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Abstract Multilevel diffractive lenses (MDLs) have emerged as an alternative to both conventional diffractive optical elements (DOEs) and metalenses for applications ranging from imaging to holographic and immersive displays. Recent work has shown that by harnessing structural parametric optimization of DOEs, one can design MDLs to enable multiple functionalities like achromaticity, depth of focus, wide-angle imaging, etc. with great ease in fabrication. Therefore, it becomes critical to understand how fabrication errors still do affect the performance of MDLs and numerically evaluate the trade-off between efficiency and initial parameter selection, right at the onset of designing an MDL, i.e., even before putting it into fabrication. Here, we perform a statistical simulation-based study on MDLs (primarily operating in the THz regime) to analyse the impact of various fabrication imperfections (single and multiple) on the final structure as a function of the number of ring height levels. Furthermore, we also evaluate the performance of these same MDLs with the change in the refractive index of the constitutive material. We use focusing efficiency as the evaluation criterion in our numerical analysis; since it is the most fundamental property that can be used to compare and assess the performance of lenses (and MDLs) in general designed for any application with any specific functionality. 

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 an inverse designed achromatic, flat, polarization-insensitive diffractive optic element, i.e., a multilevel diffractive lens (MDL), operating across a broadband range of UV light (250 nm – 400 nm) via numerical simulations. The simulated average on-axis focusing efficiency of the MDL is optimized to be as high as ∼86%. We also investigate the off-axis focusing characteristics at different incident angles of the incoming UV radiation such that the MDL has a full field of view of 30°. The simulated average off-axis focusing efficiency is ∼67%, which is the highest reported till date for any chromatic or achromatic UV metalens or diffractive lens to the best of our knowledge. The designed MDL is composed of silicon nitride. The work reported herein will be useful for the miniaturization and integration of lightweight and compact UV optical systems. 

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.