Experimentally realized in situ backpropagation for deep learning in photonic neural networks.

Integrated photonic neural networks provide a promising platform for energy-efficient, high-throughput machine learning with extensive scientific and commercial applications. Photonic neural networks efficiently transform optically encoded inputs using Mach-Zehnder interferometer mesh networks interleaved with nonlinearities. We experimentally trained a three-layer, four-port silicon photonic neural network with programmable phase shifters and optical power monitoring to solve classification tasks using "in situ backpropagation," a photonic analog of the most popular method to train conventional neural networks. We measured backpropagated gradients for phase-shifter voltages by interfering forward- and backward-propagating light and simulated in situ backpropagation for 64-port photonic neural networks trained on MNIST image recognition given errors. All experiments performed comparably to digital simulations ([Formula: see text]94% test accuracy), and energy scaling analysis indicated a route to scalable machine learning.

Why optics needs thickness.

This study shows why and when optical systems need thickness as well as width or area. Wave diffraction explains the fundamental need for area or diameter of a lens or aperture to achieve some resolution or number of pixels in microscopes and cameras. This work demonstrates that if we know what the optics is to do, even before design, we can also deduce the minimum required thickness. This limit comes from diffraction combined with a concept called overlapping nonlocality C that can be deduced rigorously from just the mathematical description of what the device is to do. C expresses how much the input regions for different output regions overlap. This limit applies broadly to optics, from cameras to metasurfaces, and to wave systems generally.

Multi-dimensional data transmission using inverse-designed silicon photonics and microcombs.

The use of optical interconnects has burgeoned as a promising technology that can address the limits of data transfer for future high-performance silicon chips. Recent pushes to enhance optical communication have focused on developing wavelength-division multiplexing technology, and new dimensions of data transfer will be paramount to fulfill the ever-growing need for speed. Here we demonstrate an integrated multi-dimensional communication scheme that combines wavelength- and mode- multiplexing on a silicon photonic circuit. Using foundry-compatible photonic inverse design and spectrally flattened microcombs, we demonstrate a 1.12-Tb/s natively error-free data transmission throughout a silicon nanophotonic waveguide. Furthermore, we implement inverse-designed surface-normal couplers to enable multimode optical transmission between separate silicon chips throughout a multimode-matched fibre. All the inverse-designed devices comply with the process design rules for standard silicon photonic foundries. Our approach is inherently scalable to a multiplicative enhancement over the state of the art silicon photonic transmitters.

Quantitative phase contrast imaging with a nonlocal angle-selective metasurface.

Phase contrast microscopy has played a central role in the development of modern biology, geology, and nanotechnology. It can visualize the structure of translucent objects that remains hidden in regular optical microscopes. The optical layout of a phase contrast microscope is based on a 4 f image processing setup and has essentially remained unchanged since its invention by Zernike in the early 1930s. Here, we propose a conceptually new approach to phase contrast imaging that harnesses the non-local optical response of a guided-mode-resonator metasurface. We highlight its benefits and demonstrate the imaging of various phase objects, including biological cells, polymeric nanostructures, and transparent metasurfaces. Our results showcase that the addition of this non-local metasurface to a conventional microscope enables quantitative phase contrast imaging with a 0.02π phase accuracy. At a high level, this work adds to the growing body of research aimed at the use of metasurfaces for analog optical computing.

Separating arbitrary free-space beams with an integrated photonic processor.

Free-space optics naturally offers multiple-channel communications and sensing exploitable in many applications. The different optical beams will, however, generally be overlapping at the receiver, and, especially with atmospheric turbulence or other scattering or aberrations, the arriving beam shapes may not even be known in advance. We show that such beams can be still separated in the optical domain, and simultaneously detected with negligible cross-talk, even if they share the same wavelength and polarization, and even with unknown arriving beam shapes. The kernel of the adaptive multibeam receiver presented in this work is a programmable integrated photonic processor that is coupled to free-space beams through a two-dimensional array of optical antennas. We demonstrate separation of beam pairs arriving from different directions, with overlapping spatial modes in the same direction, and even with mixing between the beams deliberately added in the path. With the circuit's optical bandwidth of more than 40 nm, this approach offers an enabling technology for the evolution of FSO from single-beam to multibeam space-division multiplexed systems in a perturbed environment, which has been a game-changing transition in fiber-optic systems.

Inference in artificial intelligence with deep optics and photonics.

Artificial intelligence tasks across numerous applications require accelerators for fast and low-power execution. Optical computing systems may be able to meet these domain-specific needs but, despite half a century of research, general-purpose optical computing systems have yet to mature into a practical technology. Artificial intelligence inference, however, especially for visual computing applications, may offer opportunities for inference based on optical and photonic systems. In this Perspective, we review recent work on optical computing for artificial intelligence applications and discuss its promise and challenges.

Programmable photonic circuits.

The growing maturity of integrated photonic technology makes it possible to build increasingly large and complex photonic circuits on the surface of a chip. Today, most of these circuits are designed for a specific application, but the increase in complexity has introduced a generation of photonic circuits that can be programmed using software for a wide variety of functions through a mesh of on-chip waveguides, tunable beam couplers and optical phase shifters. Here we discuss the state of this emerging technology, including recent developments in photonic building blocks and circuit architectures, as well as electronic control and programming strategies. We cover possible applications in linear matrix operations, quantum information processing and microwave photonics, and examine how these generic chips can accelerate the development of future photonic circuits by providing a higher-level platform for prototyping novel optical functionalities without the need for custom chip fabrication.

Experimental band structure spectroscopy along a synthetic dimension.

There has been significant recent interest in synthetic dimensions, where internal degrees of freedom of a particle are coupled to form higher-dimensional lattices in lower-dimensional physical structures. For these systems, the concept of band structure along the synthetic dimension plays a central role in their theoretical description. Here we provide a direct experimental measurement of the band structure along the synthetic dimension. By dynamically modulating a resonator at frequencies commensurate with its mode spacing, we create a periodically driven lattice of coupled modes in the frequency dimension. The strength and range of couplings can be dynamically reconfigured by changing the modulation amplitude and frequency. We show theoretically and demonstrate experimentally that time-resolved transmission measurements of this system provide a direct readout of its band structure. We also realize long-range coupling, gauge potentials and nonreciprocal bands by simply incorporating additional frequency drives, enabling great flexibility in band structure engineering.

Universal modal radiation laws for all thermal emitters.

We derive four laws relating the absorptivity and emissivity of thermal emitters. Unlike the original Kirchhoff radiation law derivations, these derivations include diffraction, and so are valid also for small objects, and can also cover nonreciprocal objects. The proofs exploit two recent approaches. First, we express all fields in terms of the mode-converter basis sets of beams; these sets, which can be uniquely established for any linear optical object, give orthogonal input beams that are coupled one-by-one to orthogonal output beams. Second, we consider thought experiments using universal linear optical machines, which allow us to couple appropriate beams and black bodies. Two of these laws can be regarded as rigorous extensions of previously known laws: One gives a modal version of a radiation law for reciprocal objects-the absorptivity of any input beam equals the emissivity into the "backward" (i.e., phase-conjugated) version of that beam; another gives the overall equality of the sums of the emissivities and the absorptivities for any object, including nonreciprocal ones. The other two laws, valid for reciprocal and nonreciprocal objects, are quite different from previous relations. One shows universal equivalence of the absorptivity of each mode-converter input beam and the emissivity into its corresponding scattered output beam. The other gives unexpected equivalences of absorptivity and emissivity for broad classes of beams. Additionally, we prove these orthogonal mode-converter sets of input and output beams are the ones that maximize absorptivities and emissivities, respectively, giving these beams surprising additional physical meaning.

Design of large scale plasmonic nanoslit arrays for arbitrary mode conversion and demultiplexing.

We present an iterative design method for the coupling and the mode conversion of arbitrary modes to focused surface plasmons using a large array of aperiodically randomly located slits in a thin metal film. As the distance between the slits is small and the number of slits is large, significant mutual coupling occurs between the slits which makes an accurate computation of the field scattered by the slits difficult. We use an accurate modal source radiator model to efficiently compute the fields in a significantly shorter time compared with three-dimensional (3D) full-field rigorous simulations, so that iterative optimization is efficiently achieved. Since our model accounts for mutual coupling between the slits, the scattering by the slits of both the source wave and the focused surface plasmon can be incorporated in the optimization scheme. We apply this method to the design of various types of couplers for arbitrary fiber modes and a mode demultiplexer that focuses three orthogonal fiber modes to three different foci. Finally, we validate our design results using fully vectorial 3D finite-difference time-domain (FDTD) simulations.

Reconfigurable add-drop multiplexer for spatial modes.

We show how a spatial mode can be extracted from a light beam, leaving the other orthogonal modes undisturbed, and allowing a new signal to be retransmitted on that mode. The method is self-aligning, avoids fundamental splitting losses, and uses only local feedback loops on controllable beam splitters and phase shifters. It could be implemented with Mach-Zehnder interferometers in planar optics. The method can be extended to multiple simultaneous mode extractions. As a spatial reconfigurable optical add-drop multiplexer, it is hitless, allowing reconfiguration without interrupting the transmission of any channel.

Nanoscale resonant-cavity-enhanced germanium photodetectors with lithographically defined spectral response for improved performance at telecommunications wavelengths.

We demonstrate the use of a subwavelength planar metal-dielectric resonant cavity to enhance the absorption of germanium photodetectors at wavelengths beyond the material's direct absorption edge, enabling high responsivity across the entire telecommunications C and L bands. The resonant wavelength of the detectors can be tuned linearly by varying the width of the Ge fin, allowing multiple detectors, each resonant at a different wavelength, to be fabricated in a single-step process. This approach is promising for the development of CMOS-compatible devices suitable for integrated, high-speed, and energy-efficient photodetection at telecommunications wavelengths.

How complicated must an optical component be?

We analyze how complicated a linear optical component has to be if it is to perform one of a range of functions. Specifically, we devise an approach to evaluating the number of real parameters that must be specified in the device design or fabrication, based on the singular value decomposition of the linear operator that describes the device. This approach can be used for essentially any linear device, including space-, frequency-, or time-dependent systems, in optics, or in other linear wave problems. We analyze examples including spatial mode converters and various classes of wavelength demultiplexers. We consider limits on the functions that can be performed by simple optical devices, such as thin lenses, mirrors, gratings, modulators, and fixed optical filters, and discuss the potential for greater functionalities using modern nanophotonics.

Self-aligning universal beam coupler.

We propose a device that can take an arbitrary monochromatic input beam and, automatically and without any calculations, couple it into a single-mode guide or beam. Simple feedback loops from detectors to modulator elements allow the device to adapt to any specific input beam form. Potential applications include automatic compensation for misalignment and defocusing of an input beam, coupling of complex modes or multiple beams from fibers or free space to single-mode guides, and retaining coupling to a moving source. Straightforward extensions allow multiple different overlapping orthogonal input beams to be separated simultaneously to different single-mode guides with no splitting loss in principle. The approach is suitable for implementation in integrated optics platforms that offer elements such as phase shifters, Mach-Zehnder interferometers, grating couplers, and integrated monitoring detectors, and the basic approach is applicable in principle to other types of waves, such as microwaves or acoustics.

Low-voltage broad-band electroabsorption from thin Ge/SiGe quantum wells epitaxially grown on silicon.

We demonstrate electroabsorption contrast greater than 5 dB over the entire telecommunication S- and C-bands with only 1V drive using a new Ge/SiGe QW epitaxy design approach; further, this is demonstrated with the thinnest Ge/SiGe epitaxy to date, using a virtual substrate only 320-nm-thick. We use an eigenmode expansion method to model the optical coupling between SOI waveguides and both vertically and butt-coupled Ge/SiGe devices, and show that this reduction in thickness is expected to lead to a significant improvement in the insertion loss of waveguide-integrated devices.

Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect.

We design an extremely compact photonic crystal waveguide spatial mode converter which converts the fundamental even mode to the higher order odd mode with nearly 100% efficiency. We adapt a previously developed design and optimization process that allows these types of devices to be designed in a matter of minutes. We also present an extremely compact optical diode device and clarify its general properties and its relation to spatial mode converters. Finally, we connect the results here to a general theory on the complexity of optical designs.

All linear optical devices are mode converters.

We show that every linear optical component can be completely described as a device that converts one set of orthogonal input modes, one by one, to a matching set of orthogonal output modes. This result holds for any linear optical structure with any specific variation in space and/or time of its structure. There are therefore preferred orthogonal "mode converter" basis sets of input and output functions for describing any linear optical device, in terms of which the device can be described by a simple diagonal operator. This result should help us understand what linear optical devices we can and cannot make. As illustrations, we use this approach to derive a general expression for the alignment tolerance of an efficient mode coupler and to prove that loss-less combining of orthogonal modes is impossible.

Self-aligned silicon fins in metallic slits as a platform for planar wavelength-selective nanoscale resonant photodetectors.

We propose and demonstrate a novel nanoscale resonant metal-semiconductor-metal (MSM) photodetector structure based on silicon fins self-aligned to metallic slits. This geometry allows the center wavelength of the photodetector's spectral response to be controlled by the silicon fin width, allowing multiple detectors, each sensitive to a different wavelength, to be fabricated in a single-step process. In addition, the detectors are highly efficient with simulations showing ~67% of the light (λ = 800 nm) incident on the silicon fin being absorbed in a region of thickness ~170 nm whereas the absorption length at the same wavelength is ~10 µm. This approach is promising for the development of multispectral imaging sensors and low-capacitance photodetectors for short-range optical interconnects.