Purely coherent nonlinear optical response in solution dispersions of graphene sheets

All-optical switching based on spatial self-phase modulation of Ag/violet phosphorus heterojunctions

With the increasing demand for high-performance passive nonlinear photonic devices, significant progress has been made in spatial self-phase modulation (SSPM) based on 2D nanomaterials in all-optical switches, logic gates, and information converters in recent years. However, there are still challenges in improving the responsiveness of photonic devices. In this work, we prepared a heterojunction of Ag nanoparticles deposited on the surface of violet phosphorus nanosheets (VP Ns), investigated their SSPM, and demonstrated their performance in all-optical switches. The SSPM experimental results show that compared with pure VP Ns at the same light intensity, both the maximum number and the formation time of self-diffraction rings in Ag/VP heterojunctions increase, and the nonlinear refractive index is approximately doubled. The main reason for optical nonlinearity enhancement is that the internal electric field in the heterojunction strengthens the mobility of the photogenerated carrier, thereby enhancing its optical nonlinearity. In particular, we demonstrate the performance of all-optical switches based on SSPM by utilizing the superior optical nonlinearity of Ag/VP heterojunctions. It is shown that with the increase of low-dose Ag content in heterojunctions, the switching time in the all-optical switch becomes shorter and the maximum number of self-diffraction rings of the signal light increases, although the quality of self-diffraction rings slightly decreases due to the scattering of Ag particles. The results contribute to the design and implementation of high-performance nonlinear photonic devices, based on the use of heterojunctions with low-cost preparation and a high nonlinear refractive index.

Optical nonlinearity and all-optical switching in pumpkin seed oil based on the spatial cross-phase modulation (SXPM) technique

Nonlinear optics (NLO) and its applications have attracted increasing research interest in recent years owing to their contribution to the development of photonic technology. Accordingly, in this study, we investigated the NLO response of pumpkin seed oil using the spatial self-phase modulation (SSPM) method. Significant NLO characteristics have been experimentally studied at 405 nm and 532 nm continuous wave (CW) laser wavelengths, yielding second-order nonlinear refractive index ( n 2 , t h ) values of 6.54 × 10 - 5 cm 2 / W and 2.73 × 10 - 5 cm 2 / W , respectively. The findings suggest that the absorption of the material leads to higher optical nonlinearity at shorter wavelengths owing to higher thermal effects. Furthermore, we implemented a light-controlled-light system based on the spatial cross-phase modulation (SXPM) technique employing pumpkin seed oil. We successfully achieved all-optical switching by designing the 'ON' and 'OFF' modes. The results of this study can be considered for the future development of NLO applications. Moreover, our work investigates the potential of pumpkin seed oil for designing low-cost and high-efficiency NLO devices, and this contribution opens up a novel practical avenue for oil-based optical devices.

Facile Exfoliation of Few-Layer Sn-Based Nanosheets for Self-Powered Photo-Electrochemical and All-Optical Modulation Applications

Few-layer tin (Sn)-based nanosheets (NSs) with a thickness of ≈2.5 nm are successfully prepared using a modified liquid phase exfoliation (LPE) method. Here the first exploration of photo-electrochemical (PEC) and nonlinear properties of Sn NSs is presented. The results demonstrate that the PEC properties are tunable under different experimental conditions. Additionally, Sn NSs are shown to exhibit a unique self-powered PEC performance, maintaining a good long-term stability for up to 1 month. Using electron spin resonance, active species, such as hydroxyl radicals (·OH), superoxide radicals (·O2 -), and holes (h+), are detected during operations, providing a deeper understanding of the working mechanism. Furthermore, measurements of nonlinear response reveal that Sn NSs can be effective for all-optical modulation, as it enables the realization of all-optical switching through excitation spatial cross-phase modulation (SXPM). These findings present new research insights and potential applications of Sn NSs in optoelectronics.

Strong light-matter interaction and non-linear effects in organic semiconducting CuPc nanotubes: realization of all-optical diode and switching applications

Spatial self-phase modulation based on the optical Kerr effect has gained momentum in recent years to analyse the nonlinear optical properties of 2D inorganic nanomaterials. In the present work, we investigate the strong light-matter interaction of organic semiconducting materials based on SSPM, by developing Cu-phthalocyanine (CuPc) nanotubes via a solvothermal technique. The low bandgap of CuPc facilitates the study of its nonlinear optical properties for a broad spectrum range from 671 nm to 405 nm. Intense laser light passing through the CuPc dispersion produces concentric diffraction ring patterns at the far field from which high n2 and χ(3) values, 3.667 × 10-5 cm2 W-1 and 2 × 10-3 esu, respectively, are obtained for the 405 nm laser. This strong nonlinear optical response of CuPc has been utilized to realize non-reciprocal light propagation by constructing a CuPc/SnS2 hybrid structure, which makes an effective all-optical photonic diode. In addition, the all-optical switching is presented using CuPc nanotubes based on the spatial cross-phase modulation technique. In this technique a phase change is induced in the weak signal beam modulated by the strong controlling light beam, which helps to produce all-optical logic gates and all-optical switching devices. The experimental findings of this work unravel the potentially powerful applications of CuPc nanotubes in all-optical information transmission and all-optical photonic devices.

Regular arrangement of dispersed 2D flakes detected by polarization of light

Regular arrangement of dispersed 2D flakes, as the "Wind-Chime" model, has been regarded as possible mechanism of spatial self-phase modulation. But this regular arrangement caused by the laser have not been confirmed, and the relation with the concentration of dispersed 2D flakes is still unclear. Here, the relationship between arrangement caused by electric field and polarized transmittance have been explored at first. Then, the model of flakes rotation to regular arrangement were established, which were proof by the response time by turning on/off electric field. On this basis, by building the polarization-related cross optical switch system, light-induced regular arrangement were observed and proven.

Electro-Induced Phase Transformation of a Conductive Metal-Organic Framework Film for Nonlinear Optical Switching

Achieving metal-organic frameworks (MOFs) with nonlinear optical (NLO) switching is profoundly important. Herein, the conductive MOFs Cu-TCNQ phase I (Ph-I) and phase II (Ph-II) films were prepared using the liquid-phase-epitaxial layer-by-layer spin-coating method and steam heating method, respectively. Electronic experiments showed that the Ph-II film could be changed into the Ph-I film under an applied electric field. The third-order NLO results revealed that the Ph-I film had a third-order nonlinear reverse saturation absorption (RSA) response and the Ph-II film displayed a third-order nonlinear saturation absorption (SA) response. With increases in the heating time and applied voltage, the third-order NLO response realized the reversible transition between SA and RSA. The theoretical calculations indicated that Ph-I possessed more interlayer charge transfer, resulting in a third-order nonlinear RSA response that was stronger than that of Ph-II. This work applies phase-transformed MOFs to third-order NLO switching and provides new insights into the nonlinear photoelectric applications of MOFs.

Spatial self-phase modulation excited by fractional-order linearly polarized vector fields

Compared to the integer-order vector field, the fractional-order vector field has an additional degree of control freedom, which will bring rich photophysical properties and what we believe to be novel nonlinear optical phenomena. In this work, we theoretically and experimentally investigate the focusing, propagation, and spatial self-phase modulation (SSPM) of fractional-order linearly polarized vector fields (FLPVFs). It is shown that the weak focusing field of FLPVF exhibits an asymmetric intensity distribution. Intriguingly, its state of polarization (SoP) has a hybrid polarization distribution. When this focused FLPVF propagates to the far field in free space, its SoP degenerates into a localized linearly polarization distribution. However, after the focused FLPVF passes through an isotropic nonlinear Kerr medium, its SoP exhibits a hybrid polarization distribution. Additionally, unlike the self-diffraction intensity pattern of integer-order linearly polarized vector field (ILPVF) with a concentric multi-ring structure, the SSPM pattern of FLPVF is a symmetry broken self-diffraction intensity pattern. The presented work provides a nonlinear optics approach for manipulating both the SoP and intensity distributions of the light field.

Strong non-linear optical response of Sb2Se3 nanorods in a liquid suspension based on spatial self-phase modulation and their all-optical photonic device applications

The field of nonlinear optics is constantly expanding and gaining new impetus through the discovery of fresh nonlinear materials. Herein, for the first time, we have performed spatial self-phase modulation (SSPM) experiments with an emerging anisotropic Sb2Se3 layered material in a liquid suspension for an all-optical diode and all-optical switching application. The third-order broadband nonlinear optical susceptibility (χ(3)single layer ∼ 10-9 esu) and nonlinear refractive index (n2 ∼ 10-6 cm2 W-1) of Sb2Se3 have been determined using a 671 nm laser beam. This result could be unambiguously explained by the anisotropic hole mobility of Sb2Se3. The linear relationship of χ(3) and carrier mobility emphasizes the establishment of nonlocal hole coherence, the origin of the diffraction pattern. Consequently, the time evolution of diffraction rings follows the 'Wind-Chime' model. A novel photonic diode based on Sb2Se3/SnS2 has been demonstrated using the nonreciprocal propagation of light. The self-phase modulation (SPM) technique uses laser lights of different wavelengths and intensities to demonstrate the all-optical logic gates, particularly OR logic gates. The exploration of nonlinear optical phenomena in Sb2Se3 opens up a new realm for optical information processing and communication. We strongly believe that this result will help to underpin the area of optical nonlinearities among its various applications.

Optical Logic Gates Excited by a Gauss Vortex Interference Beam Based on Spatial Self-Phase Modulation in 2D MoS2

Vortex beams with optical orbital angular momentum have broad prospects in future high-speed and large-capacity optical communication. In this investigation of materials science, we found that low-dimensional materials have feasibility and reliability in the development of optical logic gates in all-optical signal processing and computing technology. We found that spatial self-phase modulation patterns through the MoS₂ dispersions can be modulated by the initial intensity, phase, and topological charge of a Gauss vortex superposition interference beam. We utilized these three degrees of freedom as the input signals of the optical logic gate, and the intensity of a selected checkpoint on spatial self-phase modulation patterns as the output signal. By setting appropriate thresholds as logic codes 0 and 1, two sets of novel optical logic gates, including AND, OR, and NOT gates, were implemented. These optical logic gates are expected to have great potential in optical logic operations, all-optical networks, and all-optical signal processing.

Degenerate and non-degenerate all-optical switches using violet phosphorus nanosheets

As an allotrope of phosphorus, layered violet phosphorus (VP) has a wide range of applications in electronics, photonics, and optoelectronics. However, its nonlinear optical properties remain to be explored. In this work, we prepare and characterize VP nanosheets (VP Ns), investigate their spatial self-phase modulation (SSPM) effects, and develop them in all-optical switching applications. The ring forming time of SSPM and the third-order nonlinear susceptibility of monolayer VP Ns were found to be about 0.4 s and 10^-9 esu, respectively. The mechanism of SSPM formed by coherent light-VP Ns interaction is analyzed. Using the superior coherence electronic nonlinearity of VP Ns, we realize degenerate and non-degenerate all-optical switches based on the SSPM effect. It is demonstrated that the performance of all-optical switching can be controlled by adjusting the intensity of the control beam and/or the wavelength of the signal beam. The results will help us to better design and realize non-degenerate nonlinear photonic devices based on two-dimensional nanomaterials.

Laser-Induced Hole Coherence and Spatial Self-Phase Modulation in the Anisotropic 3D Weyl Semimetal TaAs

Laser-induced electron coherence is a fascinating topic in manipulating quantum materials. Recently, it has been shown that laser-induced electron coherence in 2D materials can produce a third-order nonlinear optical response spatial self-phase modulation (SSPM), which has been used to develop a novel all-optical switching scheme. However, such investigations have mainly focused on electron coherence, whereas laser-induced hole coherence is rarely explored. Here, the observation of the optical Kerr effect in 3D Weyl semimetal TaAs flakes is reported. The nonlinear susceptibility (χ⁽³⁾ ) is obtained, which exhibits a surprisingly high value (with χ o n e - l a y e r ( 3 ) \[{\bm{\chi }}_{{\bf one}{\bm{ - }}{\bf layer}}^{{\bf (3)}}\] = 9.9 × 10^-9 e.s.u. or 1.4 × 10^-16  m²  V^-2 at 532 nm). This cannot be explained by the conventional electron mobility, but can be well understood by the unique high anisotropic hole mobility of TaAs. The wind-chime model and χ⁽³⁾ carrier mobility correlation adequately explain the results, suggesting the crucial role of laser-induced nonlocal ac hole coherence. These observations extend the understanding of SSPM from 2D to 3D quantum materials with anisotropic carrier mobility and from electron coherence to hole coherence.

Third-Order Optical Nonlinearities of 2D Materials at Telecommunications Wavelengths

All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and distinctive properties have opened up new avenues for nonlinear optics and the fabrication of related devices with high performance. This paper reviews the recent advances in research on third-order optical nonlinearities of 2D materials, focusing on all-optical processing applications in the optical telecommunications band near 1550 nm. First, we provide an overview of the material properties of different 2D materials. Next, we review different methods for characterizing the third-order optical nonlinearities of 2D materials, including the Z-scan technique, third-harmonic generation (THG) measurement, and hybrid device characterization, together with a summary of the measured n₂ values in the telecommunications band. Finally, the current challenges and future perspectives are discussed.

Effects of Atypical Hydrogen Bonds and π-π Interactions on Nonlinear Optical Properties: Dimers of Triangular Structures Based on Perylene, Naphthalene, and Pyromellitic Diimides

Nonlinear optical (NLO) materials have become important materials in the field of high-speed optical devices due to the changes in light absorption and refraction caused by the photoelectric field. Compounds tend to exist as aggregates rather than single molecules, so intermolecular interactions are crucial to the nature of aggregates. Therefore, to study the effects of intermolecular interactions on nonlinear optical properties, we use a dimer simplified model and adopt the methods of controlling variables, which are the different intermolecular interactions resulting from the different stacking patterns of dimers based on the same monomer structures (2PMDI-1NDI and 2NDI-1PDI). It is found that compared with dimers involving π-π interactions, dimers involving C-H···O interactions have shorter intermolecular distances, larger intermolecular interaction energies, and smaller highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energy gaps. Moreover, the C-H···O interactions are more conducive to the intermolecular charge transfers and more beneficial for increasing the nonlinear optical response values of aggregates with respect to π-π interactions. This work provides an important basis for the influence of intermolecular interactions on nonlinear optical properties.

Visible optical nonlinearity of vanadium dioxide dispersions

Vanadium dioxide (VO2), a correlated oxide compound, is one of the functional materials extensively studied in solid state physics due to its attractive physical properties. However, the nonlinear optical response of VO2 and related all-optical applications have been paid less attention. Here, the nonlinear refractive index (n 2) and third-order nonlinear susceptibility (χ (3)) of VO2 dispersions have been acquired to be 3.06 × 10-6 cm2 W-1 and 1.68 × 10-4 esu at a wavelength of 671 nm, and 5.17 × 10-6 cm2 W-1 and 2.83 × 10-4 esu at a wavelength of 532 nm via the spatial self-phase modulation (SSPM) and spatial cross-phase modulation (SXPM) effects in the visible regime, respectively. Based on the excellent nonlinear optical properties of VO2 dispersions, the proof-of-principle functions such as optical logic or-gates, all-optical switches, and inter-channel information transfer are implemented in the visible wavelength. The experimental results on the response time of VO2 to light indicate that the formation of diffraction rings is mainly an electronically coherent third-order nonlinear optical process. The experimental results show that the VO2 dispersions exhibit an excellent nonlinear optical response and may lay the foundation for the application of VO2-based all-optical devices.

Identification of aggregated 2D cobalt tellurides using a spatial self-phase modulation technique

We report a previously unreported application of the spatial self-phase modulation (SSPM) technique for recognizing solute-solvent interaction in a suspension of 2D material. Broadband optical absorption of the 2D Co₂Te₃ leads to a nonlinear optical (NLO) susceptibility for the monolayer, i.e., χ M o n o(3) of 1.5 ×10^-9 (3.3 ×10^-9) esu at 532 (632) nm, which is 1-2 orders higher than for the 2D CoTe and CoTe₂. The fine structure of the SSPM patterns is analyzed to explore the foundations of the observed NLO effects. With increasing polarity of the liquid media, a change of 2D Co₂Te₃ from homophonous dispersion to aggregation occurs, as confirmed from in situ optical microscopy and UV-vis absorption spectroscopy. As a result, type-I (thickest outer ring) SSPM ring patterns are converted to type-II (thinnest outer ring) SSPM ring patterns. Therefore, using SSPM with a CW laser as an optical tool to identify solvent-polarity-induced aggregation in 2D materials is possible.

Light modulation based on the enhanced Kerr effect in molybdenum disulfide nanostructures with curved features

A novel type of molybdenum disulfide (MoS₂) nanoparticles (NPs) was chemically synthesized, which possessed curved features with three-dimensional (3D) freedom compared with planar two-dimensional (2D) materials. Due to the introduction of curved features, the synthesized NPs exhibited a strongly enhanced nonlinear refractive index (n₂ ∼ 10^-5 cm^-2 W^-1) and third-order susceptibility (χ⁽³⁾ ∼ 10^-7 esu), which were experimentally verified by the spatial self-phase modulation effect in the visible wavelength range. Both the nonlinear parameters were two orders of magnitude higher than their planar MoS₂ nanostructure counterparts. In addition, the relative change of the effective nonlinear refractive index Δn₂/n₂ was found to be distinctly dependent on the intensity of the applied electromagnetic field. Moreover, an all-optical modulation was experimentally realized based on the spatial cross-phase modulation effect. Our results demonstrate planar MoS₂ materials with 3D features as potential candidates for next generation all-optical applications and open a substantial approach for the design of efficient nanomaterials with favorable optical nonlinearity.

Tellurium based materials for nonlinear optical applications

Materials having broadband nonlinear optical responses find applications in photonics and optoelectronics devices. Novel materials with improved nonlinear optical properties are necessary for realizing effective all-optical switches, modulators etc. Tellurium (Te) and novel low-dimensional derivatives of Te offer intriguing nonlinear optical responses, making them promising candidates for design of various photonic devices.

Selective excitation of four-wave mixing by helicity in gated graphene

Gapless Dirac fermions in monolayer graphene give rise to an abundance of peculiar physical properties, including exceptional broadband nonlinear optical responses. By tuning the chemical potential, stacking order, and photonic structures, the effective modulation of nonlinear optical phenomena in graphene has been demonstrated in recent years. Here, we demonstrate that optical helicity can be used as an extra tuning knob for four-wave mixing in gated graphene. Our results reveal the helicity selection rule for four-wave mixing in monolayer graphene, revealing nearly perfect circular polarization. Corresponding theoretical interpretations of the helicity selection rule that are also applicable to other nonlinear optical processes and materials are presented.

All-Optical Modulation Technology Based on 2D Layered Materials

In the advancement of photonics technologies, all-optical systems are highly demanded in ultrafast photonics, signal processing, optical sensing and optical communication systems. All-optical devices are the core elements to realize the next generation of photonics integration system and optical interconnection. Thus, the exploration of new optoelectronics materials that exhibit different optical properties is a highlighted research direction. The emerging two-dimensional (2D) materials such as graphene, black phosphorus (BP), transition metal dichalcogenides (TMDs) and MXene have proved great potential in the evolution of photonics technologies. The optical properties of 2D materials comprising the energy bandgap, third-order nonlinearity, nonlinear absorption and thermo-optics coefficient can be tailored for different optical applications. Over the past decade, the explorations of 2D materials in photonics applications have extended to all-optical modulators, all-optical switches, an all-optical wavelength converter, covering the visible, near-infrared and Terahertz wavelength range. Herein, we review different types of 2D materials, their fabrication processes and optical properties. In addition, we also summarize the recent advances of all-optical modulation based on 2D materials. Finally, we conclude on the perspectives on and challenges of the future development of the 2D material-based all-optical devices.

Nonlinear dynamics of topological Dirac fermions in 2D spin-orbit coupled materials

The graphene family materials are two-dimensional staggered monolayers with a gapped energy band structure due to intrinsic spin-orbit coupling. The mass gaps in these materials can be manipulated on-demand via biasing with a static electric field, an off-resonance circularly polarized laser, or an exchange interaction field, allowing the monolayer to be driven through a multitude of topological phase transitions. We investigate the dynamics of spin-orbit coupled graphene family materials to unveil topological phase transition fingerprints embedded in the nonlinear regime and show how these signatures manifest in the nonlinear Kerr effect and in third-harmonic generation processes. We show that the resonant nonlinear spectral response of topological fermions can be traced to specific Dirac cones in these materials, enabling characterization of topological invariants in any phase by detecting the cross-polarized component of the electromagnetic field. By shedding light on the unique processes involved in harmonic generation via topological phenomena our findings open an encouraging path towards the development of novel nonlinear systems based on two-dimensional semiconductors of the graphene family.

2D layered SiP as anisotropic nonlinear optical material

Two-dimensional (2D) material of silicon phosphide (SiP) has recently been shown as a promising optical material with large band gap, fast photoresponse and strong anisotropy. However, the nonlinear optical properties of 2D SiP have not been investigated yet. Here, the thickness-dependent in-plane anisotropic third-harmonic generation (THG) from the mechanically exfoliated 2D layered SiP flakes is reported. The crystal orientation of the SiP flake is determined by the angle-resolved polarized Raman spectroscopy. The angular dependence of the THG emission with respect to the incident linear polarization is found to be strongly anisotropic with the two-fold polarization dependence pattern. Furthermore, the effect of the SiP flake thickness on the THG power is analyzed.

Microfluidic tuning of linear and nonlinear absorption in graphene oxide liquid crystals

Manipulation of the nonlinear optical response of materials plays a significant role in photonics applications; however, it may be irreversible, untunable, and uncontrollable, which makes it difficult. In this Letter, we present a mechanical-hydrodynamical approach through a microchannel to tune the nonlinear absorption response of graphene oxide liquid crystals. In this material, the optical properties depend on the flake orientation. This feature has helped us to study empirically the dependency of the nonlinear absorption coefficients to external hydrodynamical force by employing the Z-scan technique. The experimental results show that increasing the flow rate in the microchannel enhances both linear and nonlinear absorption coefficients and, as a result, reduces the laser beam transmission through the sample. It has been observed that the percentage change in the nonlinear absorption coefficient of the sample is significant due to the flow rate.

Spatial self-phase modulation of a Gaussian beam transmitted through a ferrofluid

We report on the experimental observation of the diffraction pattern formed in the far-field region when a high-power continuous-wave laser convergent or divergent Gaussian beam passes through a cuvette with ferrofluid. Two different types of diffraction rings with opposite light-intensity distribution are shown in the far field. The difference between the diffractive patterns is attributed to the interaction of the strong spatial self-phase modulation caused by the refractive index change of the medium with wavefront curvature of the input Gaussian beam. The observed behavior of the diffraction pattern dynamics is interpreted theoretically based on the Fresnel-Kirchhoff integral. The negative polarity of nonlinear refraction can be identified by the central interference profiles and the diffraction pattern. At the same time, the self-defocusing phenomena of the ferrofluid can be determined by the type of pattern. The nonlinear refraction coefficients of the ferrofluid were estimated to be ∼-2.89×10^-5cm²/W (convergent Gaussian beam) and ∼-3.53×10^-5cm²/W (divergent Gaussian beam). In addition, the corresponding third-order nonlinear optical susceptibility of the sample was also estimated as ∼1.43×10^-5esu and ∼1.75×10^-5esu, respectively. The experimental results imply a novel potential application of ferrofluid in nonlinear phase modulation devices.

Recent Advances of Spatial Self-Phase Modulation in 2D Materials and Passive Photonic Device Applications

Optical nonlinearity in 2D materials excited by spatial Gaussian laser beam is a novel and peculiar optical phenomenon, which exhibits many novel and interesting applications in optical nonlinear devices. Passive photonic devices, such as optical switches, optical logical gates, photonic diodes, and optical modulators, are the key compositions in the future all-optical signal-processing technologies. Passive photonic devices using 2D materials to achieve the device functionality have attracted widespread concern in the past decade. In this Review, an overview of the spatial self-phase modulation (SSPM) in 2D materials is summarized, including the operating mechanism, optical parameter measurement, and tuning for 2D materials, and applications in photonic devices. Moreover, some current challenges are also proposed to solve, and some possible applications of SSPM method are predicted for the future. Therefore, it is anticipated that this summary can contribute to the application of 2D material-based spatial effect in all-optical signal-processing technologies.

In-plane anisotropic third-harmonic generation from germanium arsenide thin flakes

A newly introduced two-dimensional (2D) layered germanium arsenide (GeAs) has attracted growing interest due to its promising highly in-plane anisotropic crystal structure and electronic properties for photonic and optoelectronic applications. The potential of 2D layered GeAs for many applications such as anisotropic photodetection, electronics, superconductivity and thermoelectricity is being investigated in recent studies. However, the intrinsic nonlinear optical properties of 2D layered GeAs have not been explored yet. Here, thickness- and incident polarization-dependent in-plane anisotropic third-harmonic generation (THG) from the mechanically exfoliated thin GeAs flakes is reported. Furthermore, the effect of the flake thickness on the THG conversion efficiency is shown to find the optimal thickness range for high conversion efficiency. The polarization state of the emitted THG signal is also analyzed by measuring the Stokes parameters with different polarization states of the pump beam to demonstrate the capability of controlling the intensity and polarization of TH emission. Our results will create new opportunities for advancing anisotropic optical devices used for future photonic integration, optical communication and optical information processing.

Liquid phase exfoliated boron nanosheets for all-optical modulation and logic gates

Boron nanosheets possess unique photoelectric properties, including photosensitivity, photoresponse, and optical nonlinearity. In this article, we show the interaction between light and boron nanosheets in which concentric rings formed in the far field, which attributed to the strong Kerr nonlinearity of boron nanosheets. Furthermore, the distortion, regulation and relationship between the Kerr nonlinearity and effective mass or carrier mobility of the diffraction rings of boron nanosheets have been investigated. Our work shows that the spatial self-phase modulation effect of boron nanosheets is indeed caused by nonlocal electronic coherence. In addition, we have implemented all-light modulation and all-light logic gates based on the prepared boron nanosheets. We believe that our results will provide a powerful demonstration of nonlinear photonic devices based on boron nanosheets and a reference for photonic devices based on two-dimensional materials.

2D Material Optoelectronics for Information Functional Device Applications: Status and Challenges

Graphene and the following derivative 2D materials have been demonstrated to exhibit rich distinct optoelectronic properties, such as broadband optical response, strong and tunable light-mater interactions, and fast relaxations in the flexible nanoscale. Combining with optical platforms like fibers, waveguides, grating, and resonators, these materials has spurred a variety of active and passive applications recently. Herein, the optical and electrical properties of graphene, transition metal dichalcogenides, black phosphorus, MXene, and their derivative van der Waals heterostructures are comprehensively reviewed, followed by the design and fabrication of these 2D material-based optical structures in implementation. Next, distinct devices, ranging from lasers to light emitters, frequency convertors, modulators, detectors, plasmonic generators, and sensors, are introduced. Finally, the state-of-art investigation progress of 2D material-based optoelectronics offers a promising way to realize new conceptual and high-performance applications for information science and nanotechnology. The outlook on the development trends and important research directions are also put forward.

Observation of spatial self-phase modulation induced via two competing mechanisms

Two spatial self-phase modulation (SSPM) patterns were observed in suspensions of Bi₂TeSe₂ nanosheets. Two mechanisms were found to produce SSPM with different occurrence times and power dependence. The Type I (narrow) rings are attributed to the coherent third-order nonlinear optical Kerr effect, which induces self-diffraction in 2D materials, and the Type II (wide) rings are assigned to the contribution of a thermal effect. The nonlinear refractive index of Bi₂TeSe₂ is found to be 2.30×10^-5cm²W^-1 at 700 nm. The findings described here provide an explanation for the formation of rings in 2D systems due to SSPM.

On the measurement of the nonlinear optical response of graphene dispersions using fs lasers

In this work, the nonlinear optical (NLO) response of some graphene dispersions is investigated under low (i.e., 10 Hz) and high (i.e., 80 MHz) repetition rate femtosecond (fs) laser excitation conditions, using ${Z}$Z-scan, optical Kerr effect (OKE), and a combination of ${Z}$Z-scan and thermal lensing techniques. It is shown, that the NLO response of graphene dispersions is negligible under low repetition rate fs laser excitation, while it becomes very large under high repetition rate laser excitation. In the latter case, it is shown that the observed very large NLO response arises entirely from thermal cumulative effects.

Optical Kerr effect and third harmonic generation in topological Dirac/Weyl semimetal

We study the nonlinear optical response generated by the massless Dirac quasiparticles residing around the topologically-protected Dirac/Weyl nodal points in three-dimensional (3D) topological semimetals. Analytical expressions of third-order interband nonlinear optical conductivities are obtained based on a quantum mechanical formalism which couples 3D Dirac fermions with multiple photons. Our results reveal that the massless Dirac fermions in three dimensions retains strong optical nonlinearity in terahertz frequency regime similar to the case of the two-dimensional Dirac fermions in graphene. At room temperature, the Kerr nonlinear refractive index and the harmonic generation susceptibility are found to be n₂ = 10^-11 ∼ 10^-8 m²W^-1 and χ⁽³⁾ = 10^-14 ∼ 10^-8 m²V^-2, respectively, in the few terahertz frequency regimes, which is comparable to graphene and orders of magnitudes stronger than many nonlinear crystals. Importantly, because 3D topological Dirac/Weyl semimetals possess bulk structural advantage not found in the strictly two-dimensional graphene, greater design flexibility and improved ease-of-fabrication in terms of photonic and optoelectronic device applications can be achieved. Our finding reveals the potential of 3D topological semimetals as a viable alternative to graphene for nonlinear optics applications.

Nonlinear optical response spatial self-phase modulation in MoTe2: correlations between χ(3) and mobility or effective mass

We report on an unambiguous observation of the third-order nonlinear optical effect, spatial self-phase modulation (SSPM), in a MoTe₂ dispersion. The values of the third-order nonlinear optical coefficients effectively for one-layer MoTe₂, χone-layer(3), are obtained through the SSPM method at excitation wavelengths 473, 532, 750, and 801 nm, respectively. The wind-chime model is used to explain the ring formation time. The wavelength dependence of χone-layer(3) compares well with the photo-absorption spectra. Significantly, we find a correlation between χ⁽³⁾ and the carrier mobility μ or effective mass m*, which again further supports the laser-induced ac electron coherence in 2D materials.

Thermally Induced Nonlinearity of Organic Solvents and Real-Time Visualization of the Nucleophilic Addition Reaction Using Spatial Cross-Phase Modulation

We report on the study of the thermally induced nonlinear optical (NLO) properties of the commonly used organic solvents at the near-infrared range using spatial cross-phase modulation (SXPM). The results indicate that those solvents (alcohols, formic acid, and acetic acid) with -OH and -COOH functional groups have obvious NLO effect in the near-infrared range due to the third overtone absorption of the O-H band. In addition, the NLO effect of the ketones and aldehydes is enhanced when water or nitric acid is added, because the products with -OH and -COOH are generated, respectively, according to the nucleophilic addition reactions. Finally, real-time visualization of the acetone nucleophilic addition reaction is realized by monitoring the SXPM diffraction patterns' variation with time. This work not only is of importance in studying the NLO properties of the materials, e.g, interpreting the results performed in solutions and selecting suitable solvents, but also provides a simple way to visualize chemical reactions.

Evaluation of graphene optical nonlinearity with photon-pair generation in graphene-on-silicon waveguides

We evaluate the nonlinear coefficient of graphene-on-silicon waveguides through the coincidence measurement of photon-pairs generated via spontaneous four-wave mixing. We observed the temporal correlation of the photon-pairs from the waveguides over various transfer layouts of graphene sheets. A simple analysis of the experimental results using coupled-wave equations revealed that the atomically-thin graphene sheets enhanced the nonlinearity of silicon waveguides up to ten-fold. The results indicate that the purely χ ⁽³⁾-based effective nonlinear refractive index of graphene is on the order of 10^-13 m ²/W, and provide important insights for applications of graphene-based nonlinear optics in on-chip nanophotonics.

Coherent anti-Stokes Raman spectroscopy of single and multi-layer graphene

Spontaneous Raman spectroscopy is a powerful characterization tool for graphene research. Its extension to the coherent regime, despite the large nonlinear third-order susceptibility of graphene, has so far proven challenging. Due to its gapless nature, several interfering electronic and phononic transitions concur to generate its optical response, preventing to retrieve spectral profiles analogous to those of spontaneous Raman. Here we report stimulated Raman spectroscopy of the G-phonon in single and multi-layer graphene, through coherent anti-Stokes Raman Scattering. The nonlinear signal is dominated by a vibrationally non-resonant background, obscuring the Raman lineshape. We demonstrate that the vibrationally resonant coherent anti-Stokes Raman Scattering peak can be measured by reducing the temporal overlap of the laser excitation pulses, suppressing the vibrationally non-resonant background. We model the spectra, taking into account the electronically resonant nature of both. We show how coherent anti-Stokes Raman Scattering can be used for graphene imaging with vibrational sensitivity.

Kerr Nonlinearity in germanium selenide nanoflakes measured by Z-scan and spatial self-phase modulation techniques and its applications in all-optical information conversion

Germanium selenide (GeSe) has attracted considerable research interest due to its unique photoelectric characteristics: high abundance occurrence, low toxicity, high stability, and environmentally sustainable. To the best of our knowledge, less literature is available on the nonlinear optical (NLO) properties of GeSe and on its significance of the electronic structure. In this work, the GeSe nanoflake ethanol suspensions have been studied by using liquid phase exfoliation method and then characterized by Raman, transmission electron microscopy (TEM), transmittance and atomic force microscopy (AFM). The NLO properties of GeSe suspensions with different concentration are investigated by Z-scan and spatial self-phase modulation (SSPM) methods with continuous wave laser, which are coherent with the parameter nonlinear refractive index n2 and the third order nonlinear polarizabilities χ⁽³⁾. The nonlinear refractive index n2 of GeSe dispersions basically occur in the order of 10^-9 cm²/W for Z-scan methods and 10^-6 cm²/W for SSPM technique, whereas the third-order nonlinear polarizabilities χ⁽³⁾ _total are within the range of 10^-6 esu for SSPM method. On the basis of these substantial characteristics of the NLO response and high stability of the 2D GeSe, we have experimentally studied the applications of the GeSe suspensions on all-optical information conversion technique.

Kerr Nonlinearity in 2D Graphdiyne for Passive Photonic Diodes

Graphdiyne is a new carbon allotrope comprising sp- and sp² -hybridized carbon atoms arranged in a 2D layered structure. In this contribution, 2D graphdiyne is demonstrated to exhibit a strong light-matter interaction with high stability to achieve a broadband Kerr nonlinear optical response, which is useful for nonreciprocal light propagation in passive photonic diodes. Furthermore, advantage of the unique Kerr nonlinearity of 2D graphdiyne is taken and a nonreciprocal light propagation device is proposed based on the novel similarity comparison method. Graphdiyne has demonstrated a large nonlinear refractive index in the order of ≈10^-5 cm² W^-1 , comparing favorably to that of graphene. Based on the strong Kerr nonlinearity of 2D graphdiyne, a nonlinear photonic diode that breaks time-reversal symmetry is demonstrated to realize the unidirectional excitation of Kerr nonlinearity, which can be regarded as a significant demonstration of a graphdiyne-based prototypical application in nonlinear photonics and might suggest an important step toward versatile graphdiyne-based advanced passive photonics devices in the future.

Nonlinear optical response, all optical switching, and all optical information conversion in NbSe2 nanosheets based on spatial self-phase modulation

An efficient liquid phase exfoliation method has been developed for the preparation of high quality NbSe2 nanosheets. The pure nonlinear optical properties of these nanosheets have been investigated using three different wavelength continuous wave (CW) lasers. The spatial self-phase modulation (SSPM) effect can be observed clearly in solution dispersions of (NbSe2). The experimental data show that the diffraction is caused by the third-order optical nonlinearity of NbSe2. The third-order nonlinearity susceptibility χ(3) of NbSe2 is about 10-9 e.s.u. by analyzing the experimental results. The relaxation time in the dynamic relaxation is about 1.38 s, 1.58 s, and 1.15 s for 532 nm, 671 nm, and 457 nm, respectively. In addition, the realization of all-optical switching based on SSPM, particularly two-color intrachromatic coherence, indicates that the generation of electron coherence is a universal characteristic of layered quantum materials. All optical information conversion based on the SSPM is also confirmed experimentally. Our experimental results have simple potential application prospects for NbSe2 based on its nonlinear optical response.

Giant enhancement of electronic polarizability and the first hyperpolarizability of fluoride-decorated graphene versus graphyne and graphdiyne: insights from ab initio calculations

An effective strategy based on the adsorption of alkali-metal fluorides on graphene, graphyne, and graphdiyne is presented for exploring the strong electro-optical properties, which are correlated with the TDDFT two-level model.

Intensity-dependent nonlinear refraction of antimonene dispersions in the visible and near-infrared region

Antimonene is a stable 2D allotrope of antimony that is predicted to have a direct bandgap, high third-order optical nonlinear susceptibility, and high electron mobility. These properties give it huge potential applications in photonics and optoelectronics. However, the nonlinear refractive response of antimonene dispersions, which is the key to nonlinear refraction-based devices, has not been fully investigated. In this work, we investigated the optical nonlinearities of the antimonene dispersions by spatial self-phase modulation (SSPM) at 405, 785, and 1064 nm wavelengths. The SSPM rings were observed at 405, 785, and 1064 nm, implying the broadband nonlinear optical response of antimonene dispersions from visible to near-infrared. The effective nonlinear refractive index, n₂, and the third-order susceptibility, χ⁽³⁾, of the antimonene dispersion were measured to be ∼10^-5  cm² W^-1 and ∼10^-8  esu, respectively. Furthermore, the nonlinearity of antimonene was demonstrated to be tuneable by the laser intensities. The relative change of the nonlinear refractive index, Δn_2e/n_2e, was observed to range from 14% to 63% for different intensities. Our results will be helpful for the photonic applications of antimonene in a broadband wavelength range, such as optical modulators and switchers.

Graphene's nonlinear-optical physics revealed through exponentially growing self-phase modulation

Graphene is considered a record-performance nonlinear-optical material on the basis of numerous experiments. The observed strong nonlinear response ascribed to the refractive part of graphene's electronic third-order susceptibility χ⁽³⁾ cannot, however, be explained using the relatively modest χ⁽³⁾ value theoretically predicted for the 2D material. Here we solve this long-standing paradox and demonstrate that, rather than χ⁽³⁾-based refraction, a complex phenomenon which we call saturable photoexcited-carrier refraction is at the heart of nonlinear-optical interactions in graphene such as self-phase modulation. Saturable photoexcited-carrier refraction is found to enable self-phase modulation of picosecond optical pulses with exponential-like bandwidth growth along graphene-covered waveguides. Our theory allows explanation of these extraordinary experimental results both qualitatively and quantitatively. It also supports the graphene nonlinearities measured in previous self-phase modulation and self-(de)focusing (Z-scan) experiments. This work signifies a paradigm shift in the understanding of 2D-material nonlinearities and finally enables their full exploitation in next-generation nonlinear-optical devices.

Gold nanoparticle-decorated graphene as a nonlinear optical material in the visible and near-infrared spectral range

There have been numerous reports of boosting nonlinear optical phenomena in plasmonic nanostructures through local-field enhancement as well as through intrinsic metal nonlinearities. Here, we study the possibility of plasmonic enhancement of graphene's nonlinear absorption by creating a composite material: gold nanoparticle-decorated graphene dispersed in water. To evaluate the additive effect of combining the two materials on the saturable absorption efficiency we performed a series of f-scan (modified Z-scan) measurements using femtosecond laser pulses in the broad spectral range from 530 to 1600 nm. These studies are supplemented by TEM, UV-vis, ATR and Raman spectroscopy, revealing the mechanisms behind the formation of the composite material.

Nonlinear Optics with 2D Layered Materials

2D layered materials (2DLMs) are a subject of intense research for a wide variety of applications (e.g., electronics, photonics, and optoelectronics) due to their unique physical properties. Most recently, increasing research efforts on 2DLMs are projected toward the nonlinear optical properties of 2DLMs, which are not only fascinating from the fundamental science point of view but also intriguing for various potential applications. Here, the current state of the art in the field of nonlinear optics based on 2DLMs and their hybrid structures (e.g., mixed-dimensional heterostructures, plasmonic structures, and silicon/fiber integrated structures) is reviewed. Several potential perspectives and possible future research directions of these promising nanomaterials for nonlinear optics are also presented.

Abnormal nonlinear optical properties of hybrid graphene-TiO2 nanostructures

The nonlinear optical (NLO) properties of graphene-TiO₂ nanoparticle (GNP) composite and graphene-TiO₂ nanowire composite (GNW) are investigated by spatial self-phase modulation (SSPM) and Z-scan. The SSPM results of the GNP and GNW show that they possess strong self-diffraction effects at 1100 nm and no signal at 700 nm, which is different from all previous reports of other two-dimensional materials. A possible mechanism is that NLO behaviors are dominated by TiO₂ at the visible wavelength, while by graphene at a near-infrared wavelength. The Z-scan results of the GNP and GNW show reverse saturable absorption (RSA) at 700 nm, but saturable absorption (SA) at 1100 nm. Our results demonstrate that, by choosing appropriate coupling, we could design two-dimensional materials that have specific NLO properties at particular wavelengths.