multi-level diffractive lens (MDL) with thickness $<<\#comment/>1.35\text{µ<\#comment/>}\mathrm{m}$, diameter of 4.13 mm, and $\mathrm{N}\mathrm{A}=0.9$at wavelength of 850 nm (bandwidth $\sim <\#comment/>35\mathrm{n}\mathrm{m}$). Since the MDL is created in polymer, it can be cost-effectively replicated via imprint lithography.