Editorial Board Members’ Collection Series: Nonlinear Photonics

1. Introduction

Photonics has often been defined as the key technology of the 21st century. In recent decades, the overall trend of research and development (R&D) towards the miniaturization of devices and systems, pushed by the tremendous development of microelectronics, has led to the continuous development of micro/nanophotonic devices, which have huge potential for low-cost, scalable production, as well as the integration of high-density components [1]. On the other hand, nonlinear optical phenomena play a key role both in the knowledge of the light–matter interaction and in many fields of photonics applications [2]. The combination of integrated photonics technologies with nonlinear optics, which has led to the growth of nonlinear photonics, has also opened the way for groundbreaking new devices. Their evolution would enable advanced applications to emerge not only in optical processing and computing, but also in metrology, single-molecule sensing, imaging, microscopy, mid-infrared photonics, terahertz generation, microwave photonics, biomedicine, and quantum photonics [3].

The present Special Issue (SI) entitled “Editorial Board Members’ Collection Series: Nonlinear Photonics”, aims to highlight the current state of the art, some recent advances, and perspectives for further development. As a result, this SI contains two reviews and nine research articles, which can be divided into three groups.

In the first group of papers, three papers [4,5,6] highlight new effects. Reference [4] focuses on nonclassical states of light, which are an essential resource for high-precision optical techniques, relying on photon correlations and noise reshaping. Efforts toward engineering the spatiotemporal profile of quantum states of light have already found great success ([4] and references therein). This article focuses, instead, on shaping the noise statistics of quantum states of light. Deviations from Brownian diffusion, known as anomalous diffusion (AnDi), occur when the mean square displacement (MSD) growth with time has an exponent other than one. AnDi is investigated in reference [5]. In disordered photonic systems, we can find examples in which light propagation exhibits subdiffusive behavior ([5] and reference therein). There are limited works reporting the modulation of chirped Gaussian soliton molecules in extra-cavity optical fiber modulation systems. Reference [6] concerns this issue and reports the theoretically simulated modulation of a soliton molecule that has an initial chirped Gaussian pulse shape in a 1 μm extra-cavity optical fiber modulation system.

The four papers [7,8,9,10] of the second group are devoted to the hot issue of identifying efficient device integration platforms, which justifies the continuation of fundamental studies and the search for new or advanced materials with higher nonlinear coefficients and/or better overall properties. In reference [7], attention is given to graphene, which has properties that make it very promising for various applications in photonics and optoelectronics: combining graphene with other materials, one can create a variety of waveguiding devices with better characteristics compared to waveguides made of traditional materials. In reference [8], the development of optical materials based on a nonlinear optical single crystal of lithium niobate is described. LiNbO₃ is a crystal state that has high nonlinear optical coefficients, which is crucial for the development of functional materials. Composite magnetic nanostructures are a subject of high research interest, as they provide several exciting effects absent in live nature. Among them, much attention has been paid to the studies of exchange coupling in antiferromagnetic/ferromagnetic (AFM/FM) films, which leads to the pinning effect. In reference [9], comparative studies of linear and nonlinear magneto-optical effects, under the laser-induced switching of the pinning effect in IrMn/CoFe films of various thickness of the ferromagnetic CoFe layer, is reported. The study of localized surface plasmons (LSPs) in nanoscale structures is described in reference [10]. Nanostructures are an essential step towards identifying optimal plasmonic modes that can facilitate robust optomechanical coupling and a deeper understanding of light–matter interactions at the nanoscale.

The last group of papers [11,12,13,14], two studies and two reviews, are dedicated to some of the most important application fields of nonlinear photonics. They begin with a review [11] focused on plasmonic core–shell nanoparticles in photovoltaic (PV) applications. Core–shell nanoparticles have emerged as a promising new technology with unique structural attributes and widely tunable properties. Among label-free nonlinear optical techniques, stimulated Raman scattering (SRS) microscopy plays an important role in enabling imaging systems and performing label-free imaging with high sensitivity, high spatial and spectral resolution, 3D sectioning, and fast image acquisition. In the second review [12], applications and perspectives of SRS in bio photonics are described and discussed. In reference [13], a diode-pumped solid-state (DPSS) laser, used for intracavity pump-enhanced difference frequency generation (DFG) to create a 3.5-micron laser, is presented and potential future applications in free-space optical communication are also discussed. Finally, in reference [14], microwave photonic (MWP) signal processors are presented and their intrinsic advantages such as low loss, large processing bandwidth, and strong immunity to electromagnetic interference are discussed.

2. An Overview of the Articles in This Special Issue

Systems that utilize quantum information resources generally take advantage of coherent macroscopic superposition and/or entanglement, both of which are generically found in states supported by nonlinear systems. However, optical nonlinearities are typically weak for closed systems. With the advent of epsilon-near-zero materials and polariton-enhanced scattering, commonly facilitated by electronically induced transparency, large effective nonlinearities become increasingly realistic as well. When realized in a high-Q optical resonator, strong optical nonlinearities with relatively long evolution time and low loss facilitate deterministic quantum optical state engineering.

We note that in a material with second- and third-order nonlinearities comparable in strength at optical frequencies, the interaction between field states is strongly photon-number-dependent. With this in mind, in reference [4], a theoretical method for the deterministic shaping of quantum light via photon number state selective interactions is proposed. A class of nonlinear optical resonators is individuated, which can transform many-photon wavefunctions to produce structured states of light with nonclassical noise statistics. The devices, based on parametric down conversion, utilize the Kerr effect to tune photon-number-dependent frequency matching, inducing photon-number-selective interactions. With a high-amplitude coherent pump, the number-selective interaction shapes the noise of a two-mode squeezed cavity state with minimal dephasing. The requisite material properties to build the device and highlight the remaining material degrees of freedom, which offer flexible material design, are also reported.

Recurrent neural networks (RNNs) are promising methods for the classification of anomalous diffusion trajectories, identifying temporal dependencies and sequential patterns, which are essential for characterizing anomalous diffusion processes. The integration of statistical methods with RNNs has enabled the development of robust frameworks that can detect and predict the occurrence of anomalous diffusion, even in the presence of significant noise. By leveraging these techniques, reference [5] aims to improve accuracy for identifying diffusion types without the need for extensive preprocessing or noise filtering. Therefore, it contributes to the broader application of a combination of higher-order statistics and artificial intelligence in analyzing and predicting phenomena within stochastic and noisy environments. In reference [5], feature extraction through parametric and non-parametric spectral analysis methods is explored to decode anomalously diffusing trajectories, achieving reduced computational costs compared with other approaches that require additional data or prior training. The proposed methods deliver accurate results, even with short trajectories and in the presence of noise.

A soliton molecule consists of two or more solitons, and these solitons have fixed phase differences and temporal pulse intervals between adjacent solitons. Soliton molecules can be efficiently generated in fiber laser oscillators through increasing pump power or decreasing saturable power/energy of intra-cavity saturable absorbers. The possible experimental realization techniques of soliton molecules with chirped Gaussian pulses are the constructions of passively mode-locked fiber lasers, accompanied by intra-cavity management of pump power, group-velocity dispersion, saturable absorbers, and so on.

In reference [6], the extra-cavity modulation of a soliton molecule with a chirped Gaussian pulse shape is developed in a 1 μm optical fiber system. The optical fiber modulation system can efficiently modulate temporal and frequency properties of optical soliton molecules and their orthogonal components. Different soliton parameters in orthogonal polarizations are applied to achieve controllable optical solitons’ output with specific properties in the time/frequency domain. These simulation results provide a beneficial reference value for the extra-cavity shaping of different solitons that come from nonlinear optical systems. Optimally, the reported results could pave the groundwork for industrial growth in ultrafast laser design.

It is well known that graphene has an extremely strong third-order nonlinearity compared to the commonly used dielectrics and metals; this nonlinearity results from the interaction of the charge carriers in graphene with strong electromagnetic radiation. Reference [7] focuses on the problem of a monochromatic terahertz TE-polarized wave propagation in a plane dielectric layer filled with a homogeneous isotropic medium; one of the boundaries of the waveguide is covered with a layer of graphene. On the one hand, in the study, energy losses both in the dielectric layer and in the graphene layer are neglected; the latter assumption is reasonable in the terahertz range of electromagnetic radiation (on which the paper focuses), where graphene has a strong plasmonic response and much less loss. On the other hand, this study considers the significant third-order nonlinearity resulting from the interaction of the electromagnetic wave with the charge carriers in the graphene layer. Besides studying the problem analytically, the paper presents some numerical results as well. In particular, the obtained results demonstrate how the nonlinearity in graphene affects the propagation constants and eigenwaves, providing the dispersion curves and eigenwaves for nonlinear graphene as well as for the linear one.

LiNbO₃:Mg (5.0 mol % or 0.85 wt %) is a LiNbO₃ single-crystal-based, optically highly perfect and compositionally uniform material. It has a low photorefraction effect and it is currently used for optical frequency conversion in the phase quasi-phase-matching mode on regular domain structures (PPLN—periodically-poled LiNbO₃). However, the strong single doping decreases the compositional and optical uniformity of a single-doped crystal compared with a nominally pure congruent crystal. Doping (including double and multiple doping) provides finer control than single doping, controls many properties of an LN crystal, and also influences the type and concentration of defects in a crystal, which significantly affects the magnitude of the photorefraction effect and the optical damage resistance of the crystal.

In reference [8], the features of the defect structure, compositional uniformity, and photorefractive properties in a double-doped LiNbO₃:Gd:Mg (Gd concentration of 0.003, Mg—0.65 wt % in the crystal) single crystal are investigated using several optical methods: laser conoscopy, photoinduced light scattering (PILS), optical spectroscopy, and Raman scattering. The crystal has been shown to have no photorefraction effect and high optical uniformity. Nonlinear optical coefficients are higher in perfect double-doped LiNbO₃ crystals, including those co-doped with magnesium, compared with single-doped crystals.

A promising method for the optical control of the pinning effect in antiferromagnetic (AFM) and ferromagnetic (FM) interface is laser-induced heating; namely, as the structure is heated above the blocking temperature, the pinning is destroyed. A complete reversal of the exchange bias at the AFM/FM interface can also be induced by a single femtosecond pulse of sufficiently high energy. Spin precession in magnetic structures subjected by ultrashort excitation provides extensive information on magnetic interactions. Laser pulse perturbation is found to modify the exchange bias, as evidenced by the shift of the hysteresis loop with respect to the applied DC magnetic field as observed by the magneto-optical Kerr effect [9]. In optical second harmonic generation (SHG), when applied in studies of magnetic structures, magneto-optical effects at the SHG wavelength appear with typical values of one to two orders of magnitude higher than their linear analogs such as the magneto-optical Kerr effect (MOKE). This nonlinear optical method allows one to distinguish various types of nontrivial magnetic states, such as magnetic vortices, magnetic toroidal moment, and gradients of magnetization [9].

Reference [9] is a comparative study of linear and nonlinear magneto-optical effects in IrMn/CoFe films of various thickness of the ferromagnetic CoFe layer. It demonstrates that the magneto-optical response of the pinned AFM/FM nanofilms appears with different hysteresis loop parameters in the transverse magneto-optical Kerr effect (MOKE) and interface-sensitive magnetization-induced second harmonic generation (SHG), indicating the diversity of the magnetic effects at interfaces compared to the bulk of the films.

In reference [10], localized surface plasmon (LSP) modes in a design comprising two coupled nano-ridges deposited on a gold layer with an interposing polymer spacer layer are numerically investigated. Such a structure is usually referred to as a particle-on-mirror structure. First, the LSP modes of a single nano-ridge and the analysis of its scattering cross-section in the visible and infrared ranges are examined. To enhance the plasmonic response, a thin polymer layer is placed at the middle of the ridge, which introduces additional LSP modes confined within the former. Then, the analysis is extended to the dimer configuration, which yields LSP resonances with a quality factor enhancement of approximately threefold relative to a single nano-ridge. Furthermore, the presence of the polymer layer within the ridges significantly improves plasmon field localization and the quality factor. These findings underscore the potential of nano-ridge-based structures in advancing optomechanical coupling and offering valuable insights for the development of high-performance acousto-plasmonic devices. In particular, the proposed device could help significantly improve the design of nano-acousto-optic modulators, operating in the visible or in the near-infrared ranges, that require an enhanced light–phonon coupling rate.

The field of photovoltaics (PV) continually seeks innovative material solutions to enhance the efficiency and the stability of their standard devices. In reference [11], the use of plasmonic core–shell nanoparticles in PV applications through various experimental validations is reviewed. Advancements in the design and in the control over the properties of core–shell nanoparticles are described and their integration into various solar cells, based on their ability to finely tune optical, electronic, and chemical properties, are highlighted. Experimental results for organic, perovskite, and dye-sensitized solar cells are discussed, where core–shell nanoparticles have been successfully deployed. Additionally, gaps in the current research are identified, such as the need for scalable synthesis methods and long-term stability assessments and promising new developments at the frontier of the field.

Today, fluorescence microscopy is used worldwide, despite suffering from drawbacks such as photobleaching, phototoxicity, and challenging quantification. Most small biomolecules, such as nucleosides, amino acids, fatty acids, choline, glucose, and cholesterol, are intrinsically nonfluorescent, so fluorescent tags are mandatory. Unfortunately, these tags, such as organic dyes, fluorescent proteins, or quantum dots, are all relatively larger than small biomolecules; consequently, they can severely falsify their native biochemical or biophysical properties. Therefore, label-free imaging, with high sensitivity and high chemical selectivity of unlabeled living cells, is preferable. In this framework, vibrational microscopy techniques have emerged as a powerful approach based on a chemically label-free selective contrast due to intrinsic molecule vibrations. Among them, stimulated Raman scattering (SRS) microscopy, which was adapted to microscopy only in the last two decades, is one of the most promising techniques.

Stimulated Raman scattering (SRS) microscopy is a high-speed imaging modality based on intrinsic molecular vibrations, producing chemical maps in living systems. Such capability, allowing for direct visualization without the perturbation of biological processes, has enabled a plethora of biological and medical applications. In reference [12], after introducing the basic theory and competitive effects of SRS, some crucial features for SRS microscopy implementations, such as noise, spectral bandwidth, speed, chemical sensitivity, spatial resolution, and quantum enhancement, are discussed. Finally, some SRS applications in biological and medical imaging are described. Even if certainly not exhaustive, the review aims to offer a broad overview, providing guidance for newcomers and hinting at a more detailed investigation to interested researchers in this rapidly growing field.

Free-space optical communication has seen a surge in interest, both for terrestrial and last-mile solutions, as well as optical satellite communication. Current efforts have focused on utilizing the short-wave infrared (SWIR) atmospheric transmission window, containing the 1530–1565 nm C-band used in telecommunications. However, SWIR communication suffers significantly from scintillation, scattering, and weather effects. The 3–5 μm mid-infrared (MWIR) atmospheric transmission window should offer improved signal-to-noise ratio and resistance to these adverse effects and could lead to higher link availability and reliability.

In reference [13], a diode-pumped solid-state (DPSS) laser, used for intracavity pump-enhanced difference frequency generation (DFG) to create a 3.5-micron laser, is reported. Using a 50 mm long periodically poled lithium niobate (PPLN) crystal inside the cavity of an Nd:YVO₄ solid-state laser at 1064 nm with 4.5 W pump power at 808 nm, and a 310 mW C-band signal at 1529 nm, up to 31 mW of mid-infrared output power at 3499 nm is obtained. The cavity requires no active stabilization and/or locking, and the entire cavity is <8 cm in length. The obtained output power corresponds to a black-box efficiency of 2.20% W⁻¹, which is the highest value reported to date for continuous-wave DFG based on a bulk nonlinear optical crystal with no active stabilization. Potential future applications in free-space optical communication are also discussed.

Traditional microwave signal processors relying on electronic devices exhibit significant loss and strong crosstalk, which make them suffer from limited operation bandwidths. To overcome this restriction, microwave photonic (MWP) signal processors that perform signal processing functions based on MWP technologies have found wide applications in telecommunication and radar systems. For MWP signal processors implemented by the transversal filter systems, a large number of taps, or the wavelength channels provided by multi-wavelength optical sources, are required to improve their performance. Compared to other multi-wavelength optical sources, optical microcombs can provide significantly increased numbers of wavelength channels by using compact micro-scale resonators, which is critical for improving the processing accuracy of MWP transversal signal processors. Although a range of signal processing functions have been realized, they only used Gaussian input waveforms for demonstrations, while the ability to handle various input signal waveforms is essential for practical applications.

In reference [14], the capability of microcomb-based MWP signal processors for dealing with various input signal waveforms is experimentally demonstrated. The processing accuracy of different input waveforms, including Gaussian, triangle, parabolic, super Gaussian, and nearly square waveforms, is quantified. These results provide guidance for microcomb-based MWP signal processors when processing microwave signals of various waveforms.

3. Conclusions

Although it is far from an exhaustive overview, which would not be possible due to the extensive and broad research activities in nonlinear photonics, this collection of scientific articles presents and discusses several research topics, covering interesting aspects such as new effects, promising materials, and important fields of application. It is my wish that it will serve as a stimulus for students and researchers to further expand the potential of nonlinear photonics devices via fundamental investigations and practical applications.