Nonlinear optics with structured light

The interest in tailoring light in all its degrees of freedom is steadily gaining traction,driven by the tremendous developments in the toolkit for the creation,control and detection of what is now called structured light.Because the complexity of these optical fields is generally understood in terms of interference,the tools have historically been linear optical elements that create the desired superpositions.For this reason,despite the long and impressive history of nonlinear optics,only recently has the spatial structure of light in nonlinear processes come to the fore.In this review we provide a concise theoretical framework for understanding nonlinear optics in the context of structured light,offering an overview and perspective on the progress made,and the challenges that remain.

SYNTHESIS AND CHARACTERIZATI0N OF POLYMETHACRYLATES BEARING HETEROCYCLIC AZO GROUP AND MESOGENIC GROUP FOR NONLINEAR OPTICS

The methacrylate monomers bearing mesogenic group and heterocyclicazo dye have been synthesized. The monomeric dye was copolymerized with the mesogenicmonomer using a free radical initiator to produce polymers useful for nonlinear optics. Themonomers and polymers were characterized by IR,;H-NMR, and UV-Vis spectra. Theaverage molecular weight （M;and M;） of the polymers were determined by gel permeationchromatography. The thermal properties of the polymers such as thermal stability andphase transition behavior were studied by thermogravimetric analysis, differential thermalanalysis, polarizing optical microscope and X-ray diffractometer. The results demonstratethat the synthesized polymers are crystalline polymers at room temperature and no liquidcrystalline phases were observed for all of them.

Nonlinear waves of the Hirota and the Maxwell Bloch equations in nonlinear optics

In this paper, considering the Hirota and the Maxwell–Bloch （H-MB） equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of this system through a linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions （both bright and dark breathers） of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.

Quantum Computation with Nonlinear Optics

We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features： （1） No auxiliary qubits are required in the controlled-NOT gate operation; （2） No measurement is required in the course of the computation; （3） It is resource efficient and conceptually simple.

Review on the study of Nonlinear Optics of Iridium Metal Organic Complex

Nonlinear optical materials are one of the key research objects in the field of optics, which mainly research the nonlinear effects of the interaction between luminesce and matter. Compared with inorganic nonlinear optical materials, organic nonlinear materials have outstanding advantages: strong adaptability, high flexibility, low cost, easy modification and damage resistance. In this review, the electric field induced second harmonic generation (EFISH) experimental technology is used to measure and research the nonlinearity of iridium metal complexes. And because of its structural diversity, people can design molecules according to their needs to get the best nonlinear optical response. Organic molecules with large nonlinear coefficients should have the following characteristics: asymmetric charge distribution, the delocalized nature of π electrons, and easy polarization by external electric fields, and a large π conjugated system. In recent years, metal organic compounds have become a leader in the field of optics, mainly because of their very good nonlinear optical properties. In the future, people will do more investigation on the nonlinearity of metal organic complexes. Researchers have shown great interest in iridium metal organic complexes due in particular to their attractive stability and nonlinear activity. This review mainly studies the nonlinear principle, performance test and Measurement of nonlinearity of iridium metal complexes. The nonlinear properties of other metal-metal organic complexes will not be discussed.

Synthesis of Imidazole Derivatives for Their Second-order Nonlinear Optics

The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity transparency thermal stability trade off is achieved for them.

AN EPOXY/(METHYL METHACRYLATE)INTERPENETRATING POLYMER NETWORK FOR NONLINEAR OPTICS

An interpenetrating polymer networks (IPN) consisting of an epoxy-based polymer network and a polymethyl methacrylate network were synthesized and characterized. The IPN showed only one T-g, and hence a homogeneous-phase morphology was suggested. The second-order nonlinear optical coefficient (d(33)) of the IPN was measured to be 1.72 X 10(-7) esu. The study of NLO temporal stability at room temperature and elevated temperature (100 degrees C) indicated that the IPN exhibits a high stability in the dipole orientation due to the permanent entanglements of two component networks in the IPN system. Long-term stability of second harmonic coefficients was observed at room temperature for more than 1000 h.

Light correcting light with nonlinear optics

Structured light,where complex optical fields are tailored in all their degrees of freedom,has become highly topical of late,advanced by a sophisticated toolkit comprising both linear and nonlinear optics.Removing undesired structure from light is far less developed,leveraging mostly on inverting the distortion,e.g.,with adaptive optics or the inverse transmission matrix of a complex channel,both requiring that the distortion be fully characterized through appropriate measurement.We show that distortions in spatially structured light can be corrected through difference-frequency generation in a nonlinear crystal without any need for the distortion to be known.We demonstrate the versatility of our approach using a wide range of aberrations and structured light modes,including higher-order orbital angular momentum(OAM)beams,showing excellent recovery of the original undistorted field.To highlight the efficacy of this process,we deploy the system in a prepare-and-measure communications link with OAM,showing minimal cross talk even when the transmission channel is highly aberrated,and outline how the approach could be extended to alternative experimental modalities and nonlinear processes.Our demonstration of light-correcting light without the need for measurement opens an approach to measurement-free error correction for classical and quantum structured light,with direct applications in imaging,sensing,and communication.

Nonlinear optics of two-dimensional heterostructures

Two-dimensional (2D) materials exhibit exceptionally strong nonlinear optical responses, benefiting from their reduced dimensionality, relaxed phase-matching requirements, and enhanced light-matter interaction. With additional degrees of freedom in the modulation of the physical properties by stacking 2D layers together, nonlinear optics of 2D heterostructures becomes increasingly fascinating. In this perspective, we provide a brief overview of recent advances in the field of nonlinear optics of 2D heterostructures, with a particular focus on their remarkable capabilities in characterization and modulation. Given the recent advances and the emergence of novel heterostructures, combined with innovative tuning knobs and advanced nonlinear optical techniques, we anticipate deeper insights into the underlying mechanisms and more associated applications in this rapidly evolving field.

Metal-organic frameworks for nonlinear optics and lasing

Nonlinear optics(NLO)is a crucial branch of photonics that greatly facilitates the transmission,processing,and storage of photonic signals.It meets the needs of the rapidly growing information demands of modern society.Materials with NLO properties and laser capabilities have a wide range of applications in fields such as optical communication,optical information storage,biomedical imaging,laser technology,and quantum information technology.Metal-organic frameworks(MOFs)have emerged as particularly exciting hybrid inorganic-organic porous materials that can be easily self‐assembled from corresponding inorganic metal ions/clusters and organic linkers.The structural diversity and flexibility of MOFs offer ample opportunities for the orderly or-ganization of highly hyperpolarizable chromophore molecules within confined spaces.This makes it ideal for NLO signal and laser emissions.In this review,we provide a comprehensive overview of strategies to construct MOFs with NLO and laser properties,as well as recent research developments for enhancing and adjusting these properties.Through analysis of chromophore arrangement and various interactions within the framework,we aim to gain insight into the correlation between MOF structures and optical properties.This will facilitate the design and synthesis of MOFs with excellent NLO and laser capabilities through the judicious selection of metal ions and organic linkers.Finally,we outline the future challenges and potential research directions for MOFs in NLO and laser fields.

Integrated sources of photon quantum states based on nonlinear optics

The ability to generate complex optical photon states involving entanglement between multiple optical modes is not only critical to advancing our understanding of quantum mechanics but will play a key role in generating many applications in quantum technologies.These include quantum communications,computation,imaging,microscopy and many other novel technologies that are constantly being proposed.However,approaches to generating parallel multiple,customisable bi-and multi-entangled quantum bits(qubits)on a chip are still in the early stages of development.Here,we review recent advances in the realisation of integrated sources of photonic quantum states,focusing on approaches based on nonlinear optics that are compatible with contemporary optical fibre telecommunications and quantum memory platforms as well as with chip-scale semiconductor technology.These new and exciting platforms hold the promise of compact,low-cost,scalable and practical implementations of sources for the generation and manipulation of complex quantum optical states on a chip,which will play a major role in bringing quantum technologies out of the laboratory and into the real world.

Nonlinear optics in all-dielectric nanoantennas and metasurfaces:a review

Free from phase-matching constraints,plasmonic metasurfaces have contributed significantly to the control of optical nonlinearity and enhancement of nonlinear generation efficiency by engineering subwavelength meta-atoms.However,high dissipative losses and inevitable thermal heating limit their applicability in nonlinear nanophotonics.All-dielectric metasurfaces,supporting both electric and magnetic Mie-type resonances in their nanostructures,have appeared as a promising alternative to nonlinear plasmonics.High-index dielectric nanostructures,allowing additional magnetic resonances,can induce magnetic nonlinear effects,which,along with electric nonlinearities,increase the nonlinear conversion efficiency.In addition,low dissipative losses and high damage thresholds provide an extra degree of freedom for operating at high pump intensities,resulting in a considerable enhancement of the nonlinear processes.We discuss the current state of the art in the intensely developing area of all-dielectric nonlinear nanostructures and metasurfaces,including the role of Mie modes,Fano resonances,and anapole moments for harmonic generation,wave mixing,and ultrafast optical switching.Furthermore,we review the recent progress in the nonlinear phase and wavefront control using all-dielectric metasurfaces.We discuss techniques to realize alldielectric metasurfaces for multifunctional applications and generation of second-order nonlinear processes from complementary metal–oxide–semiconductor-compatible materials.

Nonlinear optics of two-dimensional transition metal dichalcogenides

Nonlinear optics(NLO)of transition metal dichalcogenides(TMDs)is promising for the on-chip photonic and optoelectronic applications.In this review,we will survey the current progress of NLO in TMDs.First,we will brief the basic theory of the NLO in TMDs.Second,several important nonlinear processes in TMDs such as harmonic generation,four-wave mixing,saturable absorption,and two-photon absorption will be presented and their potential applications are also discussed.Third,the main strategies to tune,modulate,and enhance the NLO in TMDs are reviewed,including the excitonic effect,symmetry modulation,optical cavity enhancement,valley selection,edge state,and material phase.Finally,we give an outlook regarding some important issues and directions of NLO in TMDs.

Nonlinear optics on silicon-rich nitride--a high nonlinear figure of merit CMOS platform[Invited]

CMOS platforms with a high nonlinear figure of merit are highly sought after for high photonic quantum efficiencies, enabling functionalities not possible from purely linear effects and ease of integration with CMOS electronics. Silicon-based platforms have been prolific amongst the suite of advanced nonlinear optical signal processes demonstrated to date. These include crystalline silicon, amorphous silicon, Hydex glass, and stoichio- metric silicon nitride. Residing between stoichiometric silicon nitride and amorphous silicon in composition, silicon-rich nitride films of various formulations have emerged recently as promising nonlinear platforms for high nonlinear figure of merit nonlinear optics. Silicon-rich nitride films are compositionally engineered to create bandgaps that are sufficiently large to eliminate two-photon absorption at telecommunications wavelengths while enabling much larger nonlinear waveguide parameters （5x-500x） than those in stoichiometric silicon uitride. This paper reviews recent developments in the field of nonlinear optics using silicon-rich nitride platforms, as well as the outlook and future opportunities in this burgeoning field.

Solvent-stabilized few-layer violet phosphorus and its ultrafast nonlinear optics

Featured with high thermal decomposition temperature and layered structure,violet phosphorus(VP)offers an unparalleled stable allotrope of phosphorus to demonstrate the optoelectronic device and photonics elements with high performance at the nanoscale.Here,we report few-layer and hundreds of nanometer-sized VP with robust stability in different solvents and ambient conditions by ultrasound-assisted liquid phase exfoliation approach.For the first time,the ultrafast carrier dynamics and thirdorder nonlinear optical response of VP were investigated.Sub-picosecond timescale ultrafast carrier dynamic and ultrafast nonlinear saturable absorption of VP were demonstrated.Our findings demonstrated that VP possessed a promising potential for use in ultrafast nonlinear photonic applications such as saturable absorbers and optical switches.

Image encryption using spatial nonlinear optics

Optical technologies have been widely used in information security owing to its parallel and high-speed processing capability.However,the most critical problem with current optical encryption techniques is that the cyphertext is linearly related with the plaintext,leading to the possibility that one can crack the system by solving a set of linear equations with only two cyphertext from the same encryption machine.Many efforts have been taken in the last decade to resolve the linearity issue,but none of these offers a true nonlinear solution.Inspired by the recent advance in spatial nonlinear optics,here we demonstrate a true nonlinear optical encryption technique.We show that,owing to the self-phase modulation effect of the photorefractive crystal,the proposed nonlinear optical image encryption technique is robust against the known plaintext attack based on phase retrieval.This opens up a new avenue for optical encryption in the spatial nonlinear domain.

Aggregation-induced emission materials for nonlinear optics

Aggregation-induced emission(AIE)is a vital photophysical phenomenon that the luminogens in the concentrated or aggregated cases will engender the dramatically boosted emission in comparison with the dispersive states.Given this extraordinary emitting capacity exactly resolves the aggregation-caused quenching(ACQ)situations residing in the traditional luminophores,the booming AIE luminogens have drawn tremendous interest owing to their advanced performances and colossal potential applications in various areas.Further exploitations of AIE molecules also drive the research interests in the midst of these AIE materials toward the nonlinear optical(NLO)regime.The combination of AIE and NLO effects have nurtured some unforeseen properties of AIE materials and extended their application spheres.Therefore,some NLO-active AIE materials have been wielded in many crucial applications,for example,optical limiting,laser,bioimaging,and photodynamic therapy.Meanwhile,the impacts of aggregate on the NLO effect also deserve deep considerations and pursuits,and the modifications of aggregates promise an easy,efficient,and prompt avenue to tune the NLO properties of materials.The recent achievements and progress in the NLO properties of AIE materials have been summarized in this review.The second-order and third-order NLOs of the AIE materials have been introduced and their correlative applications have been discussed.

Graphene/phosphorene nano-heterojunction:facile synthesis, nonlinear optics, and ultrafast photonics applications with enhanced performance

Owing to its thickness-modulated direct energy band gap, relatively strong light–matter interaction, and unique nonlinear optical response at a long wavelength, few-layer black phosphorus, or phosphorene, becomes very attractive in ultrafast photonics applications. Herein, we synthesized a graphene/phosphorene nano-heterojunction using a liquid phase-stripping method. Tiny lattice distortions in graphene and phosphorene suggest the formation of a nano-heterojunction between graphene and phosphorene nanosheets. In addition, we systematically investigate their nonlinear optical responses at different wavelength regimes. Our experiments indicate that the combined advantages of ultrafast relaxation, broadband response in graphene, and the strong light–matter interaction in phosphorene can be combined together by nano-heterojunction. We have further fabricated two-dimensional(2D) nano-heterojunction based optical saturable absorbers and integrated them into an erbium-doped fiber laser to demonstrate the generation of a stable ultrashort pulse down to 148 fs. Our results indicate that a graphene/phosphorene nano-heterojunction can operate as a promising saturable absorber for ultrafast laser systems with ultrahigh pulse energy and ultranarrow pulse duration. We believe this work opens up a new approach to designing 2D heterointerfaces for applications in ultrafast photonics and other research.The fabrication of a 2D nano-heterojunction assembled from stacking different 2D materials, via this facile and scalable growth approach, paves the way for the formation and tuning of new 2D materials with desirable photonic properties and applications.

Resonantly enhanced second-and third-harmonic generation in dielectric nonlinear metasurfaces

Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.

Theoretical Studies on the Electronic Structure of Nano-graphenes for Applications in Nonlinear Optics

In this work,azulene is introduced into nano-graphene with coronene center to enhance the second-order nonlinear optical(NLO)properties.The sum-over-states(SOS)model based calculations demonstrate that dipolar contributions are larger than octupolar contributions to the static first hyperpolarizability(〈β0〉)in most nano-graphenes except those with high symmetry(e.g.,a C2v nano-graphene has octupolar contributionsΦJ=3 up to 59.0%of the〈β0〉).Nano-graphenes containing two parallel orientating azulenes(i.e.,Out-P and Out-Ps)have large dipole moments,while their ground state is triplet.Introducing B/N/BN atoms into the positions with a high spin density transfers the ground state of Out-P and Out-Ps to closed-shell singlet,and the Out-Ps-2N has a large〈β0〉of 1621.67×10−30 esu.Further addition of an electron donor(NH2)at the pentagon end enhances the〈β0〉to 1906.22×10−30 esu.The two-dimensional second-order NLO spectra predicted by using the SOS model find strong sum frequency generations and difference frequency generations,especially in the near-infrared and visible regions.The strategies to stabilize the electronic structure and improve the NLO properties of azulene-defect carbon nanomaterials are proposed,and those strategies to engineer nano-graphenes to be semiconducting while maintaining theπ-framework are exten-dable to other similar systems.