The ability to process optical signals without passing into the electrical domain has always attracted the attention of the research community. Processing photons by photons unfolds new scenarios, in principle allowing for unseen signal processing and computing capabilities. Optical computation can be seen as a large scientific field in which researchers operate, trying to find solutions to their specific needs by different approaches; although the challenges can be substantially different, they are typically addressed using knowledge and technological platforms that are shared across the whole field. This significant know-how can also benefit other scientific communities, providing lateral solutions to their problems, as well as leading to novel applications. The aim of this Roadmap is to provide a broad view of the state-of-the-art in this lively scientific research field and to discuss the advances required to tackle emerging challenges, thanks to contributions authored by experts affiliated to both academic institutions and high-tech industries. The Roadmap is organized so as to put side by side contributions on different aspects of optical processing, aiming to enhance the cross-contamination of ideas between scientists working in three different fields of photonics: optical gates and logical units, high bit-rate signal processing and optical quantum computing. The ultimate intent of this paper is to provide guidance for young scientists as well as providing research-funding institutions and stake holders with a comprehensive overview of perspectives and opportunities offered by this research field.

In free-space optical communications that use both amplitude and phase data modulation (for example, in quadrature amplitude modulation (QAM)), the data are typically recovered by mixing a Gaussian local oscillator with a received Gaussian data beam. However, atmospheric turbulence can induce power coupling from the transmitted Gaussian mode to higher-order modes, resulting in a significantly degraded mixing efficiency and system performance. Here, we use a pilot-assisted self-coherent detection approach to overcome this problem. Specifically, we transmit both a Gaussian data beam and a frequency-offset Gaussian pilot tone beam such that both beams experience similar turbulence and modal coupling. Subsequently, a photodetector mixes all corresponding pairs of the beams’ modes. During mixing, a conjugate of the turbulence-induced modal coupling is generated and compensates the modal coupling experienced by the data, and thus the corresponding modes of the pilot and data mix efficiently. We demonstrate a 12 Gbit s⁻¹ 16-QAM polarization-multiplexed free-space optical link that is resistant to turbulence.

This tutorial highlights challenges and opportunities in achieving efficient flexible optical networks. Optical signal processing may potentially increase network flexibility because of its functions' transparency, tunability, and reconfigurability. We review recent advances in high-speed optical signal processing techniques that might enable flexible networks. Various optical approaches that enable key functions are discussed, including format conversion, increases in spectral efficiency, and phase-sensitive operations. We also discuss the potential utilization of basic enabling technologies, such as optical frequency combs and optical nonlinear devices.

We experimentally investigate the potential of using ‘self-healing’ Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of thel = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.

Novel forms of beam generation and propagation based on orbital angular momentum (OAM) have recently gained significant interest. In terms of changes in time, OAM can be manifest at a given distance in different forms, including: (1) a Gaussian-like beam dot that revolves around a central axis, and (2) a Laguerre-Gaussian ( $$LG_{\ell ,p}$$L G ℓ , p ) beam with a helical phasefront rotating around its own beam center. Here we explore the generation of dynamic spatiotemporal beams that combine these two forms of orbital-angular-momenta by coherently adding multiple frequency comb lines. Each line carries a superposition of multiple $$LG_{\ell ,p}$$L G ℓ , p modes such that each line is composed of a different $$\ell$$ℓ value and multiple p values. We simulate the generated beams and find that the following can be achieved: (a) mode purity up to 99%, and (b) control of the helical phasefront from 2π-6π and the revolving speed from 0.2–0.6 THz. This approach might be useful for generating spatiotemporal beams with even more sophisticated dynamic properties.

We experimentally demonstrate that a single microresonator can emit two orthogonally polarized individually coherent combs: (i) a strong polarized soliton comb and (ii) an orthogonally polarized continuous wave seeded weaker comb, generated from the first one via cross-phase modulation, sharing the repetition rate of the soliton comb. Experimental results show that the power of the transverse electric-polarized seed can be well below the threshold of comb generation (e.g., 0.1 mW). In addition, simulations show that a dark pulse could be generated in the anomalous dispersion regime by a bright soliton when the two orthogonally polarized modes have the same group velocity in the microresonator.