An analog-AI chip for energy-efficient speech recognition and transcription

Models of artificial intelligence (AI) that have billions of parameters can achieve high accuracy across a range of tasks1,2, but they exacerbate the poor energy efficiency of conventional general-purpose processors, such as graphics processing units or central processing units. Analog in-memory computing (analog-AI)3-7 can provide better energy efficiency by performing matrix-vector multiplications in parallel on 'memory tiles'. However, analog-AI has yet to demonstrate software-equivalent (SWeq) accuracy on models that require many such tiles and efficient communication of neural-network activations between the tiles. Here we present an analog-AI chip that combines 35 million phase-change memory devices across 34 tiles, massively parallel inter-tile communication and analog, low-power peripheral circuitry that can achieve up to 12.4 tera-operations per second per watt (TOPS/W) chip-sustained performance. We demonstrate fully end-to-end SWeq accuracy for a small keyword-spotting network and near-SWeq accuracy on the much larger MLPerf8 recurrent neural-network transducer (RNNT), with more than 45 million weights mapped onto more than 140 million phase-change memory devices across five chips.

Optical horn antennas for efficiently transferring photons from a quantum emitter to a single-mode optical fiber

We theoretically demonstrate highly efficient optical coupling between a single quantum emitter and a monomode optical fiber over remarkably broad spectral ranges by extending the concept of horn antenna to optics. The optical horn antenna directs the radiation from the emitter toward the optical fiber and efficiently phase-matches the photon emission with the fiber mode. Numerical results show that an optical horn antenna can funnel up to 85% of the radiation from a dipolar source within an emission cone semi-angle as small as 7 degrees (antenna directivity of 300). It is also shown that 50% of the emitted power from the dipolar source can be collected and coupled to an SMF-28 fiber mode over spectral ranges larger than 1000 nm, with a maximum energy transfer reaching 70 %. This approach may open new perspectives in quantum optics and sensing.

Near-field probing of slow Bloch modes on photonic crystals with a nanoantenna

We study the near-field probing of the slow Bloch laser mode of a photonic crystal by a bowtie nano-aperture (BNA) positioned at the end of a metal-coated fiber probe. We show that the BNA acts as a polarizing nanoprobe allowing us to extract information about the polarization of the near-field of the slow-light mode, without causing any significant perturbation of the lasing process. Near-field experiments reveal a spatial resolution better than λ/20 and a polarization ratio as strong as 110. We also demonstrate that the collection efficiency is two orders of magnitude larger for the BNA than for a 200 nm large circular aperture opened at the apex of the same metal-coated fiber tip. The BNA allows for overcoming one of the main limitations of SNOM linked to the well-known trade off between resolution and signal-to-noise ratio.

Diabolo nanoantenna for enhancing and confining the magnetic optical field

In this Letter, we introduce a new nanoantenna concept aimed at generating a single magnetic hot spot in the optical frequency range, thus confining and enhancing the magnetic optical field on the background of a much lower electric field. This nanoantenna, designed by applying Babinet's principle to the bowtie nanoaperture, takes the shape of a diabolo. It differs from the well-known bowtie nanoantenna in that the opposing pair of metal triangles are electrically connected through their facing tips. Thus instead of a large charge density accumulating at the air gap of the bowtie nanoantenna, leading to a large electric field, a high optical current density develops within the central "metal gap" of the diabolo nanoantenna, leading to a large magnetic field. Numerical simulation results on the first nanodiabolo geometries show a 2900-fold enhancement of the magnetic field at a wavelength of 2540 nm, confined to a 40-by-40 nm region near the center of the nanoantenna.

Bowtie nano-aperture as interface between near-fields and a single-mode fiber

We present the development and study of a single bowtie nano-aperture (BNA) at the end of a monomode optical fiber as an interface between near-fields/nano-optical objects and the fiber mode. To optimize energy conversion between BNA and the single fiber mode, the BNA is opened at the apex of a specially designed polymer fiber tip which acts as an efficient mediator (like a horn optical antenna) between the two systems. As a first application, we propose to use our device as polarizing electric-field nanocollector for scanning near-field optical microscopy (SNOM). However, this BNA-on-fiber probe may also find applications in nanolithography, addressing and telecommunications as well as in situ biological and chemical probing and trapping.

Bowtie-shaped nanoaperture: a modal study

Using the N-order finite-difference time-domain (FDTD) method, we show that optical resonances of the bowtie nanoaperture (BNA) are due to the combination of a guided mode inside the aperture and Fabry-Perot modes along the metal thickness. The resonance of lower energy, which leads to the well-known light confinement in the gap zone, occurs at the cutoff wavelength of the fundamental guided mode. No plasmon resonance is directly involved in the generation of the light hot spot. We also define a straightforward relationship between the resonance wavelengths of the BNA and its geometrical parameters. This brings a simple tool for the optimization of the BNA design.

Full vectorial imaging of electromagnetic light at subwavelength scale

We propose a concept of near-field imaging for the complete experimental description of the structure of light in three dimensions around nanodevices. It is based on a near-field microscope able to simultaneously map the distributions of two orthogonal electric-field components at the sample surface. From a single 2D acquisition of these two components, the complementary electric and magnetic field lines and Poynting vector distributions are reconstructed in a volume beneath the sample using rigorous numerical methods. The experimental analysis of localized electric and magnetic optical effects as well as energy flows at the subwavelength scale becomes possible. This work paves the way toward the development of a complete electromagnetic diagnostic of nano-optical devices and metamaterials.

Polarization-dependent extraction properties of bare fiber probes

Despite their modest spatial resolution, uncoated tapered fiber probes are now widely used by the nano-optics community for mapping, with scanning near-field optical microscopy (SNOM), the nonradiative fields at the surface of optical and plasmonic microstructures and nanostructures. Given the significant complexity of the vectorial optical phenomena associated with subwavelength structures, the correct interpretation of SNOM acquisitions requires a complete and accurate understanding of the intrinsic image-formation procedure. In this theoretical study, we show that the SNOM imaging process with uncoated tapered fiber probes is highly polarization dependent and that the dominant effect is, surprisingly, the choice of optical fiber from which the tapered probe was fabricated. We demonstrate that although a tapered monomode fiber is unable to collect the component of the vector electric field parallel to the tip axis, a tapered multimode fiber can successfully collect all the three field components. However, we show that the signal from the longitudinal field component is collected only 10% as efficiently as the signal from the two transverse field components.

The impact of finite-depth cylindrical and conical holes in lithium niobate photonic crystals

The performance of lithium niobate (LN) photonic crystals (PhCs) is theoretically analyzed with transmission spectra and band diagrams as calculated by the 3-D Finite-Difference Time Domain (FDTD) method. For a square lattice of holes fabricated in the top surface of an Annealed Proton-Exchange (APE) waveguide, we investigate the influence of both finite hole depth and non-cylindrical hole shape, using a full treatment of the birefringent gradient index profile. As expected, cylindrical holes which are sufficiently deep to overlap the APE waveguide mode (centered at 2.5microm below the surface) produce transmission spectra closely resembling those predicted by simple 2-D modeling. As the hole depth decreases without any change in the cylindrical shape, the contrast between the photonic pass- and stop-bands and the sharpness of the band-edge are slowly lost. We show that this loss of contrast is due to the portion of the buried APE waveguide mode that passes under the holes. However, conical holes of any depth fail to produce well-defined stop-bands in either the transmission spectra or band diagrams. Deep conical holes act as a broad-band attenuator due to refraction of the mode out of the APE region down into the bulk. Experimental results confirming this observation are shown. The impact of holes which are cylindrical at the top and conical at their bottom is also investigated. Given the difficulty of fabricating high aspect-ratio cylindrical holes in lithium niobate, we propose a partial solution to improve the overlap between shallow holes and the buried mode, in which the PhC holes are fabricated at the bottom of a wide, shallow trench previously introduced into the APE waveguide surface.

Improving accuracy by subpixel smoothing in the finite-difference time domain

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.

Compensation for pixel misregistration in volume holographic data storage

We describe what we believe to be a novel postprocessing algorithm for compensating for misregistrations between a detector array and the coherent image of a pixelated two-dimensional data page. A lookup table of baseline local offsets is combined with the dynamically measured global offset of the received data page, producing an estimate of the total lateral shift of each small block of pixels. A serial algorithm then reallocates the appropriate portion of the signal detected by each pixel to its neighbors, accounting for both the linear and the quadratic contributions introduced by coherent illumination of square-law detectors. This procedure can relax the tight constraints on page registration, optical distortion, and material shrinkage that currently hamper page-oriented holographic storage systems. Experimental results from a pixel-matched 1-Mpixel volume holographic system are presented, showing an increase in position tolerance (for a raw bit-error rate <10(-3)) from +/-16% to +/-40% of the pixel pitch.

Volume holographic data storage at an areal density of 250 gigapixels/in.(2)

One thousand volume holographic data pages, each containing 1x10(6)pixels , are stored in a common volume of LiNbO(3) :Fe by use of the 90 degrees geometry. An effective transverse aperture of 1.6 mm x 1.6mm , realized by repetition of this experiment at each of the eight surrounding locations, results in a demonstrated areal density of 394pixels/mum (2) (254 Gpixels/in. (2)) . Short-focal-length Fourier optics provide a tightly confined object beam at the crystal; the reference beam is angle multiplexed. Data pages retrieved with a 1024 x 1024 CCD camera are processed to remap bad spatial light modulator pixels and to compensate for global and local pixel misregistration and are then decoded with a strong 8-bits-from-12-pixels modulation code. The worst-case raw bit-error rate (BER) before error correction was 1.1x10(-3) , sufficient to deliver a user BER of 10(-12) at an overall code rate of 0.61 user bits per detector pixel. This result corresponds to 1.08% of the well-known theoretical volumetric density limit of 1/lambda(3) .

Multiplexed phase-conjugate holographic data storage with a buffer hologram

We describe and demonstrate a volume holographic storage system in which a phase-conjugate object beam is reconstructed by the same reference beam that was used for recording. An intermediate hologram is used as a temporary buffer, recorded with its own reference beam and the data-bearing object beam. Reading this buffer hologram with the phase conjugate of its reference beam reconstructs the phase conjugate of the object beam, which can then be recorded into the desired volume hologram for long-term storage. This method combines the immunity to lens aberrations provided by phase-conjugate readout with the simplicity of using the same multiplexed reference beam for both recording and readout. Only a single pair of phase-conjugate reference beams is required. Experimental results are shown with a single LiNbO(3):Fe crystal used as both buffer and storage holograms and a self-pumped phase-conjugate mirror in BaTiO(3) that provides the pair of phase-conjugate reference beams.

Content-addressable data storage by use of volume holograms

Data stored as volume holograms--optical interference patterns imprinted into a photosensitive storage material--can be accessed both by address and by content. An optical correlation-based search compares each input query against all stored records simultaneously, a massively parallel but inherently noisy analog process. With data encoding and signal postprocessing we demonstrate a holographic content-addressable data-storage system that searches digital data with high search fidelity.

Thermal fixing of 10,000 Holograms in LiNbO3:Fe

We discuss thermal fixing as a solution to the volatility problem in holographic storage systems that use photorefractive materials such as LiNbO(3):Fe. We present a systematic study to characterize the effect of thermal fixing on the error performance of a large-scale holographic memory. We introduce a novel, to our knowledge, incremental fixing schedule to improve the overall system fixing efficiency. We thermally fixed 10,000 holograms in a 90 degrees -geometry setup by using this new schedule. All the fixed holograms were retrieved with no errors.

Experimental evaluation of user capacity in holographic data-storage systems

An experimental procedure for determining the relation between the number of stored holograms and the raw bit-error rate (BER) (the BER before error correction) of a holographic storage system is described. Compared with conventional recording schedules that equalize the diffraction efficiency, scheduling of recording exposures to achieve a uniform raw BER is shown to improve capacity. The experimentally obtained capacity versus the raw-BER scaling is used to study the effects of modulation and error-correction coding in holographic storage. The use of coding is shown to increase the number of holograms that can be stored; however, the redundancy associated with coding incurs a capacity cost per hologram. This trade-off is quantified, and an optimal working point for the overall system is identified. This procedure makes it possible to compare, under realistic conditions, system choices whose impact cannot be fully analyzed or simulated. Using LiNbO(3) in the 90 degrees geometry, we implement this capacity-estimation procedure and compare several block-based modulation codes and thresholding techniques on the basis of total user capacity.

Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems

We investigate the effects of interpixel cross talk and detector noise on the areal storage density of holographic data storage. A numerical simulation is used to obtain the bit-error rate (BER) as a function of hologram aperture, pixel fill factors, and additive Gaussian intensity noise. We consider the effect of interpixel cross talk at an output pixel from all possible configurations of its 12 closest-neighbor pixels. Experimental verification of this simulation procedure is shown for several fill-factor combinations. The simulation results show that areal density is maximized when the aperture coincides with the zero order of the spatial light modulator (SLM) (Nyquist sampling condition) and the CCD fill factor is large. Additional numerical analysis including finite SLM contrast and fixed-pattern noise show that, if the fixed-pattern noise reaches 6% of the mean signal level, the SLM contrast has to be larger than 6:1 to maintain high areal density. We also investigate the improvement of areal density when error-prone pixel combinations are forbidden by using coding schemes. A trade-off between an increase in areal density and the redundancy of a coding scheme that avoids isolated-on pixels occurs at a code rate of approximately 83%.

Gray-scale data pages for digital holographic data storage

The prospects for gray-scale (or multilevel) digital holographic data storage are theoretically and experimentally investigated. A simple signal-to-noise ratio (SNR) partitioning argument shows that when SNR scales as 1 over the number of holograms squared, five gray levels (log(2) 5 bits/pixel) would be expected to result in a 15% capacity increase over binary data pages. However, the additional signal-dependent noise sources present in practical systems create a baseline SNR that reduces both the optimal number of gray levels and the resulting gain in capacity. To implement gray-scale recording experimentally, we adapt the predistortion technique previously developed for binary page-oriented memories [Opt. Lett. 23, 289 (1998)]. Several new block-based modulation codes for decoding gray-scale data pages are introduced. User capacity is evaluated by an experimental technique using LiNbO(3) :Fe in the 90 degrees geometry. Experimental results show that a balanced modulation code with three gray levels provides a 30% increase in capacity (as well as a 30% increase in readout rate) over local binary thresholding.

Experimental study of the effects of a six-level phase mask on a digital holographic storage system

We measure the M/# and the bit-error rate of a digital holographic storage system with a 4f optical arrangement for three configurations: recording at the Fourier plane with and without a phase mask and recording outside the Fourier plane without a phase mask. Unexpectedly, no significant change in the dynamic range was observed when a phase mask was used to record in thick crystals. However, we show that a phase mask is a key component in a 4f digital holographic storage system if high-fidelity holograms with optimum volumetric density are to be stored.

Noise reduction of page-oriented data storage by inverse filtering during recording

Two novel techniques for eliminating deterministic noise from a page-oriented memory are presented. The first technique equalizes the output response of ON pixels by adjustment of the exposure of each pixel during the recording of each data page. A test image transmitted through the system measures the spatial nonuniformities, and the appropriate inverse filter is imposed upon the data page and recorded in the storage material. On readout, the output signal values are then spatially uniform, perturbed only by random noise sources. Experimental results of using this predistortion technique in a pixel-matched holographic storage system are shown. Under conditions of high volumetric density, raw bit-error-rate (BER) improvements of 6-8 orders of magnitude are obtained (from 10(-4) to <10(-10)). The second technique uses a phase shift during holographic storage to subtract from bright OFF pixels. Under conditions of low spatial light modulator contrast, BER improvements of 6 orders of magnitude (from 10(-2) to 10(-8)) are demonstrated.

Pixel-matched holographic data storage with megabit pages

Digital data-page holograms consisting of 1024 x 1024 arrays of binary pixels have been stored and subsequently retrieved with an optical exposure consistent with a data rate 1 Gbit /s. Each input pixel was precisely registered with a single detector pixel, and a raw bit-error rate as low as 2.4 x 10(-6) was demonstrated with global-threshold detection. To our knowledge, this is the first demonstration of the often-cited goal of holographic data storage of megabit data pages and a gigabit-per-second data rate.

Effects of multilevel phase masks on interpixel cross talk in digital holographic storage

We study the interpixel cross talk introduced to digital holographic data storage by use of a multilevel phase mask at the data-input plane. We evaluate numerically the intensity distribution at the output detector for Fourier plane hologram storage in a limited-aperture storage medium. Only the effect at an output pixel of interpixel cross talk from the four horizontal and vertical neighboring pixels is considered, permitting systematic evaluation of all possibilities. For random two-level and pseudorandom six-level phase masks, the influence of the pixel fill factor, as well as the aperture size of the storage medium, is studied. Our simulations show that, for a given aperture size, a random two-level mask is more susceptible to interpixel cross talk than is a pseudorandom six-level mask. Decreasing the pixel fill factor below 94% with a pseudorandom six-level phase mask makes it theoretically possible to have a system with no errors from interpixel cross talk if one particular 5-pixel pattern is forbidden through modulation coding. Reducing the input fill factor below 85% means that no patterns need to be excluded.

Modulation coding for pixel-matched holographic data storage

We describe a digital holographic storage system for the study of noise sources and the evaluation of modulation and error-correction codes. A precision zoom lens and Fourier transform optics provide pixel-to-pixel matching between any input spatial light modulator and output CCD array over magnifications from 0.8 to 3. Holograms are angle multiplexed in LiNbO(3):Fe by use of the 90 degrees geometry, and reconstructions are detected with a 60-frame/s CCD camera. Modulation codes developed on this platform permit image transmission down to signal levels of ~2000 photons per ON camera pixel, at raw bit-error rates (BER's) of better than 10(-5). Using an 8-12-pixel modulation code, we have stored and retrieved 1200 holograms (each with 45,600 user bits) without error, for a raw BER of <2x10(-8).

System metric for holographic memory systems

We introduce M/# as a metric for characterizing holographic memory systems. M/# is the constant of proportionality between diffraction efficiency and the number of holograms squared. Although M/# is a function of many variables in a holographic recording system, it can be measured from the recording and erasure of a single hologram. We verify experimentally that the diffraction efficiency of multiple holograms follows the prediction of M/# measured from a single hologram.

Effect of the oxidation state of LiNbO(3):Fe on the diffraction efficiency of multiple holograms

We show that the oxidation state of Fe in LiNbO(3) has two competing effects on the diffraction efficiency of multiple holograms in 90 degrees -geometry holographic storage. For crystals with moderate absorption, the saturation space-charge field is larger after high-temperature reduction treatment. However, reduction also increases absorption, which reduces the overall diffraction efficiency. We develop a theoretical model that predicts achievable diffraction efficiency as a function of oxidation state, doping level, photovoltaic field, crystal length, and region of beam overlap. We compare this model with experimental results for achievable diffraction efficiency and erasure-time constant.