Volume 14, Issue 16 - Special Issue: Guided Nonlinear Optics for Information Processing

Optical neural networks have demonstrated their potential to overcome the computational bottleneck of modern digital electronics. However, their development towards high-performing computing alternatives is hindered by one of the optical neural networks’ key components: the activation function. Most of the reported activation functions rely on opto-electronic conversion, sacrificing the unique advantages of photonics, such as resource-efficient coherent and frequency-multiplexed information encoding. Here, we experimentally demonstrate a photonic nonlinear activation function based on stimulated Brillouin scattering. It is coherent and frequency selective and can be tuned all-optically to take L eaky R e LU, S igmoid , and Q uadratic shape. Our design compensates for the insertion loss automatically by providing net gain as high as 20 dB, paving the way for deep optical neural networks.

Optical computing has gained significant attention as a potential solution to the growing computational demands of machine learning, particularly for tasks requiring large-scale data processing and high energy efficiency. Optical systems offer promising alternatives to digital neural networks by exploiting light’s parallelism. This study explores a photonic neural network design using spatiotemporal chaos within graded-index multimode fibers to improve machine learning performance. Through numerical simulations and experiments, we show that chaotic light propagation in multimode fibers enhances data classification accuracy across domains, including biomedical imaging, fashion, and satellite geospatial analysis. This chaotic optical approach enables high-dimensional transformations, amplifying data separability and differentiation for greater accuracy. Fine-tuning parameters such as pulse peak power optimizes the reservoir’s chaotic properties, highlighting the need for careful calibration. These findings underscore the potential of chaos-based nonlinear photonic neural networks to advance optical computing in machine learning, paving the way for efficient, scalable architectures.

Optical computing offers potential for ultra high-speed and low-latency computation by leveraging the intrinsic properties of light, such as parallelism and linear as well as nonlinear ultra-high bandwidth signal transformations. Here, we explore the use of highly nonlinear optical fibers (HNLFs) as platforms for optical computing based on the concept of extreme learning machines (ELMs). To evaluate the information processing potential of the system, we consider both task-independent and task-dependent performance metrics. The former focuses on intrinsic properties such as effective dimensionality, quantified via principal component analysis (PCA) on the system response to random inputs. The latter evaluates classification task accuracy on the MNIST digit dataset, highlighting how the system performs under different compression levels and nonlinear propagation regimes. We show that input power and fiber characteristics significantly influence the dimensionality of the computational system, with longer fibers and higher dispersion producing up to 100 principal components (PCs) at input power levels of 30 mW, where the PC corresponds to the linearly independent dimensions of the system. The spectral distribution of the PC’s eigenvectors reveals that the high-dimensional dynamics facilitating computing through dimensionality expansion are located within 40 nm of the pump wavelength at 1,560 nm, providing general insight for computing with nonlinear Schrödinger equation systems. Task-dependent results demonstrate the effectiveness of HNLFs in classifying MNIST dataset images. Using input data compression through PC analysis, we inject MNIST images of various input dimensionality into the system and study the impact of input power upon classification accuracy. At optimized power levels, we achieve a classification test accuracy of 87 % ± 1.3 %, significantly surpassing the baseline of 83.7 % from linear systems. Noteworthy, we find that the best performance is not obtained at maximal input power, i.e., maximal system dimensionality, but at more than one order of magnitude lower. The same is confirmed regarding the MNIST image’s compression, where accuracy is substantially improved when strongly compressing the image to less than 50 PCs. These are highly relevant findings for the dimensioning of future, ultrafast optical computing systems that can capture and process sequential input information on femtosecond timescales.

The intrinsic complexity of nonlinear optical phenomena offers a fundamentally new resource to analog brain-inspired computing, with the potential to address the pressing energy requirements of artificial intelligence. We introduce and investigate the concept of nonlinear inference capacity in optical neuromorphic computing in highly nonlinear fiber-based optical Extreme Learning Machines. We demonstrate that this capacity scales with nonlinearity to the point where it surpasses the performance of a deep neural network model with five hidden layers on a scalable nonlinear classification benchmark. By comparing normal and anomalous dispersion fibers under various operating conditions and against digital classifiers, we observe a direct correlation between the system’s nonlinear dynamics and its classification performance. Our findings suggest that image recognition tasks, such as MNIST, are incomplete in showcasing deep computing capabilities in analog hardware. Our approach provides a framework for evaluating and comparing computational capabilities, particularly their ability to emulate deep networks, across different physical and digital platforms, paving the way for a more generalized set of benchmarks for unconventional, physics-inspired computing architectures.

Mapping input signals to a high-dimensional space is a critical concept in various neuromorphic computing paradigms, including models such as reservoir computing (RC) and extreme learning machines (ELM). We propose using commercially available telecom devices and technologies developed for high-speed optical data transmission to implement these models through nonlinear mapping of optical signals into a high-dimensional space where linear processing can be applied. We manipulate the output feature dimension by applying temporal up-sampling (at the speed of commercially available telecom devices) of input signals and a well-established wave-division-multiplexing (WDM). Our up-sampling approach utilizes a trainable encoding mask, where each input symbol is replaced with a structured sequence of masked symbols, effectively increasing the representational capacity of the feature space. This gives remarkable flexibility in the dynamical phase masking of the input signal. We demonstrate this approach in the context of RC and ELM, employing readily available photonic devices, including a semiconductor optical amplifier and nonlinear Mach–Zehnder interferometer (MZI). We investigate how nonlinear mapping provided by these devices can be characterized in terms of the increased controlled separability and predictability of the output state.

Optical artificial neural networks (OANNs) leverage the advantages of photonic technologies including high processing speeds, low energy consumption, and mass production to establish a competitive and scalable platform for machine learning applications. While recent advancements have focused on harnessing spatial or temporal modes of light, the frequency domain attracts a lot of attention, with current implementations including spectral multiplexing, neural networks in nonlinear optical systems and extreme learning machines. Here, we present an experimental realization of a programmable photonic frequency circuit, realized with fiber-optical components, and implement the in-situ training with optical weight control of an OANN operating in the frequency domain. Input data is encoded into phases of frequency comb modes, and programmable phase and amplitude manipulations of the spectral modes enable in-situ training of the OANN, without employing a digital model of the device. The trained OANN achieves multiclass classification accuracies exceeding 90 %, comparable to conventional machine learning approaches. This proof-of-concept demonstrates the feasibility of a multilayer OANN in the frequency domain and can be extended to a scalable, integrated photonic platform with ultrafast weights updates, with potential applications to single-shot classification in spectroscopy.

The ability to train ever-larger neural networks brings artificial intelligence to the forefront of scientific and technical discoveries. However, their exponentially increasing size creates a proportionally greater demand for energy and computational hardware. Incorporating complex physical events in networks as fixed, efficient computation modules can address this demand by decreasing the complexity of trainable layers. Here, we utilize ultrashort pulse propagation in multimode fibers, which perform large-scale nonlinear transformations, for this purpose. Training the hybrid architecture is achieved through a neural model that differentiably approximates the optical system. The training algorithm updates the neural simulator and backpropagates the error signal over this proxy to optimize layers preceding the optical one. Our experimental results achieve state-of-the-art image classification accuracies and simulation fidelity. Moreover, the framework demonstrates exceptional resistance to experimental drifts. By integrating low-energy physical systems into neural networks, this approach enables scalable, energy-efficient AI models with significantly reduced computational demands.

On-chip computing metasystems composed of multilayer metamaterials have the potential to become the next-generation computing hardware endowed with light-speed processing ability and low power consumption but are hindered by current design paradigms. To date, neither numerical nor analytical methods can balance efficiency and accuracy of the design process. To address the issue, a physics-inspired deep learning architecture termed electromagnetic neural network (EMNN) is proposed to enable an efficient, reliable, and flexible paradigm of inverse design. EMNN consists of two parts: EMNN Netlet serves as a local electromagnetic field solver; Huygens–Fresnel Stitch is used for concatenating local predictions. It can make direct, rapid, and accurate predictions of full-wave field based on input fields of arbitrary variations and structures of nonfixed size. With the aid of EMNN, we design computing metasystems that can perform handwritten digit recognition and speech command recognition. EMNN increases the design speed by 17,000 times than that of the analytical model and reduces the modeling error by two orders of magnitude compared to the numerical model. By integrating deep learning techniques with fundamental physical principle, EMNN manifests great interpretability and generalization ability beyond conventional networks. Additionally, it innovates a design paradigm that guarantees both high efficiency and high fidelity. Furthermore, the flexible paradigm can be applicable to the unprecedentedly challenging design of large-scale, high-degree-of-freedom, and functionally complex devices embodied by on-chip optical diffractive networks, so as to further promote the development of computing metasystems.

In this work, we extend temporal reflection and refraction analogies from the case of singlemode optical fibers to multimode fibers. Specifically, we show that nonlinear multimode fibers provide novel degrees of freedom that permit us to control optical pulse interactions. We take advantage of the properties of pulses propagating in different modes, such as their group velocities, dispersion parameters, and effective mode areas, in the presence of the Kerr effect. Our study was carried out by numerically solving the multimode nonlinear Schrödinger equations for graded-index optical fibers. From this analysis, we find a useful tool to obtain novel all-optical switching and frequency conversion schemes in multimode fibers.

Controlling nonlinear pulse propagation in optical fibers is paramount for applications spanning spectroscopy and optical communication networks. However, the inherent complexity of laser pulse evolution in matter, shaped by the interplay of nonlinearity and dispersion, poses significant challenges in experimental situations. Modulation instability, a fundamental process in nonlinear fiber optics, illustrates such experimental issues due to its noise-driven nature, leading to unpredictable dynamics and thus requiring advanced control strategies. Here, we investigate noise-driven modulation instability during nonlinear fiber propagation, underlining the potential of coherent optical seeding and machine learning to jointly control incoherent spectral broadening dynamics. By introducing weak coherent seeds into an initial laser pulse, we demonstrate the ability to tailor noise-driven MI properties through fine adjustments of the seed parameters driven by evolutionary algorithms. In particular, real-time spectral characterization is achieved via time-stretch dispersive Fourier transform, enabling optimized control of spectral intensity correlations. Our experimental results highlight the effectiveness of combining coherent optical seeding with optimization techniques such as genetic algorithms, to tailor incoherent spectral fluctuations arising from the competition between coherent and incoherent nonlinear frequency conversion processes. Specifically, we show that the proposed approach can be leveraged on-demand, to shape specific correlation features in the output spectrum. The implications of our research extend beyond the sheer process of modulation instability, offering promising applications in advanced optical information processing. By demonstrating simple yet robust and flexible management strategies, this work paves the way for next-generation nonlinear photonic technologies, exploiting incoherent processes in practical optical fiber architectures.

We look back at many challenges as well as unexpected successes encountered by the Mamyshev optical regenerator, which combines spectral broadening from self-phase modulation followed by offset bandpass filtering. Initially developed for ultra-fast all-optical processing of optical telecommunications signals, the Mamyshev regenerator has become most useful in the field of high-power fiber lasers. Implemented from optical fibers, the Mamyshev regenerator is compatible with integration on an optical chip, and excellent prospects are open for this polyvalent technology.