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We report on the diffraction-free propagation of space-time wave packets (STWPs) -- a class of propagation-invariant pulsed beams -- for $\sim\!1$ km in an open-air laser range in a low-turbulence scenario. Making use of $\approx\!100$-fs pulses (bandwidth $\sim\!25$ nm) at a wavelength of $\approx\!1$ $\mu$m, we construct an STWP with a transverse width of $\approx\!2$ mm that expands to $\approx\!3$ mm after $\sim\!500$ m, and another that expands from $\approx\!8$ mm to $\approx\!10$ mm after 1 km. The propagation of the STWPs is compared to Gaussian wave packets of the same transverse spatial width and bandwidth. We establish a theoretical model that accounts for the significant factors limiting the STWP propagation distance and suggests the path to further extending this distance.

Recent theoretical work suggested upper bounds on the operating bandwidths of flat lenses. Here, we show how these bounds can be circumvented via a multi-level diffractive lens (MDL) of diameter = 100 mm, focal length = 200 mm, device thickness = 2.4{\mu} m and operating bandwidth from ? = 400 nm to 800 nm. We further combine the MDL with a refractive lens to demonstrate a hybrid telescope. By appealing to coherence theory, we show that the upper bound on relative bandwidth is surprisingly independent of lens diameter or numerical aperture, but is only limited by the bandwidth of the image sensor. Since large-area achromatic flat lenses produce significant reductions in weight over their refractive counterparts, these calculations and experiments open up opportunities for very large scale diffractive and diffractive-refractive telescopes.

In this work, we demonstrate three ultra-compact integrated-photonics devices, which are designed via a machine-learning algorithm coupled with finite-difference time-domain (FDTD) modeling. Through digitizing the design domain into "binary pixels" these digital metamaterials are readily manufacturable as well. By showing a variety of devices (beamsplitters and waveguide bends), we showcase the generality of our approach. With an area footprint smaller than ${\lambda_0}^2$, 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."

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

To date, various optimization algorithms have been employed to design and improve the performance of nanophotonic structures. Here, we propose to utilize a machine-learning algorithm viz. binary-Additive Reinforcement Learning Algorithm (b-ARLA) coupled with finite-difference time-domain (FDTD) simulations to design ultra-compact and efficient on-chip integrated nanophotonic 50:50 beam splitters (T-junctions). Here we present the design of two T-junction splitters each with a footprint of only 1.2 $��$m x 1.2 $��$m. To the best of our knowledge, these designs are amongst the smallest ever reported till date across either simulations or experiments. The simulated net power transmission efficiency for the first T-junction design is ~ 82% and the second design is ~ 80% $at 4��= 1.55 ��$m. We envision that the design methodology, as reported herein, would be useful in general for designing any efficient integrated-photonic device for optical communications systems.

The thinnest possible camera is achieved by removing all optics, leaving only the image sensor. We train deep neural networks to perform multi-class detection and binary classification (with accuracy of 92%) on optics-free images without the need for anthropocentric image reconstructions. Inferencing from optics-free images has the potential for enhanced privacy and power efficiency.

It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over a large continuous bandwidth with a single diffractive surface. We experimentally demonstrate imaging using a single flat lens of diameter > 3mm, focal length = 5mm (NA = 0.3, f/1.59) that is achromatic from 0.45um to 1um. This combination of size, NA and operating bandwidth has not been demonstrated in a flat lens before. We experimentally characterized the point-spread functions, off-axis aberrations and the broadband imaging performance. In contrast to conventional lens design, we utilize inverse design, where phase in the focal plane is treated as a free parameter. This approach attains a phase-only (lossless) pupil function, which can be implemented as a multi-level diffractive flat lens that achieves achromatic focusing and imaging., arXiv admin note: text overlap with arXiv:1907.06251

A lens performs an approximately one-to-one mapping from the object to the image planes. 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 as ~6m in our experiments. Specifically, when illuminated by collimated light at lambda=0.85mm, the MDL produced a beam that remained in focus from 5mm to ~1500mm from the MDL. The measured full-width at half-maximum of the focused beam varied from 6.6um (5mm away from MDL) to 524um (1500mm away from MDL). Since the sidelobes were well suppressed and the main-lobe was close to the diffraction-limit, imaging with a horizontal X vertical field of view of 20deg x 15deg over the entire focal range was demonstrated. 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., arXiv admin note: text overlap with arXiv:1907.06251

We designed and fabricated a flat multi-level diffractive lens (MDL) that is achromatic in the SWIR band (875nm to 1675nm). The MDL had a focal length of 25mm, aperture diameter of 8.93mm and thickness of only 2.6um. By pairing the MDL with a SWIR image sensor, we also characterized its imaging performance in terms of the point-spread functions, modulation-transfer functions, and still and video imaging.

Recently, there has been an explosion of interest in metalenses for imaging. The interest is primarily based on their sub-wavelength thicknesses. Diffractive lenses have been used as thin lenses since the late 19th century. Here, we show that multi-level diffractive lenses (MDLs), when designed properly can exceed the performance of metalenses. Furthermore, MDLs can be designed and fabricated with larger constituent features, making them accessible to low-cost, large area volume manufacturing, which is generally challenging for metalenses. The support substrate will dominate overall thickness for all flat optics. Therefore the advantage of a slight decrease in thickness (from ~2{\lambda} to ~{\lambda}/2) afforded by metalenses may not be useful. We further elaborate on the differences between these approaches and clarify that metalenses have unique advantages when manipulating the polarization states of light., Comment: 4 figures, 2 tables

It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over an almost unlimited bandwidth with a single diffractive surface. Specifically, we designed, fabricated and characterized a flat multi-level diffractive lens (MDL) that images at the wavelengths from 450nm to 850nm. We experimentally characterized the focusing efficiency, modulation-transfer function, wavefront aberrations, vignetting, distortion and signal-to-noise ratio performance of a camera comprised of this MDL and a conventional image sensor. Further, we designed two MDLs with operating wavelengths from 500nm to 15{\mu}m, and from 2{\mu}m to 150{\mu}m, respectively. With no apparent limitation in the operating bandwidth, such flat lenses could replace multiple refractive surfaces that are traditionally required for chromatic corrections, leading to thinner, lighter and simpler imaging systems with bandwidth limited primarily by the quantum efficiency of the sensor.

Optical switches are one of the most important elements of integrated photonics. Here, we designed, fabricated and characterized several nanophotonic optical switches (NOSs) in silicon that exhibit ultra-compact footprint, along with excellent extinction ratios and operating bandwidths. Simulations indicate that our best device of dimensions 3umX3um and 0.3um device height can provide about 10dB extinction ratio with a bandwidth of 12nm, centered at the design wavelength of 1550nm. Three-dimensional finite-difference time-domain analysis in conjunction with a modified version of direct binary search algorithm was used to design the nanophotonic device structure. The modulation is a result of optical modulation of the refractive index of a photochromic material and an optimized geometry of the digital metamaterials that comprise the device. The devices are CMOS fabrication compatible and examples of ones designed using multi-state geometric optimization that will lead to a new class of ultra-compact and multi-functional active integrated-silicon devices., Comment: arXiv admin note: substantial text overlap with arXiv:1712.02835

We demonstrate imaging over the visible band using a single planar diffractive lens. This is enabled via multi-level diffractive optics that is designed to focus over a broad wavelength range, which we refer to as an achromatic diffractive lens (ADL). We designed, fabricated and characterized two ADLs with numerical apertures of 0.05 and 0.18. Diffraction-limited focusing is demonstrated for the NA=0.05 lens with measured focusing efficiency of over 40% across the entire visible spectrum (450nm to 750nm). We characterized the lenses with a monochromatic and a color CMOS sensor, and demonstrated video imaging under natural sunlight and other broadband illumination conditions. We use rigorous electromagnetic simulations to emphasize that ADLs can achieve high NA (0.9) and large operating bandwidth (300nm in the visible spectrum), a combination of metrics that have so far eluded other flat-lens technologies such as metalenses. These planar diffractive lenses can be cost-effectively manufactured over large areas and thereby, can enable the wide adoption of flat, low-cost lenses for a variety of imaging applications.

Optical modulators are one of the most important elements of photonic circuits. Here, we designed, fabricated and characterized a nanophotonic all optical modulator (NOM) in silicon that is an order of magnitude smaller than any previous silicon modulators, and exhibits an extinction ratio and operable spectrum that are an order of magnitude larger than alternatives. Simulations indicate that our device can provide about 9.5dB extinction ratio with a bandwidth of 10nm, centered at 1.55um, corresponding to extinction ratio per device length of about 3.2dB/{\mu}m. Our device is fully compatible with standard complementary metal-oxide-semiconductor (CMOS) fabrication processes. The device is an example of a photonic device designed using multi-state topological optimization and will lead to a new class of ultra-compact and multi-functional active integrated-silicon devices., Comment: 10 pages, 4 figures

By placing a diffractive element in front of an image sensor, we are able to multiplex the spectral and angular information of a scene onto the image sensor. Reconstruction of the angular-spectral distribution is attained by first calibrating the angular-spectral response of the system and then, applying optimization-based matrix inversion. In our proof-of-concept demonstration, we imaged the 1D angle and the spectrum with resolutions of 0.15o and 6nm, respectively. The information is reconstructed from a single frame, thereby enabling snapshot functionality for video-rate imaging., I have added two sentences regarding potential conflict of interest due to patent filing and a startup company

Multi-spectral imagers reveal information unperceivable to humans and conventional cameras. Here, we demonstrate a compact single-shot multi-spectral video-imaging camera by placing a micro-structured diffractive filter in close proximity to the image sensor. The diffractive filter converts spectral information to a spatial code on the sensor pixels. Following a calibration step, this code can be inverted via regularization-based linear algebra, to compute the multi-spectral image. We experimentally demonstrated spectral resolution of 9.6nm within the visible band (430nm to 718nm). We further show that the spatial resolution is enhanced by over 30% compared to the case without the diffractive filter. We also demonstrate Vis-IR imaging with the same sensor. Furthermore, our camera is able to computationally trade-off spectral resolution against the field of view in software without any change in hardware as long as sufficient sensor pixels are utilized for information encoding. Since no absorptive color filters are utilized, sensitivity is preserved as well. Finally, the diffractive filters can be easily manufactured using optical lithography and replication techniques.

Machine learning (ML) has been widely applied to image classification. Here, we extend this application to data generated by a camera comprised of only a standard CMOS image sensor with no lens. We first created a database of lensless images of handwritten digits. Then, we trained a ML algorithm on this dataset. Finally, we demonstrated that the trained ML algorithm is able to classify the digits with accuracy as high as 99% for 2 digits. Our approach clearly demonstrates the potential for non-human cameras in machine-based decision-making scenarios.