Physical neural networks (PNNs) harness the intrinsic complexity of physical systems to perform neural computation, potentially at speeds and energy efficiencies inaccessible to conventional digital hardware. Yet, a principled framework for quantifying and predicting their computing accuracy across diverse substrates has remained elusive. Here we introduce the Hotelling Trace Criterion (HTC), a task-conditioned measure of PNN- state separability that can be evaluated without training. We demonstrate that it predicts PNN classification performance with high fidelity across highly nonlinear optical fibres, vertical-cavity surface-emitting lasers, and coupled nonlinear oscillator networks, for benchmark tasks of different difficulty. Classification loss follows a power law in HTC, with Pearson correlation coefficients exceeding 0.99 for MNIST and ≈0.97 for Fashion-MNIST, noteworthy experimental and simulated data from physically distinct systems collapse onto a single scaling curve determined by the task rather than the substrate. Applying HTC layer-by-layer during training further reveals that gradient-based optimisation distributes representational capacity unevenly across PNN layers, providing a quantitative diagnostic of training and architecture efficiency invisible to standard loss monitoring. Crucially, once the scaling exponent is established from a small number of trained calibration systems, all further performance predictions require no training since performance can be derived from the much more efficient HTC measurement. These results establish HTC as a substrate-agnostic figure of merit for comparing and scaling PNNs, advancing the field further towards a complete theory connecting fundamental hardware parameters to task performance through universal scaling laws.

The ability to process and act on data in real time is increasingly critical for applications ranging from autonomous vehicles, three-dimensional environmental sensing, and remote robotics. However, the deployment of deep neural networks (DNNs) in edge devices is hindered by the lack of energy-efficient scalable computing hardware. Here, we introduce a fanout spatial time-of-flight optical neural network (FAST-ONN) that calculates billions of convolutions per second with ultralow latency and power consumption. This is enabled by the combination of high-speed dense arrays of vertical-cavity surface-emitting lasers (VCSELs) for input modulation with spatial light modulators of high pixel counts for in-memory weighting. In a three-dimensional optical system, parallel differential readout allows signed weight values for accurate inference in a single shot. The performance is benchmarked with feature extraction in You-Only-Look-Once (YOLO) for convolution at 100 million frames per second (MFPS), and in-system backward propagation training with photonic reprogrammability. The VCSEL transmitters are implementable in any free-space optical computing systems to improve the clockrate to over gigahertz, where the high scalability in device counts and channel parallelism enables a new avenue to scale up free space computing hardware.

Vertical-cavity surface-emitting lasers (VCSELs) are key enabling components in high-speed data communication, sensing, and integrated photonics. However, combining high modulation bandwidth, stable single-mode emission, and power efficiency in a compact and manufacturable design remains a challenge. We demonstrate that replacing the conventional p-side distributed Bragg reflector (DBR) with a monolithic high-index-contrast grating (MHCG) enables a new class of high-performance VCSELs with scalable and tunable optical properties. Using this approach, we achieve modulation bandwidths up to 30 GHz, matching dual-DBR reference devices, confirming that the MHCG maintains high modulation speed. The highest bandwidths were achieved with oxide apertures up to 7 µm, ensuring a low current density, which is beneficial for extending device lifetime. The MHCG provides strong polarization and mode selectivity, resulting in linearly polarized single-mode emission with a side-mode suppression ratio of >40dB across the entire operating current range. Additionally, up to 6 nm wavelength tuning was achieved across five adjacent VCSELs by varying the MHCG geometry. We thus establish the MHCG as a powerful tool for engineering next-generation high-speed VCSELs with precise control over emission characteristics for a wide range of application scenarios.

Abstract Artificial neural networks (ANNs) represent a fundamentally connectionist and distributed approach to computing, and as such they differ from classical computers that utilize the von Neumann architecture. This has revived research interest in new unconventional hardware for more efficient ANNs rather than emulating them on traditional machines. To fully leverage ANNs, optimization algorithms must account for hardware limitations and imperfections. Photonics offers a promising platform with scalability, speed, energy efficiency, and parallel processing capabilities. However, fully autonomous optical neural networks (ONNs) with in-situ learning are scarce. In this work, we propose and demonstrate a ternary weight high-dimensional semiconductor laser-based ONN and introduce a method for achieving ternary weights using Boolean hardware, enhancing the ONN’s information processing capabilities. Furthermore, we design an in-situ optimization algorithm that is compatible with both Boolean and ternary weights. Our algorithm results in benefits, both in terms of convergence speed and performance. Our experimental results show the ONN’s long-term inference stability, with a consistency above 99% for over 10 h. Our work is of particular relevance in the context of in-situ learning under restricted hardware resources, especially since minimizing the power consumption of auxiliary hardware is crucial to preserving efficiency gains achieved by non-von Neumann ANN implementations.

Vertical cavity surface emitting lasers (VCSELs) are high performance quality and low cost light sources in many optoelectronic components. Polarization stable single mode (SM) emission over a large spectral bandwidth at high ambient temperatures is an important prerequisite for many applications such as microscale atomic clocks, gas sensing, optical coherence tomography, and optical interconnects. At the same time, it is important to maintain a simple and robust VCSEL device design concept. A hybrid monolithic high index contrast grating (MHCG) distributed Bragg reflector (DBR) VCSEL design showing mono‐linearly polarized, true single mode (SM) emission over a thermally tuned wavelength range >9 nm and excellent performance at ambient temperatures up to 80 °C is reported. Spectral tuning is achieved solely by intrinsic heating induced by the injection current, offering a low power budget and robust tuning mechanism compared to other wavelength‐swept devices, while achieving about double the tuning range of standard single‐mode VCSELs. The devices are fabricated by conventional nanoprocessing techniques, and the device architecture exhibits the robustness of standard VCSELs with a simple monolithic one‐mesa structure.

A new operation regime of VCSELs is observed: the Bose-Einstein condensation (BEC) of photons. We obtained coherent ground mode emission from the fundamental mode of a broad-area (23-µm diameter) VCSEL and a spectrum following the predictions of thermodynamic theory. Moreover, in very broad-area (80-µm diameter) VCSELs, we observed inhomogeneous emission and found signatures of the coexistence of conventional photon lasing and thermalised photon gas at different positions.

Vertical-cavity surface-emitting lasers (VCSELs) with monolithic high contrast gratings (MHCGs) as top coupling mirrors are highly attractive nanophotonic components with manyfold application prospects due to their small size footprint, energy efficiency, and wavelength flexibility. We report on the design, fabrication, and characterization of the static properties of 980 nm MHCG VCSELs and compare their performance to that of conventional double distributed Bragg reflector (DBR) VCSELs of comparable design. To increase the MHCG's optical power reflectance at 980 nm and the width of the optical stopband for single-mode behavior and improved energy efficiency, we add a 5.5-period p-doped DBR beneath the MHCG grating, thus forming a composite DBR plus MHCG top coupling mirror. With such a low number of supporting DBR mirror pairs, the MHCG characteristic dominates the output performance of the resulting devices. Our systematic study includes a variation of the grating period $P$, the grating fill factor $F$, and the oxide aperture diameter $\phi$. We report record static light output power-current-voltage (LIV) performance for our MHCG DBR VCSELs with threshold currents as low as 0.25 mA, wallplug efficiencies of 8%, optical output powers exceeding 1.6 mW, and stable linearly polarized emission with orthogonal polarization suppression ratios $>33$ dB. By varying the grating designs, record current-induced wavelength tuning ranges up to 13.4 nm and single mode emission with a side-mode suppression ratio of up to 46 dB, and $>40$ dB even beyond thermal rollover, are achieved. Moreover, the MHCG DBR VCSELs feature excellent thermal properties with thermal resistance of only 2.46 K/mW, and we observe grating design dependent side mode suppression behavior; from normal oxide aperture diameter dependent number of side modes up to oxide aperture diameter independent single mode emission up to 9 $\mu$m oxide aperture diameter. Overall, our study demonstrates that MHCGs, as a key source of optical power reflectance, can be strategically designed to tailor a VCSEL's output characteristics. By varying the MHCG geometry, we can produce side-by-side VCSELs (on the same epitaxial wafer) with vastly different emission and performance properties. By supporting a broader range of resonance wavelengths and enabling post-growth wavelength tuning, MHCG-based DBR VCSELs offer significant potential for applications in 2D VCSEL arrays, data transmission, sensing, and imaging.

We demonstrate large-scale VCSEL-based computing for convolution neural networks with spatial fanout and high clockrates. We achieved 9 parallel channels with >5 bits precision at 100-million shot-per-second, with in-system training over 93.4% accuracy.

Artificial neural networks (ANNs), have become ubiquitous and revolutionized many applications ranging from computer vision to medical diagnoses. However, they offer a fundamentally connectionist and distributed approach to computing, in stark contrast to classical computers that use the von Neumann architecture. This distinction has sparked renewed interest in developing unconventional hardware to support more efficient implementations of ANNs, rather than merely emulating them on traditional systems. Photonics stands out as a particularly promising platform, providing scalability, high speed, energy efficiency, and the ability for parallel information processing. However, fully realized autonomous optical neural networks (ONNs) with in-situ learning capabilities are still rare. In this work, we demonstrate a fully autonomous and parallel ONN using a multimode vertical cavity surface emitting laser (VCSEL) using off-the-shelf components. Our ONN is highly efficient and is scalable both in network size and inference bandwidth towards the GHz range. High performance hardware-compatible optimization algorithms are necessary in order to minimize reliance on external von Neumann computers to fully exploit the potential of ONNs. As such we present and extensively study several algorithms which are broadly compatible with a wide range of systems. We then apply these algorithms to optimize our ONN, and benchmark them using the MNIST dataset. We show that our ONN can achieve high accuracy and convergence efficiency, even under limited hardware resources. Crucially, we compare these different algorithms in terms of scaling and optimization efficiency in term of convergence time which is crucial when working with limited external resources. Our work provides some guidance for the design of future ONNs as well as a simple and flexible way to train them.

We design, fabricate, characterize, and compare 980 nm vertical cavity surface emitting lasers (VCSELs) with monolithic high contrast gratings (MHCGs) as top coupling mirrors. The MHCG is a series of parallel, rectangular stripes etched into a uniform GaAs epitaxial surface layer via electron-beam lithography and inductively coupled reactive ion etching, with specific grating period, height, and fill factor (defined as the grating bar width divided by the grating period). To boost the MHCG's optical power reflectance at 980 nm and the width of the optical stopband we add a 5.5-period p-doped distributed Bragg reflector (DBR) beneath the MHCG grating, thus forming a composite DBR plus MHCG top coupling mirror. The bottom n-doped DBR is a conventional all-semiconductor AlGaAs/GaAs DBR with 37-periods on a GaAs substrate. We fabricate single 980 nm DBR MHCG VCSELs with two oxide aperture diameters on quarter wafer pieces from starting 3-inch diameter VCSEL epitaxial wafers. Each quarter wafer contains six complete unit cells, and each unit cell is a two-dimensional array of single VCSELs in 16 rows and 15 columns. We for example set a constant but different grating period in five of the unit cells and vary the grating fill factors from column to column and we vary the oxide aperture diameters from 1 to 9 m in the rows, thus yielding a large variety of VCSEL diodes with differing MHCG parameters for us to compare. We perform room temperature on-wafer probe testing of the static optical output power-current-voltage (LIV) characteristics and emission spectra and compare the impact of the grating designs on these test results. We report record static LIV performance for our DBR MHCG VCSELs with threshold current below 1 mA and optical output power exceeding 1.3 mW. We observe room temperature bias current dependent mode emission for example single mode wavelength tuning ranges up to 12 nm.

We experimentally demonstrate an autonomous, fully tunable and scalable optical neural network of 400+ parallel nodes based on a large area, multimode semiconductor laser. We implement hardware compatible, online learning strategies based on reinforcement learning and evolutionary strategies and evaluate them in terms of performance and energy cost. Our system achieves high performance and a high classification bandwidth of 15KHz for the MNIST dataset. Our approach is highly scalable both in terms of classification bandwidth and neural network size due to our device's short response time (nanosecond).

We measure the spectral emission and the small-signal modulation frequency response of our 980 nm VCSEL arrays across OM2 multiple-mode optical fiber (MMF) patch cords and for the first time across free space (air) via optical fiber collimators (small focusing triplet lenses with optical fiber connectors) separated by 0.4 m up to 5 m. The VCSELs in our arrays are electrically in parallel but optically uncoupled, with an aim toward mitigating scintillation and speckle loss mechanisms in high bit rate free space data streams. We measure the center (mean) wavelength and the root-mean-square spectral width of our VCSEL arrays as a function of forward bias current, both across MMF and across free space. We find the spectral results are nearly identical within fractions of a nanometer. We similarly measure the S21 (s-parameter) small signal modulation frequency response of our arrays from 0.05 to 40 GHz, across fiber and across free space, and extract and plot the -3 dB bandwidths as functions of forward bias current. We achieve bandwidths up to 25 and 30 GHz for 3-element arrays with 9 and 7 micrometer oxide aperture diameters (phi), respectively, and find the bandwidths are nearly identical when comparing data transfers across OM2 MMF patch cords versus across the MMF plus a section of free space.

Photons are the first ever particles considered in the Bose-Einstein statistics and the most abundant bosons in nature. Surprisingly, photonic gases were one of the latest to demonstrate Bose-Einstein condensation (BEC) [1], despite many analogies developed over the years between laser physics and BEC. Recently, semiconductor lasers have been proposed to be a promising direction in photon BECs at room temperature [2].

Via standard nonreturn-to-zero two-level pulse amplitude modulation we achieve record single channel bit rates of 20 to 30 gigabits-per-second across free space with a 7-element top-emitting 980 nm vertical cavity surface emitting laser array - an enabling step toward energy-efficient Next Generation optical wireless communication systems.

We present experiments on reservoir computing (RC) using a network of vertical-cavity surface-emitting lasers (VCSELs) that we diffractively couple via an external cavity. Our optical reservoir computer consists of 24 physical VCSEL nodes. We evaluate the system's memory and solve the 2-bit XOR task and the 3-bit header recognition (HR) task with bit error ratios (BERs) below 1% and the 2-bit digital-to-analog conversion (DAC) task with a root mean square error (RMSE) of 0.067.

We experimentally demonstrate a fully tunable and scalable neural network of 350+ parallel nodes based on a semiconductor laser, our system achieves high performance and a high classification bandwidth of 15KHz for the MNIST dataset.

Two-dimensional hexagonal VCSEL arrays with up to 37 VCSELs per array and emitting at 940 nm to 1020 nm are produced on GaAs substrates. Arrays with variable oxide aperture diameters and new processing geometries, with a focus on optimizing the tradeoffs in optical output power, bandwidth, power conversion efficiency, and emitted far field pattern for applications in optical wireless communications are characterized and compared. Standard on wafer probing and packaged array tests are performed including terrestrial free space measurements demonstrating the viability of the core VCSEL array technology for fifth, sixth, and next generation optical wireless systems.